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Microwave opacity of phosphine: Application to remote sensing of the atmospheres of the outer planets

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R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
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• •
Microwave Opacity of Phosphine
Application to Remote Sensing of
the Atmospheres of the
Outer Planets
A Thesis
Presented to
The Academic Faculty
by
James Patrick Hoffman
In Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy in Electrical Engineering
Georgia Institute of Technology
April 2001
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
UMI Number: 3004542
UMI
UMI Microform 3004542
Copyright 2001 by Bell & Howell Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
Bell & Howell Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Ml 48106-1346
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Microwave Opacity of Phosphine:
Application to Remote Sensing of the
Atmospheres of the Outer Planets
Approved:
Dr. Paul G.
Chairm
Dr. David R. DeBoer
Dr. Waymond R. Scott
Date approved by Chairman ^ /_ J f c
200/
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
To Kristin
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Acknowledgments
I present this thesis, not only as a culmination of the objective findings contained within its
pages, but also as an answer to a question, often asked, that is posed in many forms: Why
struggle with the difficult when the easy is readily accomplished? This question is inherent
in the erroneous assumption that advances in understanding or technology will occur, not
by the willful application of effort, but through some inevitable entitlement of existence. I
say that discovery is not inevitable, that it is achieved through the conscious effort of those
with the ability and desire to expand understanding. Those I acknowledge in the following
have shared their ability with me when mine was found lacking and have provided their
inspiration when my desire faltered. It has been both an honor and a privilege to know each
of them.
First, I thank my advisor, Dr. Paul G. Steffes. I could not have completed this work
without his inestimable guidance, continual encouragement, and boundless enthusiasm.
One could not ask for a better advisor in terms of technical ability or personal support
throughout one’s graduate career. I thank Dr. David R. DeBoer for sharing with me his
experience and insight. With the superb guidance I received from my advisor, Dr. Steffes,
I neither expected nor deserved an unofficial second advisor with the ability and patience
of Dr. DeBoer. It is a tribute to the depth in the excellence of the Georgia Tech faculty that
I was able to work closely with two professors of such ability and dedication. I also thank
the following faculty committee members for their time and effort in carefully reviewing
my thesis: Dr. W. R. Scott, Dr. R. K. Feeney, and Dr. W. L. Chameides.
I thank the following for their invaluable comments and suggestions on my work:
Dr. Marc Kolodner (John’s Hopkins-APL), Dr. Imke dePater (Berkeley), Dr. Jon Jenkins
(SETI), Dr. Bryan Butler (NRAO), and the community of engineers and scientists of the
American Astronomical Society-Division of Planetary Science.
My education would be incomplete if it were not for my comrades-in-arms, my
fellow graduate students. I thank Brian Wilson for his friendship (and excellent cooking!)
dating back to our undergraduate years. Our constant disagreements over course-work
provided me with greater understanding than most lectures. I thank Jeff Piepmeier for
acting as a sounding board for ideas and for his friendship. Every time I hear of contrail
conspiracies or cattle abductions I will be reminded of the late nights we spent on the
fifth floor crunching data and listening to the surreal Art Bell. I thank Jordan Rosenthal
for sharing his mastery of Matlab and for his friendship. I thank Caroline Clower, David
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Peters, Jeff and Janelle Piepmeier, and others in student government for their friendship. I
also thank my fellow fifth floor inhabitants for their help and friendship: Ms. Mary Jane
Chappell, Ae Chalodhom, Priscilla Mohammed, and Allen Petrin.
I could never have sustained myself throughout the years of effort without the sup­
port I received from my family. Above all I thank my wonderful wife, Kristin. My endeav­
ors in higher education have spanned a decade and we have been together through all but
my freshman year. I cannot conceive of accomplishing my goals without the support she
has provided me. I thank my parents, Theodore and Caroline Hoffman, for expecting my
best and for forgiving my worst. I thank my brothers, Michael and Timothy, and my sisters,
Patricia, Kathy, and Susan, who embody so many of the different qualities I admire. I must
also thank my furry four-legged friend Curly, for keeping me company into the wee hours
of the night more times than I can recall.
Finally, I thank the U.S. taxpayers for their continued support of the National Aero­
nautics and Space Administration, which in turn, supports this work through the Planetary
Atmospheres Program under grant NAG5-4190.
v
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Do not let your fire go out, spark by irreplaceable spark, in the hopeless swamps
of the approximate, the not-quite, the not-yet, the not-at-all. Do not let the hero
in your soul perish, in lonely frustration for the life you deserved, but have
never been able to reach. Check your road and the nature of your battle. The
world you desired can be won, it exists, it is real, it is possible, it’s yours.
-Ayn Rand
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R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Summary
Understanding the composition of the atmospheres of the outer planets1 is crucial to un­
derstanding planetary and solar system formation and evolution processes. The microwave
region of the electromagnetic spectrum probes deeper into the atmospheres of the outer
planets than does the visible or infrared spectrum and thus is an important component of
planetary observations. The deep levels probed by microwaves are sensitive to regions
where pressures are many bars, therefore an understanding of pressure-broadened absorp­
tion from gaseous constituents is vital if one wants to interpret observations correctly. In
the past, many laboratory measurements were conducted on the pressure induced absorp­
tion of important atmospheric gases, such as ammonia. However, microwave (centimeter
wavelength) absorption due to phosphine ( P f / 3 ) has never been measured in the laboratory.
Difficulties in simultaneously matching synthetic (modeled) microwave emission
spectra with observations from ground-based radio telescopes, radio occupation experi­
ment results and in-situ probe data have prompted many to conclude that an additional
microwave absorber, such as phosphine, is likely responsible.
The pressure broadened absorption of gaseous phosphine has been measured in
the laboratory under simulated conditions for outer planet atmospheres. Phosphine ab­
'The outer planets, which include Jupiter, Saturn, Uranus and Neptune, are also known as the gas giants
or the Jovian planets.
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sorption is shown to be stronger than theoretical calculations indicate by more than an
order of magnitude at long centimeter wavelengths. A new laboratory measurement-based
formalism has been developed for computation of absorptivity of gaseous phosphine in a
hydrogen-helium atmosphere. Application of this formalism shows that, in equal abun­
dance, phosphine is a stronger absorber at long centimeter wavelengths than is ammonia.
This result contradicts the widely-held assumption that ammonia is the single dominant
microwave absorber in outer planet atmospheres.
A re-examination of the Voyager radio occultation experiment results at Saturn
and Neptune reveal that the inferred ammonia abundance for both planets requires super­
saturation if ammonia is assumed to be the only major source of microwave opacity. The
new formalism for phosphine opacity is applied to a reinterpretation of results of the Voy­
ager radio occultation experiment results at Saturn and Neptune. Results indicate phos­
phine mixing ratios of 3-12 ppm and 1-3 ppm for Saturn and Neptune respectively will
account for the additional opacity over ammonia and hydrogen sulfide saturation.
An existing disk-average radiative transfer model has been updated to include the
new formalism and has been applied to the Saturn and Neptune atmospheres. Results from
the updated radiative transfer model indicate best-fit deep abundances of « 468 ppm N H 3,
6-12 ppm P H i and 31 ppm H 2S for Saturn, and « 94 ppm N H 3, 2-3 ppm P H 3 and 300600 ppm H 2S for Neptune. Both results are consistent with those from the re-interpretation
of Voyager radio occultation experiments and with observations o f the microwave emission
spectra of those planets.
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Also, a new ray-tracing-based elliptical-shell local radiative transfer model has been
developed to aid in prediction and eventually interpretation of measurement results from
the Cassini RADAR/radiometer. The ability of the Cassini radiometer to detect phosphine
has been investigated. Results indicate that Cassini will detect phosphine at Saturn and will
be capable of mapping phosphine variations on the order of 0.6 — 1.'2ppm. This sensitivity
will likely be limited primarily by uncertainties in ammonia abundance.
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X
Contents
Acknowledgments
iii
Summary
vi
List of Tables
xi
List of Figures
xii
1 Introduction
1.1 Research Objectives and O rg an izatio n ............................................................
1
2
2 Laboratory Measurements of Phosphineunder Outer Planet Conditions
5
2.1 Motivation for Laboratory M e a su re m e n ts......................................................
6
2.2 Foundation for Laboratory M easu rem en ts......................................................
7
2.3 Electromagnetic Manifestation of Absorption by Molecular G a s ...............
9
2.4 P ro c e d u re ............................................................................................................ 11
2.5 Measurement S y s te m ......................................................................................... 14
2.6 R esults.................................................................................................................... 18
2.7 Measurement u ncertainty....................................................................................... 20
3 Phosphine Microwave Opacity Formalism
31
3.1 Phosphine Spectrum ............................................................................................. 32
3.1.1 Phosphine Inversion:Ammonia as an A nalogue.......................................35
3.2 Formalism D ev elo p m en t....................................................................................... 39
3.2.1 Phosphine Opacity versus Ammonia O p a c ity ........................................ 47
3.3 Re-interpretation of Voyager Radio Occultation Experiment Results: Did
Voyager See P h o s p h in e ? ........................................................................................47
3.3.1 S a tu rn ............................................................................................................49
3.3.2 N eptune.........................................................................................................52
3.3.3 Jupiter............................................................................................................58
4 Radiative Transfer Model
59
4.1 Thermo-chemical M o d e l.......................................................................................60
4.2 RTM: Opacity C ontributions.................................................................................61
4.3 Radiative Transfer M o d e l....................................................................................... 67
4.4 Radiative Transfer T h e o r y .................................................................................... 68
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4.5
Localized Radiative Transfer M o d e l ......................................................................74
4.5.1 Ray-tracing D e s c rib e d ................................................................................76
4.5.2 Ray-tracing Algorithm M athem atics......................................................... 79
4.5.3 Ellipsoid R a y -T ra c in g ............................................................................... 83
4.5.4 B e a m -fo rm in g ............................................................................................ 86
4.6 Application of the Radiative Transfer M o d e ls ......................................................93
4.6.1 Disk-average Saturn Radiative Transfer R e s u lts ......................................93
4.6.2 Saturn Local RTM: Will Cassini See P h o s p h in e ? .................................118
4.6.3 Disk-average Neptune R T M .................................................................... 129
5
Summary and Conclusions
132
5.1 Centimeter Wavelength Absorption of P h o s p h in e ..............................................132
5.2 Conclusions Regarding the Re-interpretations of Voyager Radio Occulta­
tion E x p e rim e n ts ................................................................................................... 133
5.3 Application of the Local Radiative Transfer Model to the Cassini RADAR/Radiometer at S a tu rn ............................................................................................. 133
5.4 Directions for Future S tu d ie s ................................................................................. 134
5.4.1 Laboratory S tu d ie s .................................................................................... 134
5.4.2 Ground Based O b se rv a tio n s.................................................................... 136
5.4.3 Improvements to the Localized Radiative Transfer M o d el....................136
5.5 Uniqueness and C o n trib u tio n s ..............................................................................137
5.5.1 Laboratory W o r k ....................................................................................... 137
5.5.2 A p p lic a tio n s .............................................................................................. 138
5.6 Publications and P rese n tatio n s..............................................................................139
Bibliography
142
Vita
150
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xii
List of Tables
2 .1 Results of phosphine opacity measurements at room temperature. Gas mix­
ture composition: 82.6% H2 , 9.2% He, 8.2% PH3 .......................................... 19
2.2 Results of phosphine opacity measurements at 213 Kelvin. Gas mixture
composition: 82.6% H2, 9.2% He, 8.2% PH3 ........................................................27
2.3 Results of phosphine opacity measurements at 213 Kelvin. Gas mixture
composition: 88.0% H2, 9.8% He, 2.2% PH3 ........................................................28
2.4 Results of phosphine opacity measurements at 175 Kelvin. Gas mixture
composition: 88.0% H2, 9.8% He, 2.2% PH3 ........................................................29
3.1 Phosphine line intensities. This table includes all o f phosphine’s published
lines up to 40 GHz, as well as phosphine’s first rotational line at 267 GHz.
All of the lines discussed in the text are listed. The intensities given are the
current published values and the column Intensity Multiplier contains the
intensity weighting factors described in the text. For a listing of all model
parameters, please refer to Table 3.2........................................................................43
3.2 Parameters for a Van Vleck-Weisskopf line-shape based centimeter-wavelength opacity model for phosphine.........................................................................45
3.3 Solar abundances of important atmospheric constituents, as reported by
Anders and Grevasse (1989)................................................................................. 49
4.1 H 20 formalism parameters......................................................................................... 65
4.2 Listing of observations compiled from van Der Tak et al. 1999, Grossman
(1990), de Pater and Dickel (1982) and Briggs and Sackett (1989)................. 96
4.3 Listing of models discussed in text, f Model F includes a 10% super­
saturation of ammonia, f f Model G includes a 20% super-saturation of
ammonia......................................................................................................................97
4.4 Model Brightness Temperature Results for disk-average, nadir and 75 de­
grees zenith angle.....................................................................................................124
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xiii
List of Figures
2.1
2.2
2.3
Schematic of the laboratory measurement system. System includes gashandling, thermal, microwave, and data collection subsystems....................... 15
March 15 laboratory measurements showing pressure dependence. Mea­
surements were taken at a temperature of 213 Kelvin and a mixing ratio of
82.6%H2, 9.2%tfe,and 8 .2 % P # 3. The 1, 3, and 5 bar measurements are
connected with solid, short-dashed, and long-dashed lines, respectively. . . 26
Comparison of two separate laboratory measurements, each taken at a tem­
perature of 175 Kelvin, at a pressure of 3 bars for a mixing ratio of 88.0%
H2, 9.8% H e, 2.2% P H Z..........................................................................................30
3.1
Phosphine’s molecular spectrum. Intensity and frequency of each of phosphine’s spectral lines................................................................................................. 33
3.2 An examination of phosphine’s spectrum below 500 GHz. Note the first
rotational line ,J = 1 -> 0, at 266.9 GHz ...........................................................34
3.3 Comparison of various centimeter-wavelength phosphine opacity models
with laboratory measurements. All models are based on the Van VleckWeisskopf line-shape with the same physical conditions as the March 22
(3-bar) measurement; a mixing ratio of 88.0%H2, 9.8% He, and 2.2% PH3,
a pressure of 2.87 bars, and a temperature of 213 K. The model approxi­
mating phosphine opacity using only its first rotational line (J = 1 -* 0)
is depicted by the long-dash line. The model using the full published phos­
phine catalog is shown by the short-dash line, which is indistinguishable
from the model including only the lines below (in frequency) phosphine’s
J = 1 -> 0 line (solid-line)...................................................................................... 36
3.4 Comparison of various centimeter-wavelength phosphine opacity models
with laboratory measurements. All models are based on the Van VleckWeisskopf lineshape with the same physical conditions as the March 22
(3-bar) measurement; a mixing ratio of 88.0%H2, 9.8%He, and 2.2% PH3,
a pressure of 2.87 bars, and a temperature of 213 K. The model approxi­
mating phosphine opacity using only its first rotational line (J = 1 —> 0)
is depicted by the long-dash line. The model using the full published phos­
phine catalog is shown by the short-dash line, which is indistinguishable
from the model including only the lines below (in frequency) phosphine’s
J = 1 —►0 line. The solid line depicts our new centimeter-wavelength
phosphine opacity model, and the discrete points with error-bars are the
laboratory measurements..........................................................................................46
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3.5 Comparison of the PH3 and NH3 centimeter-wavelength opacities at 1 bar
and 298 Kelvin. The mixing ratio for each is 82.6% i/2>9-2% He, and 8.2%
of either NH3 or PH3. The solid line depicts ammonia’s opacity modeled
using Spilker’s Ben-Reuven line-shape (1993), while the dashed line de­
picts ammonia’s opacity using the Van Vleck-Weisskopf line-shape. The
discrete points with error-bars are measured data for phosphine under the
same conditions as the models................................................................................. 48
3.6 Profile of phosphine abundance inferred from the S- and X-band Voyager
2 radio science experiments at Saturn. Opacity values were inferred from
ammonia abundance reported by Lindal et al. (1985). A saturated level
of ammonia is assumed and the resulting opacity subtracted from the total
opacity inferred. The residual opacity is attributed to phosphine. Detec­
tions by Weisstein and Serabyn (1994) and Orton et al. (2000) are listed.
The Orton detection is interpolated as described in Orton et al. (2000). A
solar abundance (Anders and Grevesse, 1989) of phosphine is shown as
reference......................................................................................................................53
3.7 Comparison of the vertical opacity profile inferred from the Voyager radio
occultation experiments at Saturn (Lindal, 1985), with calculated opacity
profile assuming an atmosphere dominated by a saturation abundance of
ammonia..................................................................................................................... 54
3.8 Profile of PH3 abundance inferred from the Voyager 2 radio science ex­
periment at Neptune. Opacity values were inferred from NH3 abundance
reported by Lindal et al. (1992) and the opacity due to the saturation va­
por pressure level of H2S has been subtracted. The remaining opacity is
attributed to PH3. The error in PH3 abundance is inferred from the error
in opacity stated by Lindal in terms of an error in the NH3 mixing ratio
of ±150ppb. A solar abundance (Anders and Grevesse, 1989) of PH3 is
shown as reference...............................................................................................57
4.1 Geometry of the radiative transfer model.......................................................... 73
4.2 A two dimensional graphic example of the ray-tracing process. An offnadir (left) and a limb sounding case (right) are shown. Two possible out­
comes for the limb-sounding case are shown. d3 shows the ray exiting the
atmosphere, while dc shows critical refraction (total internal reflection). . . 77
4.3 Vector implementation of Snell’s Law using Heckbert’s method (1989). . . 82
4.4 Comparison of approximations to oblate spheroidal volumes. A 2D pro­
jection of a Darwin de Sitter spheroid is compared to 2D projection of an
ellipsoid. Both are normalized to a maximum extent o f unity at the equa­
tor. A unity-radius circle is provided for reference. Note that no difference
between the two results is clearly discernible.................................................. 85
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4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
Top view of synthetic beamsampled antenna pattem.The axes indicate the
deflection from boresight as would occur for a Nadir-look with the space­
craft aligned with the x-axis at a distance of 6 Saturn radii from the surface
of the planet (360,000 km).................................................................................... 88
Side view of the synthetic beamsampled antenna pattern. The axes indicate
the deflection from boresight as would occur for a Nadir-look with the
spacecraft aligned with the x-axis at a distance of 6 Saturn radii from the
surface of the planet (360,000 km)...........................................................................89
A two dimensional graphic example of rotating and translating the beamsamples. Once the beam-pattem is generated (with the z-axis as its axis
of symmetry), the beamsamples are then rotated to the orientation of the
boresight of the spacecraft antenna. The origin of the beamsamples, which
originally was the origin of the coordinate system, is translated to the origin
of the spacecraft antenna........................................................................................... 91
Synthetic disk-average emission spectra for Saturn. A solar model is pro­
vided as reference. For composition of other models, see text.............................99
Temperature/Pressure profiles for models (A)and (B)........................................ 100
Synthetic disk-average emission spectra results from models A (thick-line),
A2 (dash-line), and A3 (thin-line). Model (A) is taken from the best-fit
model by Briggs and Sackett (1989).................................................................... 101
Vertical mixing ratio for model (A).......................................................................102
Cloud structure for model (A). The 13.78 GHz weighting functions are
shown for Nadir and 72-degree zenith angles....................................................... 103
Synthetic disk-average emission spectra results from models B (thick-line)
and B3 (dash-line).................................................................................................... 105
Vertical mixing ratio for model (B)....................................................................... 106
Cloud structure for model (B). The 13.78 GHz weighting functions are
shown for Nadir and 72-degree zenith angles....................................................... 107
Synthetic disk-average emission spectra results from models C (thin-line)
and C2 (thick-line). Model (A) (dash-line) isprovided for comparison. . . . 109
Vertical mixing ratio for model (C).....................................................................110
Synthetic disk-average emission spectra results from model D (dash-line).
Model (A) (thick-line) is provided for comparison.............................................. I l l
Vertical mixing ratio profile for model (D)...........................................................112
Comparison of the vertical opacity profile inferred from the Voyager radio
occultation experiments at Saturn (Lindal, 1985), with calculated opacity
profile assuming an atmosphere including a saturation abundance of am­
monia and a range of deep phosphine abundances (5,10,20-times solar).
Phosphine is modeled to decay with altitude to match the decay rate ob­
served by Orton et al. (2000)................................................................................ 115
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4.21 Solid-line: Cloud structure as generated from the thermochemical model
for solar abundance. Dashed-line: 2 x solar. Weighting functions for nadir
and 75 degree zenith angle observations are provided......................................... 119
4.22 Relative contributions to opacity from ammonia and phosphine for nadir
and 75 degrees zenith angle.....................................................................................121
4.23 Relative contributions to opacity from ammonia and phosphine for models
(B) and (B 3 ).............................................................................................................122
4.24 Relative contributions to opacity from ammonia and phosphine for nadir
observations of models (B) and (G)....................................................................... 125
4.25 Relative contributions to opacity from ammonia and phosphine for 75 de­
gree zenith angle observations of models (B) and (G)......................................... 126
4.26 Measured and synthetic emission spectrum (models) of Neptune. The dis­
crete circles and squares with error-bars are VLA and single-dish measure­
ments, respectively. A listing of these observations may be found in de Pa­
ter and Richmond (1989). The synthetic emission spectrum is based on the
DeBoer and Steffes ( 1996a) Neptune model using the new measurementbased phosphine opacity model detailed in this paper. Both models include
0.5x solar ammonia, 4x solar phosphine. The upper dash-line model shown
is for lOx solar, while the lower (darker) solid-line model is for 20x solar. . 130
5.1 Predicted 9.3 mm (32 GHz) vertical opacity profile of a Satumian atmo­
sphere dominated by a saturation abundance of ammonia and phosphine.
The vertical mixing ratio profile of phosphine follows that of the Orton et
al. (2000) detections, with a deep mixing ratio of 0, 10 and 20-solar. . . . .
xvi
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135
1
CHAPTER 1
Introduction
Over the last quarter-century each of the outer planets (Jupiter, Saturn, Uranus, Neptune)
has been visited by unmanned spacecraft; not since Galileo’s first telescope has there been
such an improvement in our ability to investigate the reaches of our solar system. With the
capability of bringing instruments within close proximity of planets and the ever-improving
technology of earth-based instruments, our current ability to scrutinize the planets is truly
unprecedented. As is the case in any worthwhile endeavor, new abilities and new informa­
tion reveal more questions than answers. In seeking an understanding of planetary forma­
tion or searching for worlds capable of sustaining life, many of the broad questions that
arise require improved understanding of the molecular composition of the outer planets.
Much of this work is accomplished through a comparison of various observations of
the planets with appropriate models. A lack of laboratory measurements of the microwave
attenuation of atmospheric constituents has been cited as a major hindrance to atmospheric
modeling of the outer planets (de Pater and Mitchell, 1993). The objective of this work has
been to improve the abilities of the planetary science community to investigate the chemical
composition of outer planet atmospheres through laboratory measurements of phosphine’s
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
microwave attenuation and application of these results to microwave measurements of the
outer planets. Though phosphine has been detected in the atmospheres of Jupiter and Saturn
using millimeter wavelength techniques ((Noll and Larson, 1990), (Weisstein and Serabyn,
1994b), (Weisstein and Serabyn, 1994a), and (Orton et al., 2000)), its affect on the mi­
crowave (A > 1cm) spectrum has been uncertain since, prior to this work, no laboratory
measurements of phosphine had been conducted at microwave frequencies.
For some time, phosphorus chemistry in the upper atmospheres of the outer planets
has been been cited as the possible cause for the colors red and yellow observed at Jupiter
and Saturn (Noy et al., 1981; Owen and Terrile, 1981). The photolysis of P H 3 may ac­
count for the reds and reddish-brown seen in Jupiter, while formation of P4 may produce
yellows (Wayne, 1995). However, the presence of phosphine in the outer planets was in
doubt, since the other phosphorus-bearing molecules are thermochemically favored under
conditions present in outer planet atmospheres (Prinn and Lewis, 1975; Fegley and Prinn,
1985; Borunov et al., 1995). The presence of phosphine in the outer planets was finally
confirmed in 1985 (Bregman et al., 1985).
1.1
Research Objectives and Organization
This thesis describes the first ever series of measurements of phosphine’s centimeter-wave­
length opacity in a hydrogen-helium atmosphere. These measurements have been con­
ducted at pressures from one to six bars and at temperatures from 175-298 Kelvin. A
formalism that accurately predicts the 1-30 GHz opacity of phosphine under conditions
2
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
characteristic of the Jovian planets has been developed and is described in detail. The
formalism is then applied to the re-interpretation of Voyager radio occultation measure­
ments at Saturn and Neptune. Phosphine abundance is inferred from the Voyager results,
for the first time, and is shown to be consistent with atmospheric models and independent
observations. Finally, an elliptical-shell local radiative transfer model has been developed
to support the RADAR/radiometer instrument on the Cassini-Satum orbiter. Predictions
of the microwave absorption expected to be encountered by the Cassini radio science ex­
periment have been calculated. These predictions include an analysis of the likelihood of
detecting phosphine in the upper atmosphere of Satum.
While the results of this research are of use in any Jovian atmospheric model that
includes phosphine as a constituent, the main focus of this work and the measurement
frequencies used in this work where chosen specifically to support interpretation of the
Voyager radio occultation experiment (2.2 and 8.3 GHz)1, the Galileo entry probe radio at­
tenuation experiment (1.5 GHz), the Cassini RADAR/radiometer (13.3 GHz), the National
Radio Astronomy Observatories (NRAO) Very Large Array (VLA) and the Cassini radio
science experiment (2.2, 8.3, 21.6 and 26.9 GHz).
In Chapter 2 the experimental apparatus used to conduct the microwave measure­
ments is described along with the theoretical background for these measurements. The
results of the laboratory measurements are presented.
In Chapter 3 the new centimeter-wavelength phosphine model is developed, de­
1The frequencies listed refer to the laboratory measurements that support specific missions or instruments,
which are not necessarily identical to specific mission or instrument frequencies.
3
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scribed and compared to experimental data. Also, the formalism is applied to re-interpretation of the microwave attenuation inferred from the Voyager radio occultation experi­
ments.
In Chapter 4 radiative transfer modeling is discussed. The DeBoer and Steffes
(1996) disk-average radiative transfer model is modified to include the new phosphine for­
malism and re-applied to Saturn and Neptune. Also, a new local ray tracing-based radiative
transfer model is described and applied to predictions for the Cassini-Satum mission.
In Chapter 5 a summary of the conclusions and contributions is provided along with
suggestions for future work.
4
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
5
CHAPTER 2
Laboratory Measurements of Phosphine
under Outer Planet Conditions
Theoretical calculations of the microwave absorption spectrum of gaseous molecules can
be made from classical theories and include resonant line strengths and frequencies which
exist in the form of the GIESA and JPL (Poynter and Pickett, 1985) catalogs, but are
sometimes unable to accurately predict the absorption spectrum o f molecules under a wide
range of temperature, pressure, and mixing ratio conditions, which exist in planetary at­
mospheres. Laboratory measurements of these molecules, under simulated atmospheric
conditions, are better able to provide absorption spectra over the frequency range and ac­
tual environmental conditions of the atmospheres being observed (see, for example, (Joiner,
1991; Kolodner, 1997)).
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
2.1
Motivation for Laboratory Measurements
Microwave absorption in the atmospheres of the outer planets has been observed in ra­
dio occultation experiments, inferred from ground-based radio emission studies, and in­
ferred from the Galileo probe radio science experiment at Jupiter (Folkner et al., 1998).
As observational data of the microwave absorption and emission from the outer planets
have accumulated and improved, studies reveal inconsistencies between atmospheric mod­
els exposing a lack of complete understanding of the structure of those atmospheres. For
example, the ammonia abundance inferred from earth-based radio emission measurements
of Neptune (de Pater et al., 1991) is inconsistent with the ammonia abundance inferred
from Voyager 2 radio occultation measurements made in the 1989 Neptune flyby (Lindal,
1992). At the time of the Lindal interpretation, ammonia had been thought to be the likely
cause of the preponderance of microwave opacity in outer planet atmospheres (see, for ex­
ample (Berge and Gulkis, 1976)). However, the Lindal ammonia abundance is problematic
for two reasons: It requires a super-saturation o f ammonia and results in a centimeter wave­
length brightness temperature spectrum that is inconsistent with observations (DeBoer and
Steffes, 1996a). The inconsistency prompted dePater to investigate the affect of hydrogen
sulfide (H2S) on the atmosphere of Neptune (de Pater et al., 1991). However, this work
was hampered by the lack of laboratory measurements of H 2S under applicable condi­
tions, and it was concluded that Voyager was most likely detecting ammonia. The work
of dePater prompted new laboratory measurements of hydrogen sulfide (H2S) (DeBoer and
Steffes, 1994). While DeBoer and Steffes showed that H 2S was more opaque than previ­
6
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
ously modeled, the Neptune atmospheric model still required an additional molecule, such
as phosphine (PH3), to reconcile Voyager and ground-based measurements.
Phosphine has been detected in the atmospheres of the outer planets (see e.g. (Noll
and Larson, 1990). More recently phosphine was detected at microwave frequencies in
the atmospheres of Jupiter (Weisstein and Serabyn, 1996) and Saturn (Weisstein and Serabyn, 1994a) in amounts, relative to its solar abundance (Anders and Grevesse, 1989), of
approximately one and ten times, respectively. The DeBoer and Steffes model (1996a)
required a 15 times solar abundance of phosphine in Neptune’s atmosphere, which ap­
peared to follow a trend from Jupiter to Saturn, but such large amounts had never been
detected at Neptune. However, the actual microwave absorption spectrum of phosphine
was highly uncertain, since only a single set of laboratory measurements of its microwave
or millimeter-wavelength opacity under Jovian conditions had been reported (Pickett et al.,
1981) at that time. This measurement was at phosphine’s first rotational line (J = 1 -> 0)
at 266.9 GHz and phosphine’s opacity in the spectral region from one to thirty GHz is
practically independent of its J = 1 -* 0 line, as is shown in section 3.1.
2.2
Foundation for Laboratory Measurements
Absorption or emission by gaseous molecules in the microwave or millimeter-wave spec­
tral range is due to the interaction of the molecule’s electric or magnetic dipole moment
with an incident electromagnetic field. Gases absorb (or emit) electromagnetic radiation at
7
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
frequencies related to transitions in the energy states of its constituent molecules by
where E u and Ei represent the upper and lower energy states of the molecule, h represents
the Planck constant (h = 6.624 x 10~34), and f ui is the absorption (or emission) frequency.
Radiation is absorbed when a molecule’s total energy transitions from a lower to a higher
state, emission is the reverse process. Since the processes are inverse, all further discussion
will focus on absorption.
An isolated molecule’s total internal energy consists of three types of energy states:
electronic, vibrational, and rotational energy. Microwave spectra primarily consist of rota­
tional energy transitions with the notable exception of molecular inversion, which is a spe­
cial case of a vibrational transition (Harris and Bertolucci, 1989). Phosphine and ammonia,
both symmetric-top molecules, exhibit molecular inversion transitions. Since energy states
are quantized it follows from equation 2.1 that the absorption frequencies are also discrete.
While this is true for an isolated molecule and approximately true for very low pressure
spectroscopy, a number of processes broaden spectral lines (Townes and Schawlow, 1955)
as pressure is increased (see section 3.2). In the region of interest to planetary radio science
techniques, the effect of pressure broadening typically dominates over other broadening
mechanisms, such as Doppler broadening.
Whatever the cause of the allowable energy transitions, the molecule will absorb
energy from an incident field, or emit energy at the frequencies of the transitions. This
interaction is observable either as a decrease in power transmission through the medium
8
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
or as emission from the medium at the transition frequencies. Both phenomena form the
basis for passive remote sensing observations. Techniques for measuring the absorption
of energy from an incident electromagentic field in a laboratory are covered extensively in
Townes and Schawlow (1955).
2.3
Electromagnetic Manifestation of Absorption by Molec
ular Gas
In a homogeneous, isotropic, lossless dielectric medium, such as vacuum, forward traveling
electric and magnetic waves follow the equations
E( x) = E 0e~>k\
(2.2)
H( x) = H0e~ikx
(2.3)
respectively, where k is the wavenumber, which is equal to U y/jli, where u is radial fre­
quency, /i is the permeability, and e is the permittivity of the medium. By definition, the
opacity of a gas is its ability to absorb electromagnetic radiation. Energy loss in a homoge­
neous, isotropic, lossy dielectric medium manifests itself as a decrease in the amplitude of
the waves and may be accommodated in Maxwell’s Equations through the introduction of
a complex permittivity term
e = e'-js"
9
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(2.4)
so that the wavenumber of the electric and magnetic wave equations becomes
k = ujy/JH = u \Z n (e ' - je")
(2.5)
which can be separated into the propagation constants a and /3(Ramo et al., 1994):
jk = q + jp =
[l - j ( f ) ]
(2-6>
where a is called the attenuation or absorption coefficient and 8 is called the phase constant.
These may be separated yielding equations for a and 3:
(2.7)
a = uj
8 =u
The real
(c')
and imaginary
(c" )
+ 1
\
( 2 .8 )
components are not independent and are related by Kra-
mers-Kronig relation (Balanis, 1989). The explicit frequency dependence of equations 2.7
and 2.8 can be removed by taking their ratio:
(2.9)
\
The term
V^1 + ( ^ )
+1
which appears in both the numerator and denominator of equation 2.9, is the
loss tangent of a gaseous medium:
e"
.
— = ta n d =
1
(2 . 10)
Q gas
where Qgas is the quality factor of the gaseous medium, which is an important quantity
addressed in section 2.4. For a low-loss gas,
s"
1
— = tan 5 = ——
Q gas
1.
10
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(2. 11)
With this assumption, equation 2.9 can be approximated as,
within a 0.5% error for absorptivities less than lOAd B / k m (Spilker, 1990). Since the phase
constant is defined as
(2.13)
the absorption coefficient can be written as
The important inference of equation 2.14 is that if Qgas can be measured and A is known
then
cv,
the opacity or absorptivity, can be calculated. The procedure for how this is accom­
plished in the laboratory is outlined in section 2.4.
2.4
Procedure
The opacity of a low-loss gas may be inferred from its effect on the quality-factor, or Q,
of a microwave cavity resonator. Since the Q of a resonator is related to the energy loss
per cycle, and the Q may be directly measured by f o / b w , where f o and bw are the center
frequency and 3-dB bandwidth of a resonance, any change in Q may be related to the
attenuation of the gas. As just related, the ’’quality factor” or Q of the gas itself is related
to its opacity by,
7r
1
e' A
7T
Qga, A
11
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
(2.15)
where e' and e" are the real and imaginary permittivity of the gas, and a is the absorptivity of
the gas mixture in Nepers/km (Np/km) and A is the wavelength in km. 1 The measurements
necessary to determine Q gas are straight-forward. While ideal cases simplify theory and
clarify understanding, they rarely hold true in practice. Therefore, in an effort to present the
laboratory procedure clearly, the ideal case will be presented with corrections for physical
perturbations introduced where corrections are needed. The approach used involves filling
a high-quality-factor cavity resonator with a lossy-gas mixture. The quality factor of a
loaded (test-gas-filled) resonator is,
1
1
1 + - —1 + ——
1
+ —
Q ’laaded
Qgas
Qc
Q e xtl
(2.16)
Qext2
where Q\noaded is the measured2 quality factor of the loaded resonator system, Qgas is the
quality factor of the gas under test, Qc is the quality factor of the evacuated cavity resonator,
and Q „ fl,2 represent external coupling losses. In the ideal case, Qc and Q extt,2 are all
infinite, therefore, the measured Q is equal to the Q of the test gas. In reality, Q c is limited
by losses inherent to the cavity resonator, such as ohmic losses in the cavity walls due to
finite conductivity and leakage of energy from the resonator through the mode suppression
slits. The external quality factors, Q exn,2 . represent a loss in energy in the cavity due to
coupling through the antenna probes and can be estimated by calculating the transmissivity,
£ = 1 0 hF,
(2.17)
l Note that an attenuation constant, or absorption coefficient, or absorptivity o f 1 Np/km = 2 optical
depths/km (often expressed as km “ l) = 20logi0e ( x 8.686) dB/km, where the first notation is the natural
form used in electrical engineering, the second is the prevalent form used in physics and astronomy, and the
third is the common (logarithmic) form. The third form is used to avoid a possible ambiguity o f a factor o f 2.
:The superscript ’m ’ denotes a measured quantity.
12
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
where S is the insertion loss measured in decibels, and by using the relation (Matthaei et al.,
1980),
t =
2
—
Q ext
(2.18)
therefore,
2Q m
(2.19)
where Q m is the measured quality factor for a loaded or unloaded resonator. Assuming the
external Q ’s are equal for the symmetric cavities, one can substitute Qext from equation
2.19 for Qext in equation 2.16, giving
1
1
V ^loaded
1
V^uuc
( 2 .20 )
loaded
where tloaded and tvac are the transmissivities for the loaded and vacuum measurements
respectively. Quac is the measured quality factor of the resonator under vacuum. By defi­
nition the gas quality factor (Qga3) is zero for the vacuum measurement, therefore, the loss
contribution of the Q„ac measurement include only the system losses. Due to the inherent
non-idealities described, two measurements are necessary to correctly calculate Qgas. This
differential measurement enables the removal of losses, which cannot be directly measured
or calculated and are not attributable to the opacity of the gas. However, since the refractivity of any gas ((n — 1) x 106), where n is refractive index) is non-unity, a shift in the
center frequency of the resonator’s resonance occurs with the test gas present. This shift
in frequency results in a change in the coupling of the resonator and distribution of the
induced wall currents, changing the quality factor of the resonance. This effect is called
dielectric loading (see e.g., (Joiner, 1991)). Dielectric loading effects can be removed by
13
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
performing a measurement of the quality factor of the resonance with a lossless test gas.
By introducing enough lossless gas to shift the center frequency of the resonance by the
same amount as when the cavity was loaded with the test gas, this reference measurement
matches, as closely as possible, the conditions of the loaded measurement. This reference
measurement with the lossless gas is called the matched measurement, as opposed to the
vacuum or loaded measurements. Using the matched measurement instead o f the vacuum
measurement equation 2.20 becomes
1
1 — \/tloaded
Qgas
Q loaded
1 —\ /
tm atched
^
Q matched
Now that Qgas is in terms of measurable quantities, the absorption or opacity of the gas
under test can be calculated by substituting equation 2.21 into equation 2.15,
^ 7r / 1 — Vtloaded
^ \
Qloaded
1 —V tm a tch ed \
Qmatched
J
The quality factor in each case is measured, as previously mentioned, as
Q = zr
bw
(123)
where f 0 and bw are the center frequency and 3-dB bandwidth of the resonance.
2.5
Measurement System
The measurement apparatus used in this work, shown in Figure 2.1, is similar to that used
in Steffes and Jenkins (1987), and DeBoer and Steffes(1994). The apparatus is comprised
14
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
£2
Isolator
High
Resolution
Spectrum
; Analyzer
Cavity
Resonator
rad: 13.1 cm
Temperature Chamber ( 170K
PC
Vacuum
Pump
Figure 2.1: Schematic of the laboratory measurement system.
handling, thermal, microwave, and data collection subsystems.
PH,
Scrubber
System
System includes gas-
15
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of four subsections: a gas-handling subsystem, a thermal subsystem, a microwave sub­
system, and a data collection subsystem. The gas handling system consists of a pressure
vessel capable of sustaining pressures from vacuum to 6 bars, which is located inside of
an ultra-low temperature freezer, a phosphine-gas-mixture bottle, a nitrogen bottle, a num­
ber of needle-valves, a vacuum-pump, a vacuum gauge, a pressure gauge, and phosphine
scrubbing canisters all connected by seamless stainless steel piping. The low tempera­
tures required for simulating outer planet conditions (175-298 K) were achieved using an
ultra-low temperature freezer. The temperature was monitored using a J-type thermocou­
ple, which was inserted into a receptacle that protruded into the pressure vessel cavity. A
low-temperature laboratory-grade thermometer mounted in the freezer cabinet was used as
backup, however, it measured the ambient temperature of the cabinet and not the interior
of the pressure vessel. At the heart of the microwave system are two silver-plated circularcylindrical microwave cavity resonators, which are located inside of the pressure vessel.
The resonant frequencies possible for a given resonator are dependent on its size and shape
and may be transverse electric (TE) or transverse magnetic (TM) in nature.
TE modes typically have higher quality factors than TM modes, as no current is
induced between the walls and ends of a cylinder. (Since the resonator lids are fastened,
and not welded, they may introduce extra losses.) The large resonator, with a radius of
13.12 cm and a height of 25.42 cm, is used for measurements at 1.51 GHz (T E Qn mode
or L-band or 20 cm), 2.25 GHz (TE on or S-band or 13.3 cm), and 8.3 GHz ( T E i ^ u or
X-band or 3.6 cm) is placed at the bottom of the pressure vessel. The small resonator, with
16
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a radius of 2.5 cm and a height of 4.9 cm, is used for measurements at 13.3 GHz (T £ 2 2 1 or
Ku-band or 2.3 cm), 21.6 GHz (T E q33 or K-band or 1.4 cm), and 27 GHz (T E 036 or Kaband or 1.1 cm) and is mounted to the top plate of the pressure vessel. Mode suppression
slits are cut into both resonators in an effort to cut down on degenerate TM modes with
low quality factors. Coupling to each resonator is accomplished using two closed-loop
antenna-probes oriented to maximize the quality factors of TE0mn modes. One probe for
each resonator is connected to a microwave sweep oscillator, and one probe each is con­
nected to the spectrum analyzer. All cables (RG-142b for the large resonator and 0.085”
semi-regid cables for the small resonator) connect through the top plate of the pressure
vessel via hermetically-sealed bulkhead feed-throughs. The output of the source (sweep
oscillator) was isolated from the load (resonator) using an S-band isolator for the L and Sband measurements and an X-band isolator for X-band measurements. For the Ku, K, and
Ka band measurements the source was isolated using a 10 dB attenuator, which effectively
yields 20 dB isolation for the sweeper. The sources for the Ku, K, and Ka-band measure­
ments were initially two HP8690B Sweep Oscillators with appropriate plug-in modules,
however, starting with the measurements made on 9/9/99 an HP83650B Swept Signal Gen­
erator was used for all frequencies. The source for all L, S, and X-band measurements was
the HP83650B generator. The resulting spectrum was measured using an HP8564E Spec­
trum Analyzer. The data were collected by personal computer from the spectrum analyzer
via a GPIB interface. The bandwidth of the resonance (necessary for retrieving opacity )
is measured by computer, which significantly improves accuracy. The computer system is
17
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described in detail in DeBoer and Steffes (1996b).
2.6
Results
Data were collected on the microwave properties of PH3 on seven different occasions at fre­
quencies of 1.51 (TEon). 2.25 (TE013 ), 8.3 (TEli3,13), 13.3 (TE 221 ), and 21.6 GHz (TE033 ).
An additional frequency, 27 GHz (TE036 X was added in later measurements to better char­
acterize phosphine’s opacity in the spectral region approaching 32 GHz to support one of
Cassini’s Radio Science Subsystems (RSS). Each measurement session was performed at a
fixed mixing ratio and temperature, with measurements taken at each frequency and pres­
sures ranging from one to six bars (see Figure 2.2). The temperature and mixing ratio were
varied between sessions in order to retrieve the temperature dependence of phosphine’s
opacity and phosphine’s self-broadening parameter, respectively. One o f two mixtures were
used in each session; 82.6%H2, 9.2% He, 8.2% P H 3, hereafter called the eight —percent
phosphine mixture, and 88.0% #2.9.8%He, 2.2%PH$ called the tw o —percent phosphine
mixture. The specialty gas vendor analyzed the mixtures and certified each to be within 2%
of its stated mixing ratio (i.e., 8.2 ± 0.164%, 2.2 ± 0.044%).
18
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 2.1: Results of phosphine opacity measurements at room temperature. Gas mixture
composition: 82.6% H 2, 9.2% He, 8.2% PH3
Date
T
(K)
P
(bar)
V
(GHz)
a measured
(dB/km)
8/5/98
298
5.08
1.51
2.25
8.3
13.3
21.6
1.51
2.25
8.3
13.3
21.6
1.51
2.25
8.3
13.3
21.6
1.51
2.25
8.3
13.3
21.6
1.51
2.25
8.3
13.3
21.6
1.51
2.25
8.3
13.3
21.6
4.72
10.33
38.30
48.12
49.42
3.90
6.63
16.90
16.30
21.89
1.50
1.93
2.04
3.00
3.83
5.176
10.35
54.33
63.2775
74.13
4.16
7.06
17.83
17.56
14.65
3.08
4.53
7.85
9.06
12.68
3.04
1.00
12/2/98
292
6.14
3.04
2.02
a
± (db/km)
0.41
0.49
1.20
7.30
2.10
0.43
0.33
1.34
5.04
2.19
0.26
0.34
3.60
4.71
2.39
0.07
0.18
0.51
2.32
6.96
0.15
0.18
0.32
1.88
7.23
0.10
0.15
0.36
1.39
5.94
alpha modeled
(dB/km)
4.74
9.38
39.47
47.91
52.63
4.03
7.02
17.36
18.89
19.60
1.49
1.79
2.14
2.16
2.16
0.00
3.85
0.95
0.00
2.33
0.11
1.45
0.12
0.26
1.09
0.00
0.15
0.00
0.03
0.48
5.03
10.27
53.54
69.34
79.22
4.16
7.29
18.34
20.01
20.79
3.27
5.00
8.77
9.14
9.30
4.12
0.19
2.46
6.86
0.53
0.00
1.62
2.59
1.70
0.72
3.66
9.11
6.60
0.00
0.32
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
X*
The results of opacity measurements of the eight-percent mixture at room temper­
ature are listed in Table 2.1 and cold temperature ( « 2 1 3 /0 results are listed in Table 2.2.
The opacity results of the 2-percent mixture measurements are listed in Tables 2.3 and 2.4
for temperatures of 203 K and 175 K, respectively. These tables also include measurement
uncertainties as derived in section 2.7 and modeled opacities as developed in section 3.2.
It is obvious from the data that the 27 GHz measurements have large errors. This is due to
contamination of the 27 GHz resonance by neighboring resonances. Also, the data mea­
sured using the small resonator (13.3, 21.6, and 27 GHz) show significantly larger errors
than the data measured with the large resonator. This is due, in a large part, to the high
sensitivity of the smaller resonator to changes in coupling and thus transmissivity. With the
exception of the 27 GHz data and a few erroneous measurements from the small resonator,
the resulting errors are small and the data is highly self-consistent.
A comparison of results from two different measurements under the same experi­
mental conditions is shown in Figure 2.3. These two sets of measurements, which were
taken for the two-percent phosphine mixture at a temperature of 175 Kelvin and at a pres­
sure of three bars, are consistent within experimental uncertainty.
2.7
Measurement uncertainty
The uncertainty in the opacity measurements of this work is similar to that described in
detail in DeBoer and Steffes (1994), but with the addition of uncertainties in transmissivity
and imperfect matching. Also the spectrum analyzer used is a different model with lower
20
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
instrument uncertainties. The uncertainty in the physical quantities of pressure and temper­
ature are estimated to be within ± 0.1 bar of the stated pressure and within ± 1 Kelvin of
the stated temperature. The uncertainty in the stated mixing ratio of phosphine due to its
adsorption into the metallic surfaces of the pressure chamber and resonator is estimated to
be less than 250 ppm. This estimate was found by measuring the amount of latent phos­
phine detected in the nitrogen used to flush the evacuated system. This uncertainty is well
within the vendor’s uncertainty in the mixing ratio of 2 percent o f their stated mixing ratio.
Uncertainties in the microwave calculation of absorption are due to uncertainties in
the measured quantities used to calculate opacity and imperfect dielectric matching. The
basic measurable quantities required to calculate opacity (Eq. 2.22) are bandwidth, center
frequency, and transmissivity. Errors in bandwidth and center frequency are due to electri­
cal noise and instrumental uncertainties. Electrical noise is considered to be uncorrelated,
therefore the mean of many measurements is the best estimator of the true measurement
and the sample variance (S/v), weighted by the confidence coefficient (B),
o f, =
(2.24)
yields the best error estimate. A confidence coefficient of B = 1.88 results in a confidence
level of 90% for each set of ten independent measurements taken (Papoulis, 1991). The
variance in the center frequency and bandwidth are calculated and recorded for each set of
measurements.
This gives an estimate of the error due to electrical noise, but instrument errors must
also be estimated. The standard deviations for center frequency and bandwidth measure-
21
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
ments, respectively, are estimated by (Hewlett-Packard, 1997),
U r 7 y rs jiin c e x a l) /o + 0.15 R B W + Q M S P A N + 10Hz
» B W ( 4 x 10'7 y rs jin c e .c a l) +
+ 2 iS D H z ,
(2.25)
(2.26)
where / 0, RBW, SPAN, N, and LSD are the center frequency, resolution bandwidth, fre­
quency span, mixer integer, and least significant digit of the bandwidth measurement.
Errors in transmissivity are dominated by systematic errors that are difficult to com­
pensate for directly due to difficulties in measuring transmissivity, bandwidth and center
frequency simultaneously. The long-term temperature stability of the spectrum analyzer,
ldB/°C (Hewlett-Packard, 1997), contributes the largest error to the measurement of trans­
missivity. Also, small changes in the temperature of the freezer over time affect the me­
chanical connections between the resonator and its probes and between the probes and the
bulkhead feed-throughs. This change affects the coupling and therefore the transmissivity
by a small, but non-trivial, amount. Finally, since the operator of the measurement must
connect and re-connect some of the electrical connections between the resonator and the
microwave equipment during the measurement process, slight changes in these electrical
connections also have some affect on the transmissivity. Recall that transmissivity is cal­
culated from the insertion loss 5 using equation 2.17. Typical values of insertion loss for
the measurements were -30 dB for L-band, -22 dB for S-band, -17 dB for X-band, -23 dB
for Ku-band, -9 dB for K-band, and -10 dB for Ka-band. Typical values for the short-term
variation (within a measurement set) of insertion loss were (in dB), 0.2 (L), 0.16 ( S ) , 0.4
(X ), 0.23 (Ku), 0.56 (K) and 0.57 (Ka), and the long-term variation (between measurement
22
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
sets) of insertion loss were (in dB) 0.7 (L), 0.5 (S), 1 (X), 0.4 (Ku), 5 (K) and 0.8 (Ka).
Since the variations in insertion loss were systematic, averaging over several measurements
would not improve estimates of the standard deviation. Therefore, the short-term error was
derived for each frequency band during each measurement set by tracking the changes in
insertion loss in the three reference measurements conducted at vacuum. In the course of
a complete set of measurements, the three sets of vacuum measurements are made at the
beginning, middle, and end of each measurement set. Variations in transmissivity are cal­
culated by applying equation 2.17 to the maximum difference between the insertion loss
measurements of the three vacuum measurements for each measurement frequency. The
error in transmissivity is then mapped into an error in opacity by calculating the maximum
and minimum opacity due to these variations, by equation 2.22. The variance (ofranj) is,
as usual, calculated as the square of the standard deviation. Estimates for transmissivity
errors are consistent with expected errors due to uncertainties in the long-term temperature
stability of the spectrum analyzer (Hewlett-Packard, 1997) and to the repeatability of the
microwave connections (Hewlett-Packard, 1988).
Errors due to imperfect matching of dielectric loading are also dominated by sys­
tematic effects. Recall that ideally, dielectric matching removes all differences in the mea­
surement of the quality factor that are due to the refractivity of the test gas. Although every
attempt is made to match the frequency-shift perfectly, differences do occur. Determining
the amount of error due to this mismatch requires two steps. First, a series of measurements
of system Q where taken at vacuum and at various pressures using nitrogen, which is the
23
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
lossless reference gas used in all experiments. The greatest change in quality-factor per
hertz of frequency shift was found for each band. Second, the difference between the ideal
and the actual frequency shift in dielectric matching is calculated and that difference is then
multiplied by the quality-factor-error per hertz. The error in opacity due to the mismatch
is again found by mapping the error in matching into an error in opacity by equation 2 .2 2 .
The worst case is assumed and the error is modeled as the difference between the maxi­
mum and minimum opacity calculated from equation 2.22. This error is modeled as the
maximum extent of the error due to imperfect dielectric matching, with the nominal value
for opacity in the middle of the maximum and minimum calculated opacities. Therefore,
the standard deviation is calculated as half of the maximum error and the variance (a jiel) is
simply the square of this value.
The worst case error due to electrical noise and instrumentation uncertainty is cal­
culated as per DeBoer and Steffes (1994),
4 = «> + <r?> - 2 <r2ur?)
(2.27)
where
(2.28)
0Q0A
(2.29)
(2.30)
where the subscript i is for u and I denoting equations for the unloaded and loaded res­
onator, respectively, and 7 Ut/, /o(u,o>
A /Ui/ represent the 1 —\ / i terms from the numera24
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
tor in equation 2.20, center frequency, and bandwidth of the unloaded and loaded resonator,
respectively. The lcr uncertainty of the measured gas absorption due to the instrumentation
uncertainty and electrical noise is then,
, 8.6867T
an — ± — -— o\pdB/m
A
(2.31)
The total lcr uncertainty of the measured gas absorption is the quadrature sum of the vari­
ances,
GTotal = \ f ° n + ° L l + b r a n s '
25
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
( 2-32)
10'
10‘.2
.0
10
0
5
15
10
20
25
30
Frequency (GHz)
Figure 2.2: March 15 laboratory measurements showing pressure dependence. Mea­
surements were taken at a temperature of 213 Kelvin and a mixing ratio of 82.6%#2>
9.29c//e,and &.2%PH3. The 1,3, and 5 bar measurements are connected with solid, shortdashed, and long-dashed lines, respectively.
26
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 2.2: Results of phosphine opacity measurements at 213 Kelvin. Gas mixture composition: 82.6% H2, 9.2% He, 8.2% PH3_________________________________________
V
Date
T
P
a measured
a
alph a modeled
X2
(dB/km)
(dB/km)
(K) (bar) (GHz)
± (db/km)
1.51
9/9/99 213 2.09
5.42
0.15
5.60
0.21
2.25
9.04
0.34
9.58
2.53
8.3
23.22
0.95
22.21
1.10
13.3
24.30
1.13
23.90
0.12
21.6
28.75
24.68
0.34
6.95
1.51
3.14
3.16
1.01
0.30
0.01
2.25
4.22
4.19
0.2
0.01
8.3
6.31
0.29
5.69
4.53
13.3
5.67
1.37
5.80
0.01
21.6
27.82
5.64
5.85
15.19
3/15/00 213 5.15
1.51
7.29
0.24
7.12
0.51
2.25
14.72
14.77
0.75
0.00
121.34
8.3
86.74
2.51
96.13
13.3
117.56
116.96
7.32
0.01
21.6
215.35
90.49
136.88
0.18
27.0
198.81
38.89
142.26
2.11
1.51
2.94
6.36
0.53
6.40
0.01
2.25
11.75
12.04
0.29
0.33
8.3
47.52
3.41
39.58
3.51
13.3
44.22
2.48
45.16
0.14
21.6
75.97
110.73
47.96
0.01
27.0
59.14
48.64
37.06
0.08
1.51
1.10
3.56
3.46
0.07
0.36
2.25
4.86
0.61
4.73
0.03
8.3
7.87
1.59
6.71
0.17
13.3
8.07
2.11
6.86
0.33
21.6
76.78
77.80
6.93
0.19
27.0
24.81
30.76
6.95
0.34
27
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 2.3: Results of phosphine opacity measurements at 213 Kelvin. Gas mixture compo­
sition: 88.0% H2, 9.8% He, 2.2% PH3
Date
3/22/00
T
(K)
P
(bar)
213
5.36
2.87
1.12
(GHz)
a measured
(dB/km)
1.51
2.25
8.3
13.3
21.6
27.0
1.51
2.25
8.3
13.3
21.6
27.0
1.51
2.25
8.3
13.3
21.6
27.0
2.04
4.29
25.30
33.58
33.46
57.08
1.85
3.18
10.22
10.62
13.53
7.46
0.92
1.22
1.91
0.58
10.85
6.41
V
a
alp h a modeled
± (db/km)
0.19
0.34
1.68
4.25
68.52
13.70
0.28
0.41
0.67
1.70
8.32
15.67
0.16
0.37
0.59
2.08
8.45
13.89
(dB/km)
2.12
4.30
23.20
31.53
37.39
39.03
6.40
12.04
39.58
45.16
47.96
48.64
3.46
4.73
6.71
6.86
6.93
6.95
28
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
X2
0.19
0.00
1.56
0.23
0.21
1.74
0.00
0.00
0.71
0.05
0.05
0.08
0.00
0.00
0.05
0.35
1.14
0.11
Table 2.4: Results of phosphine opacity measurements at 175 Kelvin. Gas mixture compo­
sition: 88.0% H2, 9.8% He, 2.2% PH3
Date
3/31/00
T
(K)
175
P
(bar)
3.15
1.01
4/4/00
175
3.08
1.01
V
(GHz)
1.51
2.25
8.3
13.3
21.6
27.0
1.51
2.25
8.3
13.3
21.6
27.0
a measured
(dB/km)
a
± (db/km)
alpha modeled
(dB/km)
X2
2.15
3.92
17.54
21.13
21.03
16.44
1.06
1.48
2.45
2.14
2.10
7.50
0.25
0.47
0.81
4.66
4.31
14.70
0.21
0.31
0.010.39
2.55
5.10
8.23
2.36
4.53
18.34
22.34
24.59
25.16
1.21
1.70
2.57
2.64
2.67
2.68
0.69
1.68
0.96
0.07
0.68
0.35
0.53
0.49
0.10
0.04
1.51
2.25
8.3
13.3
21.6
27.0
1.51
2.25
8.3
13.3
21.6
27.0
2.20
4.13
17.50
15.24
27.48
20.10
1.15
1.67
2.56
1.60
-0.60
2.93
0.15
0.34
0.71
2.40
10.80
17.17
0.18
0.21
0.41
1.83
10.97
10.65
2.35
4.49
17.74
21.45
23.51
24.03
1.21
1.70
2.57
2.64
2.67
2.68
0.99
1.17
0.11
6.69
0.14
0.05
0.11
0.02
0.00
0.32
0.09
0.00
29
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0.34
10'
E
co
■o
10
1
o
CO
Q.
o
_ L
,o
10
0
5
10
15
20
25
30
Frequency (GHz)
Figure 2.3: Comparison of two separate laboratory measurements, each taken at a temper­
ature of 175 Kelvin, at a pressure of 3 bars for a mixing ratio of 88.0% f y , 9.8% H e, 2.2%
P H 3.
30
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
31
CHAPTER 3
Phosphine Microwave Opacity
Formalism
The purpose of the laboratory measurements described in Chapter 2 is to produce a math­
ematical formalism for the calculation of phosphine absorption at centimeter wavelengths,
over a range of temperatures and pressures, in a hydrogen-helium atmosphere. To be useful
in atmospheric modeling the formalism must be as simple as possible, while being widely
applicable. To this end the fitting for the formalism is based, as much as possible, on
established absorption models in wide use in the planetary atmospheric community.
To this end the existing theoretically derived line catalog (Poynter and Pickett,
1985) for phosphine is examined, along with the some of the assumptions inherent in their
calculation of phosphine lines. Phosphine is also compared with its well-studied chemical
analogue, ammonia.
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
3.1
Phosphine Spectrum
Phosphine has a rich microwave and millimeter-wave spectrum, including weak collisionally-induced lines at microwave frequencies, and stronger rotational lines at millimeter
and sub-millimeter wavelengths (Poynter and Pickett, 1985) (see Figure 3.1). From an
examination of phosphine’s spectrum below 500 GHz, depicted in Figure 3.2, it is obvious
that the intensity of the J = 1 -> 0, at 267 GHz, is far greater than any other individual
line. However, attempts to approximate phosphine’s opacity by ignoring the seemingly
minor contribution of the lower frequency collisionally-induced lines and including only
the high intensity J = 1 -> 0 line may be useful in the millimeter (or short cm) region, but
grossly under-state the opacity in the low GHz or long centimeter wavelength region.
The contributions to phosphine’s calculated centimeter-wavelength opacity by all
published (Poynter and Pickett, 1985) absorption lines from the J = 1 -> 0 line and
higher, compared to the contributions from all published lines below J = 1 -> 0 is shown
in Figure 3.3. Note that, for the conditions of outer planet atmospheres, the contribution
from the J = 1 -+ 0 line, and all lines above, is negligible compared to the contribu­
tions from the collisionally-induced lines. Note, the theoretical absorption models used
in this figure are discussed in section 3.2. Comparison of laboratory measurements of
phosphine opacity, under the same conditions as the theoretical models, are included in
Figure 3.3 and indicates serious deficiencies in theoretical phosphine opacity at centimeter
wavelengths. Phosphine’s measured microwave opacity is more than an order of magni­
tude greater than that calculated by the best theoretical model, which includes all published
32
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0 .0 6
0.05
_N 0.04
2
I
0.03
E
c
>> 0.02
c
0
C
0.01
266.9 GHz
-
0.01
0
1000
2000
3000
4000
5000
6000
Frequency (GHz)
Figure 3.1: Phosphine’s molecular spectrum. Intensity and frequency of each of phos­
phine’s spectral lines.
33
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Intensity (nm 2-M H z)
-2
-10
-12
-1 6 -
265.9 GHz
-18
0
50
100
150
200
250
300
350
400
450
500
F req u en cy (GHz)
Figure 3.2: An examination of phosphine’s spectrum below 500 GHz. Note the first rota­
tional line ,J = 1
0, at 266.9 GHz
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
phosphine absorption lines. Therefore, any centimeter wavelength model that neglects the
collisionally-induced lines is grossly inaccurate.
A number of explanations could account for the deficiencies seen in theoretical cal­
culations of phosphine opacity. The properties of phosphine’s 267 GHz line have been
measured (Pickett et al., 1981) and are included in the theoretical models of phosphine,
therefore its possible contributions to the calculation error are considered negligible. The
most plausible alternatives include an underestimate of the intensities and/or line broaden­
ing parameters of the collisionally-induced lines or contributions from phosphine’s inver­
sion spectrum, which is not included in published catalogs (Poynter and Pickett, 1985) and
therefore, not included in the model.
3.1.1
Phosphine Inversion: Ammonia as an Analogue
Phosphine (PH3) is a symmetric-top molecule that forms a pyramidal shape, like ammonia
(NH3), with three hydrogen atoms at the base of the pyramid and the larger phosphorus
molecule at the apex. Nitrogen (N), phosphorus (P), and arsenic (Ar) are all fifth column
molecules and are thus expected to share some similar properties. Since the microwave
properties of ammonia have been investigated much more extensively than phosphine (see
eg. Townes and Schawlow (1955) and Kakar (1975)), similarities between the molecules
may be invoked to extrapolate properties o f phosphine that are yet unknown. For example,
all three molecules undergo molecular inversion, where the molecular-pyramid turns itself
inside-out when the N, P, or As-atom tunnels through the plane of the hydrogen atoms,
35
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
-4
Frequency (GHz)
Figure 3.3: Comparison of various centimeter-wavelength phosphine opacity models with
laboratory measurements. All models are based on the Van Vleck-Weisskopf line-shape
with the same physical conditions as the March 22 (3-bar) measurement; a mixing ratio of
88.0%H2, 9.8%He, and 2.2% PH3, a pressure of 2.87 bars, and a temperature of 213 K.
The model approximating phosphine opacity using only its first rotational line (J = 1 —>0)
is depicted by the long-dash line. The model using the full published phosphine catalog is
shown by the short-dash line, which is indistinguishable from the model including only the
lines below (in frequency) phosphine’s J = 1 -> 0 line (solid-line).
36
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
see (Kroto, 1992). For a pyramidal molecule, such as ammonia, potential minima occur
when the nitrogen atom is on either side of the plane of the hydrogen atoms. While the
inversion transition is between two vibrational states, which would typically be associated
with infrared frequencies, the energy gap between the two vibrational levels is such that
the transition between them is at microwave frequencies. For other pyramidal molecules,
such as phosphine, the potential barrier of inversion is greater and the associated inversion
frequency is lower. This may appear to contradict the relationship between the energy and
the frequency of transition, however, as the height of the potential barrier between the two
minima is increased the energy gap between the two vibrational states is decreased. The
energy/frequency relationship is not violated since the inversion process is due to tunneling
through the barrier rather than by exceeding the potential barrier (Townes and Schawlow,
1955). For ammonia, this process dominates its microwave spectrum with a set of inversion
lines centered at approximately 24 GHz.
However, care must be exercised when making such comparisons due to the very
basic differences between these elements, such as atomic radius, atomic mass, bond angle,
and electronegativity. A classical physics approach can be used to obtain some qualitative
understanding of molecular inversion (Townes and Schawlow, 1955). Compared to a ni­
trogen atom’s atomic radius (0.7
A),
a phosphorus atom ( 1 .1 0
A) is over 50%
larger and
arsenic ( 1.21 A) is even larger (Zumdahl, 1989). From this alone, one expects it to be more
difficult for the phosphorus atom to pass through the plane of the hydrogen atoms, and this
is indeed the case. More quantitative methods for determining the resonant frequency of
37
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
molecular inversions examine the height of the potential barrier inhibiting the inversion.
Ammonia, with a potential barrier of 2077 cm -1 , has an inversion spectrum at approxi­
mately 24 GHz, while phosphine, with a potential barrier of 6085 cm -1 , has a calculated
inversion spectrum at approximately 140 kHz and arsine (AsH3), with a potential barrier of
11,220
cm-1, has a calculated inversion spectrum at approximately one-half cycle per year
(Townes and Schawlow, 1955).
The existence of a phosphine inversion spectrum is theoretically sound, as discussed
in Townes and Schawlow (1955). However, phosphine inversion occurs very slowly com­
pared to experimental observation by high-resolution spectroscopy and has yet to been de­
tected (Kroto, 1992). Since its inversion occurs so slowly Kroto postulates that phosphine
inversion can safely be ignored. Also, Poynter et. al. (1985) do not include phosphine in­
version lines in their Submillimeter, Millimeter, and Microwave Spectral Line Catalog since
the contribution of the inversion spectrum is expected to be negligible due to the extremely
low intensities calcualted for the inversion spectrum (private communication Ed Cohen).
These assumptions are tested in the formalism modeling effort described in section
3.2. As will be discussed, the existing theoretically-based models for phosphine, using the
JPL catalog (Poynter and Pickett, 1985) do not match laboratory measurements without an
increase in total intensity in the A > 2cm region. Additionally, the impact of an added
inversion line is investigated in order to determine if the omission o f phosphine’s inversion
spectrum is the cause for the intensity deficiency exposed by the laboratory measurements.
38
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
3.2
Formalism Development
In order to develop a formalism with the broadest possible application over temperature,
frequency, pressure, and mixing ratio, every effort was made to base the formalism on pre­
vious quantum mechanical models. Theoretical calculations of the microwave absorption
spectrum of gaseous molecules may be made from classical theories that include resonant
line strengths and frequencies that have been computed and are compiled, for example,
in the JPL catalog (Poynter and Pickett, 1985). Using these lines the absorption from a
collisionally broadened gas, as a function o f frequency may be calculated by,
(3.1)
where, for line j, Aj is the absorption at the line center, A u3 is the line-width, and Fj is the
line-shape function(Townes and Schawlow, 1955).
The absorption at the line center may be calculated from the JPL catalog (Poynter
and Pickett, 1985) as,
where n is number density, S,(T ) is the intensity of line j, which is scaled from the intensity
calculated (see (Poynter and Pickett, 1985)) at a reference temperature T q as,
e - h c E t/ k T _ e - h c E h/k T
kcEt/kT0
hcEh /k T 0
(3.3)
(h c / k ) E , ( l / T - l / T 0)
where the temperature dependence term
77
is approximately 1.5 for symmetric-top mol­
ecules, such as phosphine, and unity for linear molecules, such as hydrogen. The Ei and
E h are the lower and upper state energies, respectively, in units of inverse-centimeters.
39
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
The resulting expression for line center absorption is then,
f T ay +l
106P (6ar)
aj
(3.4)
~ nkgTAv.
where the line-w idth for a mixture of gases is calculated by,
(' y )'
= y .
I
where A i/° is the line broadening parameter and
G H :'
(3-5)
is its temperature dependence for gas i
and line j in units of GHz/bar and Pi is the partial pressure of gas i in bars. The temperature
dependence of the line broadening parameter may be calculated by,
A v OC r-(m + l)/2 (m -l) _ T ~S.
where 1 <
m
q
.6)
< oo. For neutral gases m — 3 is a lower limit, therefore, £ falls between 0.5
and 1.0.
T he Ben-Reuven (1966) (BR) and Van Vleck-Weisskopf (1945) (VVW) lineshapes
(Fj in equation 3.1)
are useful for planetary atmospheres (see, for example (Bergeand
G ulkis, 1976)). The
B R lineshape is similar to the W W lineshape with the addition of
a cou p lin g element (£) and a pressure shift term (5), which incorporate line coupling and
frequency shift of line centers. With ( and 5 set to zero, the B R lineshape simplifies to the
VVW lineshape. The BR lineshape is:
-
,
n
2 ( v V {Av - Q v 2 + { Av + Q [(r/0 + 6)2 + At/2 - £2]
F { v .v 0, A v ^ 16) = - —
1- 2 -------------; (3.7)
7T \ v 0J
[u2 - (uo + 6)~ - A v 2 + C2] + 4i/2Al/2
and the W W lineshape is:
F {v ,v 0.A v ) = —
Av
.{vo — v) + A v 2
+
Av
{vq + v) + A v 2
40
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
(3.8)
The parameters available for fitting this model to laboratory measurements are the
line broadening parameter (Ai/?-), and its temperature dependence (£), the coupling coef­
ficient (C), and the pressure shift term (5) if the BR line-shape is used, or just Ai/,° and
£ for the VVW line-shape. However, a comparison o f phosphine’s theoretical absorption
model with laboratory measurements reveals order-of-magnitude discrepancies in the low
GHz range, see Figure 3.3, suggesting a need for additional line-center intensity. Two
likely sources for the deficiency in intensity are the absence from the JPL catalog of phos­
phine’s very low frequency inversion spectrum lines and the fact that none of the intensities
of the centimeter-wavelength lines in the catalog have ever been measured. While many
variations of model fits have been tried, four main types of model fits were examined: BR
and VVW with an additional artificial inversion line, and BR and VVW without an added
inversion line but with scaled line intensities. The intensity weighting factors developed
in this work are empirically derived from the laboratory measurements of the continuum
absorption spectrum of pressure broadened phosphine.
The formalism is fit to laboratory data using a multi-variable simplex fitting func­
tion to minimize the weighted objective function,
meas
(3.9)
(C “ )
where a™™3,acnalc, and cr™ea3 are the laboratory measurement, model result, and laboratory
measurement error, respectively. The weighting serves to decrease the significance of data
points with larger errors. As discussed above, since the lines including and above the
J = 1 ->• 0 have little influence on the centimeter-wavelength spectrum and the properties
41
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
of the J = 1 -» 0 line have been measured by Pickett, el al (1981), their results were used
for all lines at and above 267 GHz and as seed values for model fitting of the other lines.
The ratio of hydrogen to helium foreign gas broadening was fixed at approximately 1.96,
which is consistent with the Pickett, et al (1981) measurement and measurements by Levy
and Lacome (1993).
In addition to making
, £, and £ free parameters, weighting factors for the
intensities were also made free parameters. A sub-set of measured data was used to fit the
model, and the remaining measurements were used in an attempt to independently verify
the model. Also, since a larger number of free parameters increases the chances of finding
a non-physical model to fit the data, a model that fit the data with the fewest free parameters
was sought. Using this methodology, model parameters which were highly insensitive were
removed from the free parameter list and set equal to their seed value.
The lines lower in frequency than the first rotational line (J = 1 -► 0) are collisionally induced rotational lines and have never been measured directly so weightings were
sought to fit the data. Note that the intensity weightings developed in this work are em­
pirically derived from the laboratory measurements of the pressure broadened phosphine
spectrum described in section 2.6. The first forty lines of the JPL catalog (Poynter and
Pickett, 1985) (62 kHz-27.3 GHz) exhibit changes only in the sign of its secondary quan­
tum number K (see Table 3.1). Since the rotational energy is not affected by sign changes
in K these lines will be referred to as elastic collision lines in order to simplify discussion.
The other collisionally induced lines (40.6 GHz-239.4 GHz) below the first rotational line
42
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
(J =
1
-»
0)
do exhibit changes in total rotational energy and will be referred to as the
inelastic collision lines.
Table 3.1: Phosphine line intensities. This table includes all of phosphine’s published lines
up to 40 GHz, as well as phosphine’s first rotational line at 267 GHz. All of the lines
discussed in the text are listed. The intensities given are the current published values and
the column Intensity Multiplier contains the intensity weighting factors described in the
text. For a listing of all model parameters, please refer to Table 3.2.
Frequency
GHz
612E-6
939E-6
255.9E-6
434.1E-6
6413E-6
1.5E-3
1.7E-3
3 3E-3
J.2E-3
70E-3
13.00E-3
1400E-3
27 IE-3
235E-3
50.6E-3
569E-3
91 4E-3
0.1054
0 1607
0.1839
0 2754
0.3058
0 4610
0.4879
0.7517
0.7553
M 238
12130
1.6368
1.9125
13295
32484
4,4477
5.9907
79501
10.4087
13.4603
172103
21.7756
27 2852
40.5922
Intensity
n m 3 .W H :
8.73776E-17
U 023E -17
4.36717E-17
177971E-15
1.41677E-16
386189E-16
192146E-14
90261E-16
1.7143SE-13
1.83696E-15
6 8 6 I2 E -I3
3 29686E-I5
52723E-15
107539E-12
757705E-15
504313E-12
985825E-15
1024E-U
I 16788E-14
1 78649E-11
126648E-14
173086E-U
1.26212E-14
3.71364E-11
4.5436E-11
1.1601 IE-14
5.04778E* 11
9.S5598E-15
5.12979E-II
7.75354E-15
4.79844E-11
4.15I45E-U
3.33734E-11
150207E-1I
I.75428E-11
1.15398E-II
7.1351E-12
4.15432E-I2
128139E-12
I.I8277E-I2
S28932E-12
Lower State Energy
cm - 1
48.6168
6719774
787.7483
84.2149
911.1441
KM3.1162
128.6891
1183.6120
1810238
13315745
244.2004
1489 9440
1655.6592
315.1972
1829.6606
394.9894
20118948
483.5490
22013204
580.8443
2400.9171
686.8397
2607 6976
801.4958
924.7687
28217232
10566099
30461244
11969664
3278.1270
1345.7813
15019945
1668-5445
18413715
2024.4212
2214.6520
2413.0431
2619.6065
2834.4031
3057.5633
2415-5451
Upper State
(JK )
33
t2-6
136
4-3
14-6
15 6
53
16-6
6-3
17 6
73
18-6
19 6
8-3
20-6
93
21 6
10-3
22-6
113
236
12-3
24-6
133
14-3
256
15 3
26-6
16-3
276
17 3
18-3
19 3
20-3
21 3
22-3
23 3
24-3
25 3
26-3
2 31
Lower State
(J K)
3-3
126
13-6
43
146
15-6
5-3
166
63
176
7-3
186
19-6
8 3
206
9-3
21-6
10 3
226
11-3
23-6
12 3
24 6
13-3
143
25-6
15-3
266
16 3
27-6
17-3
18 3
19-3
203
21-3
223
23-3
24 3
25*3
2 63
2 32
239.3912
266.9447
7.44389E-10
0.000380803
804806
0.0000
4 1
10
44
00
Intensity
Multiplier
176
17 6
176
176
176
176
176
176
176
2.76
176
17 6
17 6
36.65
17 6
36.65
176
36.65
176
36.65
176
36.65
176
36.65
36.65
176
36.65
176
36.65
176
36.65
36.65
36.65
36.65
36.65
36.65
36.65
36.65
36.65
36.65
t
1
ii
I
I
I
For both the W W and BR models, all fitting attempts reduced the artificial in­
version line to an insignificant level, therefore, the inversion line models were abandoned.
This is consistent with both the JPL catalog and Kroto (1992). Further fitting attempts re-
43
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
vealed that the centimeter-wavelength region is insensitive to the inelastic collision lines,
therefore, these lines were reset to their nominal values. The remaining free parameters
appeared important, along with a single intensity weighting factor for all elastic collision
intensities. With this single value the model fit oscillated between a higher and lower inten­
sity weighting factor, which alternately fit the lower frequency data or the higher frequency
data, but not both simultaneously. Many attempts to split the elastic collision lines into
two or three regions based on quantum mechanics were attempted. The result was a sin­
gle weighting for all elastic collision intensities below a magnitude of (10“ 11 n m 2 MHz)
and a single weighting for those above. Table 3.1 includes the intensity weighting factors
to identify the two sets of lines described. For a more complete set of model parameters,
see Table 3.2. The elastic collisionally induced lines below magnitude (10- u n m 2 MHz)
have quantum numbers of A: =
6
for all values of J, or K=3 with values of J less than 8 .
The remaining elastic collision lines have higher intensities and have quantum numbers of
K = 3 and J from
8
to 26. All parameter weights were then split along these lines. This
scheme yielded the best fit for both the W W and BR models. The resulting W W model
fit was slightly better than the BR (without setting the coupling-element and pressure shift
terms in BR to zero). Since the W W is not only simpler to employ, but also requires a
fewer number of free parameters, it is chosen as the best fit model. Therefore, the coupling
(,' and the pressure shift S are set to zero, reducing the model to the W W case. Also, the
line broadening parameter temperature dependence £ for self broadening and foreign gas
broadening were set to 0.7 and 1, respectively. These were the nominal or seed values,
44
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 3.2: Parameters for a Van Vleck-Weisskopf line-shape (1945) based centimeter wave­
length opacity model for phosphine. The listed quantum transitions include only the first
forty lines, called elastic collision lines in this work, of the phosphine catalog listed in the
JPL catalog (Poynter and Pickett (1985)). For all lines, £Hydrogen and £Helium are set equal
to 0.75, and £phosPhme is set equal to unity. Townes and Shawlow(1955) give a value of
m = 3 for symmetric-top molecules such as phosphine and ammonia, using equation 3.6,
this yields a £ of unity.
Elastic Collision
Lines (J,K)
K = 6 or A' = 3 ,J <
.7 = 8 - 26,K = 3
Other
Intensity Weighting
8
2.76
36.65
I
Broadening Paramete rs (GHz/Bar)
Hydrogen Helium
Phosphine
0.7205
1.4121
0.4976
0.5978
0.3050
3.1723
3.2930
1.6803
4.2157
which are the same values as ammonia models (see e.g. (Ben-Reuven, 1966).)
The resulting best fit model is therefore based on the JPL catalog (Poynter and
Pickett, 1985) and the Van Vleck Weisskopf line-shape (Vleck and Weisskopf, 1945). The
empirically derived model parameters are shown in Table 3.2. Note that no artificial inver­
sion lines have been added to the model. Model results are provided alongside laboratory
measurements in Tables 2.1,2.2,2.3, and 2.4. The goodness of the fit is given by x 2, which
is equivalent to a single term of the summation in equation 3.9,
2 _ (offeai ~ < alc)
X2 = V n , _ , 2
•
(3-10)
A x 2 of less than unity implies that the error between measured and modeled values is less
than the error of the laboratory measurement. With the exception of a few outlying data
points, the model agrees quite well with the measured data. A graphical example of the
comparisons between the previous opacity model, the new measurement-based model and
the measured data is shown in Figure 3.4.
45
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
o 10
(0
Q.
0
5
15
10
20
25
30
Frequency (GHz)
Figure 3.4: Comparison of various centimeter-wavelength phosphine opacity models with
laboratory measurements. All models are based on the Van Vleck-Weisskopf lineshape
with the same physical conditions as the March 22 (3-bar) measurement; a mixing ratio of
88.0%H2, 9.8% H e, and 2.2% PH3, a pressure of 2.87 bars, and a temperature of 213 K.
The model approximating phosphine opacity using only its first rotational line (J = 1 -> 0)
is depicted by the long-dash line. The model using the full published phosphine catalog is
shown by the short-dash line, which is indistinguishable from the model including only the
lines below (in frequency) phosphine’s J = 1 -> 0 line. The solid line depicts our new
centimeter-wavelength phosphine opacity model, and the discrete points with error-bars are
the laboratory measurements.
46
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
3.2.1 Phosphine Opacity versus Ammonia Opacity
Phosphine and ammonia opacities are compared, under the same environmental conditions
of 1 bar pressure and 298 Kelvin and 8.2% o f either ammonia or phosphine, in Figure 3.5.
Both the Ben-Reuven and Van Vleck-Weisskopf line-shapes are shown for ammonia. The
resulting comparison suggests that at wavelengths greater than approximately 7-cm, the
per-molecule opacity of phosphine exceeds that of ammonia. In the atmospheres of the
outer planets, constituent abundances are generally related to the relative solar abundances
of such constituents. Since the solar abundance of ammonia (1.873 x 10-4 (Anders and
Grevesse, 1989)) exceeds that of phosphine (6.22 x 10“" (Anders and Grevesse, 1989)),
it would be expected that centimeter-wavelength opacity from ammonia would far exceed
that from phosphine. However, because of the lower saturation vapor pressure of ammonia,
the abundance of phosphine can be on the same order as that of ammonia in the upper
tropospheres of the outer planets.
3.3
Re-interpretation of Voyager Radio Occupation Ex­
periment Results: Did Voyager See Phosphine?
The initial results from laboratory measurements, shown in Figure 3.5, suggest that at wave­
lengths greater than 7 cm, the per-molecule opacity of phosphine exceeds that of ammonia.
This has been confirmed with the complete set o f laboratory measurements of phosphine
opacity. At shorter wavelengths, ammonia’s opacity far exceeds phosphine’s, but at 20-
47
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
10 '
1
E 10
BR
10
WW
1
0
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 3.5: Comparison of the PH3 and NH3 centimeter-wavelength opacities at 1 bar and
298 Kelvin. The mixing ratio for each is 82.6%H2, 9.2% H e, and 8.2% of either NH3
or PH3. The solid line depicts ammonia’s opacity modeled using Spilker’s Ben-Reuven
line-shape (1993), while the dashed line depicts ammonia’s opacity using the Van VleckWeisskopf line-shape. The discrete points with error-bars are measured data for phosphine
under the same conditions as the models.
48
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 3.3: Solar abundances of important atmospheric constituents, as reported by Anders
and Grevasse (1989).
____________________
8.346 x 1 0 -1
h2
He
1.623 x lO "1
1.424 x 10"3
H20
C H \ 6.043 x 10"4
n h 3 1.873 x lO"4
h 2s
30.81 x 10"6
p h 2 0.622 x 10“ 6
and 13.3-cm wavelengths phosphine is actually more opaque than ammonia. Since the
solar abundance of ammonia (1.873 x 10_4(Anders and Grevesse, 1989)) is orders of mag­
nitude higher than that of phosphine (6.222 x 10_7(Anders and Grevesse, 1989)) it might
be expected that the centimeter-wavelength opacity from ammonia would dominate every­
where in outer planet atmospheres. However, since phosphine’s saturation vapor pressure is
significantly higher than that of ammonia, the abundance of phosphine can be on the same
order as ammonia in the upper tropospheres of the outer planets. Thus, phosphine may
be the dominant source of centimeter wavelength opacity in the upper tropospheres of the
outer planets. Therefore, the new formalism for phosphine microwave opacity is employed
to reinterpret the Voyager radio occupation measurements at Saturn and Neptune. Note that
the solar abundance values referred to in this work are listed in Table 3.3 for reference.
3.3.1
Saturn
Two Voyager spacecraft have encountered Saturn (see (Stone and Miner, 1981; Stone and
Miner, 1982)). Radio occupation experiments were performed, in which transmission from
a spacecraft transmitter are recorded (see (Tyler et al., 1981) and (Tyler et al., 1982)) as
49
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
the spacecraft flies by the planet. As the spacecraft flies by the planet, the planet’s atmo­
sphere is eventually in the line-of-sight between the spacecraft and the earth-based receivers
(NASA’s Deep Space Network). From the doppler-shift and attenuation of the transmis­
sion, a vertical profile of atmospheric opacity may be inferred (see eg. (Lindal e ta i, 1981;
Lindal et al., 1985)). This vertical profile may then be used to infer the presence of and to
estimate the abundance of molecules in the upper atmosphere. The Voyager radio occultation experiments at Saturn used two transmitters, one at 2.3 GHz (S-band) and 8.4 GHZ
(X-band).
Lindal et al (1985) attributed all of the inferred microwave opacity from the Voy­
ager 2 radio occultation experiment at Saturn to ammonia. At the time of the Lindal work,
ammonia had been thought to be the only likely candidate for significant microwave ab­
sorption in the outer planets (Berge and Gulkis, 1976). The resulting amount of ammonia is
problematic. First, the inferred ammonia abundance exceeds the saturation vapor pressure
of ammonia over the region of the measurement. Also, atmospheric models with an ammo­
nia abundance consistent with Lindal are difficult to match to radio emission observations.
Microwave radiative transfer models, described in section 4.3, indicate an ammonia
abundance in the upper atmosphere that is reduced from its deep abundance (Briggs and
Sackett, 1989a; Grossman, 1990), through formation of an ammonium hydrogen sulfide
cloud (see section 4.6.1 for discussion) and do not include the effects of phosphine.
Since the work of Briggs and Sackett (1989), Grossman (1990), and Lindal (Lindal
et al., 1985) detections of phosphine at Saturn have been accumulating and are reasonably
50
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
consistent to within the stated errors. Noil and Larson (1990) detected a phosphine abun­
dance of 7(+3, —2) x 10-6 at pressures greater than 400 millibar. Weisstein and Serabyn
(1994a) detected a level of phosphine of approximately 5 times its solar abundance at about
the one bar pressure level, and Orton et al. (2000) detected a phosphine mixing ratio of ap­
proximately 4.1 x 10-7 at the 150 millibar pressure level to 1.2 x 10-5 at the 645 millibar
level. In light of these consistent detections of phosphine and the newly discovered cen­
timeter wavelength opacity of phosphine, the interpretation of Voyager radio occultation
results are revisited.
Unfortunately, the raw opacity data inferred by Lindal has been lost, therefore, the
vertical ammonia profile reported in (Lindal et al., 1985) has been converted back into an
opacity profile. This was done using the Berge and Gulkis ammonia model (1976), which
Lindal et al. (1985) used for calculations. Also, the Saturn helium abundance was set to
Lindal’s reported value of approximately 5%, which is consistent with the value of 0.034 ±
0.024 reported by (Conrath et al., 1984). Once this was complete, the ammonia abundance
was assumed to follow its saturation vapor pressure and the opacity due to this amount
of ammonia was recomputed using the more accurate Spilker model (1993). Also, in this
calculation the helium abundance is increased to 0.14 to reflect the more recent results
(0.11 - 0.16) reported by (Conrath and Gautier, 2000). Using the formalism described in
section 3.2, the remaining or residual opacity is attributed to phosphine.
The resulting vertical profile of phosphine is shown in Figure 3.6. (An approximate
error of ± 0.001 dB/km is assumed, based on the signal-to-noise ratios achieved during
51
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
the Voyager 2 encounter at Saturn.) The opacity inferred at altitudes below the one bar
pressure level is from S-band (2.3 GHz) data and the region above is from X-band (8.4
GHz) data. This straightforward analysis agrees extremely well with the observations of
Noll and Larson (1990), Weisstein and Serabyn (1994a), and Orton et al. (2000). Orton
et al. suggest that their deeper phosphine detection of 1.2 x 10-5 at the 645 millibar level
should remain fairly constant at even deeper pressures, and may represent the deep abun­
dance of phosphine. This claim is also consistent with Voyager radio occultation results as
interpreted in this work.
Figure 3.7 shows a comparison of the absorption profile inferred from the Voyager
radio occultation experiments at Satum and the absorption profile resulting from the Briggs
and Sackett best fit model atmosphere. The opacity of the atmosphere at the pressure levels
(0.8-1.3 bar) sensed by the Voyager radio occultation experiments is dominated by the sat­
uration vapor pressure level of ammonia. Therefore, increasing the deep level abundance
of ammonia will not increase the opacity in the atmosphere at these pressure levels. Neither
the Briggs and Sackett model atmosphere nor any other model failing to include an addi­
tional microwave absorbing constituent, such as phosphine, will match the Voyager radio
science experiment opacity profile.
3.3.2
Neptune
Before heading toward interstellar space, the Voyager 2 spacecraft had its last planetary
encounter in our solar system when it performed a close fly-by of Neptune in August 1989
52
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0.1
Weisstein & Serabyn
0.3
Noll & Larson
<00.5
(0
£
Orton et al
£ 0 .7
3
</>
(A
Residual Phosphine X-band
£ 0 .9
1.1
Residual Phosphine S-band
1.3
0.0E+00
5.0E-06
1.0E-05
1.5E-05
2.0E-05
Mixing Ratio
Figure 3.6: Profile of phosphine abundance inferred from the S- and X-band Voyager 2 ra­
dio science experiments at Saturn. Opacity values were inferred from ammonia abundance
reported by Lindal et al. (1985). A saturated level of ammonia is assumed and the result­
ing opacity subtracted from the total opacity inferred. The residual opacity is attributed to
phosphine. Detections by Weisstein and Serabyn (1994) and Orton et al. (2000) are listed.
The Orton detection is interpolated as described in Orton et al. (2000). A solar abundance
(Anders and Grevesse, 1989) of phosphine is shown as reference.
53
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0.7
0.8
X -B and
0.9
S -B an d
0.01
0.005
0.015
Absorption (dB/km)
Figure 3.7: Comparison of the vertical opacity profile inferred from the Voyager radio
occultation experiments at Saturn (Lindal, 1985), with calculated opacity profile assuming
an atmosphere dominated by a saturation abundance of ammonia.
54
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
(Stone and Miner, 1989). As with Saturn, radio occultation experiments were performed to
infer an atmospheric opacity profile. At Neptune Lindal (1992) again attributed the entirety
of the inferred microwave opacity from the Voyager 2 radio occultation experiment to am­
monia. However, models based on laboratory measurements and observations made since
Lindal’s attempts to interpret the Voyager results cast doubt upon a Neptune troposphere
dominated by gaseous ammonia. Comparison of observation with radiative transfer models
have shown that the upper atmosphere of Neptune is more likely dominated by hydrogensulfide (see eg. (de Pater et al., 1991; DeBoer and Steffes, 1996a)). The radiative transfer
models for Neptune are discussed in more detail in section 4.6.3.
Since H>S and NH3 react in equal parts to form an ammonium hydrosulfide cloud
(NH.tSH) (see, (Lewis and Prinn, 1980; Gulkis et al., 1978) and (Romani et al., 1989)),
it effectively depletes ammonia; therefore, if the H2S abundance exceeds that of NH3, as
a hydrogen-sulfide dominant atmosphere would suggest, NH3 will be absent from the up­
per troposphere and is, thus, not responsible for the opacity inferred from the Voyager
radio occultation experiments. Since phosphine and hydrogen sulfide are the only other
constituents thought to be present in sufficient quantities in Neptune’s troposphere with
substantial microwave opacity, the microwave opacity inferred by the Voyager radio occul­
tation experiment can be attributed to a combination of phosphine and hydrogen sulfide.
As was done for radio occultation results for Saturn (section 3.3.1), the Neptune
NH3 abundance profile reported by Lindal (1992) is mapped back to the corresponding 3.6
cm (X-band) absorption. A saturation level of H2S is assumed and the resulting absorption
55
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
is subtracted from the total absorption inferred from the ammonia level reported by Lindal.
The residual absorption is then attributed to phosphine using the new formalism. The
resulting vertical abundance profile for PH$ is shown in Figure 3.8. At the deepest level
probed (6.3 Bars) results indicate a maximum abundance of phosphine between 1 and 5
times solar. The error bars shown in Figure 3.8 are based on Lindal’s stated uncertainty of
150 parts-per-billion of ammonia at the deepest level probed (6.3 Bars) which corresponds
to an opacity uncertainty of approximately 0.003 dB/km. As will be shown in section 4.6.3,
this result is consistent with disk-average radiative transfer models of Neptune.
56
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
O.OE+OO
1.0E-06
2.0E-06
3.0E-06
4.0E-06
Figure 3.8: Profile of PH3 abundance inferred from the Voyager 2 radio science experiment
at Neptune. Opacity values were inferred from NH3 abundance reported by Lindal et al.
(1992) and the opacity due to the saturation vapor pressure level of H2S has been subtracted.
The remaining opacity is attributed to PH3. The error in PH3 abundance is inferred from the
error in opacity stated by Lindal in terms of an error in the NH3 mixing ratio of ±150ppb.
A solar abundance (Anders and Grevesse, 1989) of PH3 is shown as reference.
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
3.3.3
Jupiter
A vertical opacity profile for Jupiter’s atmosphere at 1.5 GHz was inferred from the excess
attenuation in the radio link between the Galileo spacecraft and Galileo probe as the probe
descended through Jupiter’s atmosphere (Folkner et al., 1998). The ammonia abundance
required by the inferred opacity profile (3.6 ±0.5-times solar abundance) was larger than
expected (1-1.3-times solar abundance) (dePater and Massie, 1985). Since phosphine has
been found to be more opaque, on a per-molecule basis, than is ammonia, especially at 1.5
GHz, it is possible that unaccounted for phosphine opacity contributed to this discrepancy.
However, under the conditions of the local atmosphere of the Galileo Probe’s descent path,
a minimum of a 20-times solar abundance of phosphine is required to significantly alter the
inferred ammonia mixing ratio profile. To account for the totality of the discrepancy a 50times solar abundance of phosphine is required. These high levels o f phosphine abundance
are not supported by observations or by more localized measurements conducted using the
Galileo Probe Mass Spectrometer (Niemann et al., 1998).
58
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
59
CHAPTER 4
Radiative Transfer Model
In the previous chapter a new formalism for computing the microwave absorption from
phosphine was developed. This formalism was then employed to re-interpret the Voyager
radio occultation experiment results. In this chapter the results of disk-averaged radiative
transfer models for Saturn and Neptune are presented,
In this chapter thermochemical modeling is described in section 4.1 and the theory
of radiative transfer is described in section 4.4. The new phosphine formalism is incor­
porated into an existing disk average radiative transfer model and applied to Saturn and
Neptune in section 4.6.1. The formulation of an elliptical-shell, ray-tracing-based, local
radiative transfer model (LRTM) is described in detail in section 4.5. The new local ra­
diative transfer model is employed to calculate the emission spectra from models of Sat­
urn’s atmosphere, at a frequency of 13.78 GHz, to examine the sensitivity of the Cassini
RADAR/radiometer to phosphine abundance. This is discussed in section 4.6.2.
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
4.1
Thermo-chemical Model
In general, the composition and structure of the atmospheres o f the outer planets cannot be
retrieved unambiguously from emission spectra measurements. To infer atmospheric struc­
ture from observation, the synthetic (modeled) emission spectra from model atmospheres
are fitted to results from observations. The emission spectra are computed using the theory
of radiative transfer, or radiative transfer models, which model the transfer of electromag­
netic energy through the atmospheric models (Chandrasekhar, 1946). Radiative transfer
modeling is discussed in more detail in the following sections. A thermo-chemical model
(TCM) is used to construct the model atmosphere that is required as input into radiative
transfer models (see eg. (Atreya and Romani, 1985)). This model defines the physical
properties and chemical composition of homogeneous layers of the atmosphere. Some of
the first thermochemical models were developed by Weidenschilling and Lewis (1973).
The TCM for this work is taken from (DeBoer and Steffes, 1996a) and is more thoroughly
considered in (DeBoer, 1995).
The construction begins, in general, from some assumption of the deep abundance
of atmospheric constituents. The temperature pressure profile (T-P) is then computed as­
suming an adiabatic atmosphere and may be bootstrapped using T-P profiles resulting from
observations (see eg. (Lindal et al., 1985; Lindal, 1992)). The next atmospheric layer is
determined from the change in pressure (and temperature) and each constituent’s partial
pressure is compared to its saturation vapor pressure. If the partial pressure exceeds the
computed saturation vapor pressure an appropriate amount of gas is removed as conden-
60
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
sate (cloud).
Once the constituent abundance, temperature, and pressure in each layer has been
defined, the absorption of each layer must be calculated. The absorption of electromagnetic
energy by the gaseous constituents in each layer are calculated as described in the following
section.
4.2
RTM: Opacity Contributions
The radiative transfer model implemented in this work requires the determination of ab­
sorption in units of optical depths per unit centimeter (a from Eq. 2.22) for each layer of
the atmosphere. Absorption formalisms, like the phosphine formalism developed in this
work, are required for each constituent assumed to contribute to the absorption of elec­
tromagnetic energy over the frequency range of the model. For this work the absorption
contributions of gaseous phosphine, ammonia, hydrogen sulfide, water, and hydrogen are
included. Scattering from cloud condensates has an insignificant effect on the centimeter
emission spectrum of outer planet atmospheres and is neglected in the local RTM (Joiner,
1991). Scattering due to Saturn’s rings is highly variable and is more significant at cen­
timeter wavelengths, thus no attempt will be made to sense the portions of the atmosphere
occulted by the rings.
Phosphine
The phosphine formalism is discussed in detail in Chapter 3 of this work. As pre­
viously stated, the laboratory measurements of the opacity of phosphine are more than
61
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
an order of magnitude greater than previously modeled for centimeter wavelengths. This
result combined with detections of phosphine in Saturn’s upper atmosphere (Noll and Lar­
son, 1990; Weisstein and Serabyn, 1994a; Orton et al., 2000) at levels of approximately
10-20 solar, indicate that phosphine is an important molecule in models of Saturn. Both
the disk-average model1 and the local radiative transfer model, described in the following
sections, are the first radiative transfer models to include a laboratory-measurement-based
formalism for phosphine opacity.
Ammonia
Ammonia is the dominant absorber in the centimeter wavelength spectrum of the
outer planets, including Saturn. The ammonia formalism used in the local RTM in this
work is from Spilker (Spilker, 1993). The disk-average radiative transfer model, which
is the DeBoer and Steffes (1996) model, uses a combination of the Spilker model and
the Joiner-Steffes model (Joiner and Steffes, 1991). While the Spilker model is superior
to other ammonia models at centimeter wavelengths, the Joiner-Steffes model is used for
ammonia opacity calculations above 40 GHz, due to instability in the Spilker model at
higher frequencies ( / >40 GHz). For the local RTM to be valid above 40 GHz a similar
combination would need to be implemented. The Spilker model is a modified version of the
Berge and Gulkis Ben-Reuven formalism (1976), which uses the Ben-Reuven line-shape
multiplied by a correction factor (C). The parameters of the Spilker Ben-Reuven formalism,
in which the units are bars (pressure), Kelvin (temperature), gigahertz (frequency) and
‘The disk-average radiative transfer model used in this work is the DeBoer and Steffes (1996) model
adapted to include the new phosphine formalism.
62
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
decibels-per-kilometer (absorption), are as follows,
{
7 h2 = 2-34
1
2.122e T/116.8
p .,
-
>(9024-2fe) _
(=)
(4.1)
0.9918 + PH,
where,
r = 8.79e-T/83
T
3000
(4.2)
(?)
(4.3)
7vff3(j) = 0.747JvW3(j)PiY//3 ( “p " )
(4.4)
7 He =
0.46 +
Pffe
2
300 \ 3
(T " )
?H '
=
(°-28 ik) Ph•{W)
S n h 3u) =
(4‘5)
(4.6)
_
(0 -507m
m ) ) P nh*
(^)
(4.8)
8 = - 0 A oP nh 3
C = -0 .337 +
T
110.4
(4.7)
T2
70600
(4.9)
where C is a correction term that scales the resulting Ben-Reuven line-shape. The result is
in units o f dB/ k m .
63
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Hydrogen Sulfide
The hydrogen sulfide model used in this work is that of DeBoer and Steffes (1994).
Hydrogen sulfide absorption does not contribute greatly to the total absorption of any given
layer in the Saturn model. This is especially true at the frequency of interest to the local
radiative transfer model (13.78GHz) . H 2S does affect the abundance of ammonia, since
it is able to remove ammonia through the formation of an N H ^ S H cloud (Romani et al.,
1989). H>S is included since large amounts, as in a H 2S -dominant atmosphere, may have
some impact on the emission at 13.78G H z . The DeBoer hydrogen sulfide formalism is
also based on the Ben-Reuven line-shape. The broadening parameter due to H2, He, H 2S
has the form,
(4.10)
where.
(4.11)
7 He = 1-20
(4.12)
7 ° h2s ~ 5-78*,
(4.13)
and the remaining parameters, in units of bar, Kelvin, and gigahertz, are as follows,
C= 7
(4.14)
5 = 1.28 Pff2s
(4.15)
f = 0.7.
(4.16)
64
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 4.1: H i 0 formalism parameters.
i
1
2
3
4
5
6
7
8
9
10
fo
22.23515
183.31012
323
325.1538
380.1968
390
436
438
442
448.0008
E’
644
196
1850
454
306
2199
1507
1070
1507
412
A
1.0
41.9
334.4
115.7
651.8
127.0
191.4
697.6
590.2
973.1
7 Hi
2.395
2.400
2.395
2.395
2.390
2.395
2.395
2.395
2.395
2.395
7 He
0.67
0.71
0.67
0.67
0.63
0.67
0.67
0.67
0.67
0.67
7 h 2o
10.67
11.64
9.59
11.99
12.42
9.16
6.32
8.34
6.52
11.57
€ h ->
0.900
0.950
0.900
0.900
0.850
0.900
0.900
0.900
0.900
0.900
%He
€ h 2o
0.515
0.490
0.515
0.490
0.540
0.515
0.515
0.515
0.515
0.515
0.626
0.649
0.420
0.619
0.630
0.330
0.290
0.360
0.332
0.510
(f DeBoer’s formalism uses this value for the self broadening term (7?/2s ) for all
but four frequencies, which have been directly measured. The self broadening is 5.38,6.82,
5.82 and 5.08
for the lines at 168,216,300 and 393 GHz (Helminger el al., 1972;
Helminger et al., 1977).) The resulting absorption is in units of
Water Vapor
Water vapor affects microwave emission from deep layers of the atmosphere of
Saturn. Water vapor abundance is not well constrained, but since water vapor begins to
condense at pressures greater than 10 bars at Saturn it has little affect on the computed
brightness temperature at wavelengths shorter than 20 centimeters ( / > 1.5 GHz) (Good­
man, 1990). Inclusion of water vapor absorption allows the local radiative transfer model to
be applied at lower frequencies and also for application of the model to investigate spatial
or temporal variations. The water vapor model used in this work is an adaptation of the ter­
restrial model described in Ulaby (1981), which was based upon the work of Waters (1976).
65
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
This model includes ten rotational transition frequencies up to 448 GHz. The kinetic, or
Gross, line-shape is used with an empirical correction term derived by Gaut and Reifenstein (1971). The Ulaby expression, which was intended for nitrogen-oxygen dominant
atmospheres (ie. Earth), is adapted for use with Jovian atmospheres, which are hydrogenhelium dominant, as in Goodman (Goodman, 1969). This is accomplished by replacement
of the pressure term with (0.81P//3 + 0.25Pfje) as in, for example, Joiner (1991) and De­
Boer (1995). This formalism, which incorporates measurements of water vapor’s H2/H e
line broadening parameters (Dutta et al., 1993), is the same as that used in DeBoer(1995).
The formalism, in units of in units of bar, Kelvin, and gigahertz, is as follows,
a„,0 = 5.34 x 10=P„!0 ( « ) I £ A ,e - * r r
i=i
) +4f %
(4.17)
+ 0 .1 6 % ^ ( ^ g ) 2 1 (0.81 P Hi + 0.35PHe) f 2
where
7
is calculated using Eq. 4.10 and the parameter values listed in Table 4.1.
The result is in units of ^ / k m Collisionally Induced Molecular Hydrogen Absorption
Molecular hydrogen (H 2) does not have have a permanent dipole moment, but may
absorb energy through transient dipole moments induced by collision. Collisions may oc­
cur with any molecule in the atmosphere, but the transient hydrogen dipoles are due mainly
to hydrogen-hydrogen, hydrogen-helium, and hydrogen-methane collisions. Methane is
included in the model for the purpose of calculation of molecular hydrogen absorption,
but it has no permanent dipole moment itself and does not contribute significantly to the
observed emission (Jenkins, 1992). The formalism for collisionally induced molecular hy-
66
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
drogen absorption used in this work is from Joiner and Steffes (1991). The Joiner-Steffes
model is an adaptation of the more complex empirical model by Borysow et al. (1985)
with the incorporation of temperature and pressure dependencies from Goodman (1969).
The formalism, in units of bar, Kelvin, and gigahertz, is as follows,
1.545 x 10~6
a "2 = ----------y i---------
+ 1.382 P f f e
+ 9.322Pcff4
(4.18)
The result is in units of dB/km.
4.3
Radiative Transfer Model
Atmospheric modeling allows one to both compare theory with observation and to inves­
tigate the impact of altering physical parameters. O f particular interest to planetary radio
science are radiative transfer models. Since radio emissions from Jupiter were first de­
tected (Burke and Franklin, 1955) theorists have investigated natural radio emissions from
the planets. The theory of radiative transfer allows one to model the emission of electro­
magnetic energy from the atmospheres2 of the planets. An in-depth treatment of radiative
transfer may be found in Chandrasekhar (1946).
Given that the thermo-chemical model (TCM), discussed in section 4.1 allows one
to investigate the effects that altering base constituent values will have on atmospheric
: Radiative transfer models of terrestrial planets must, in general, include the effects o f the planetary
surface.
67
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
structure, a radiative transfer model (RTM) is then calculated, which can be compared
with observational data (see eg. (dePater and Massie, 1985)). Both the disk-averaged
and local radiative transfer models described in this work derive the vertical atmospheric
structure from the DeBoer and Steffes thermo-chemical model described in (DeBoer and
Steffes, 1996a) and (DeBoer, 1995), with one notable change. The DeBoer TCM does not
include a removal mechanism for phosphine. Since this work has shown that phosphine is
likely a contributor to the upper atmospheric emission spectra of Saturn and Neptune, the
phosphine profile at Saturn has been altered to reflect the observed depletion rate inferred
from observation by Orton (2000).
4.4
Radiative Transfer Theory
Radiative transfer theory is developed from the study of energy as it passes through a
medium, or in this case an atmosphere. The atmosphere is assumed to be in local ther­
modynamic equilibrium. A system in thermodynamic equilibrium, if initially at rest, after
exchanging heat with its surroundings and doing work on the surroundings is again at rest
(Holton, 1992) which allows a local temperature (T) to be defined for each point in the
atmosphere. Under this assumption the emission coefficient and absorption coefficient can
be related by Kirchhoff’s law (Chandrasekhar, 1946).
If the instantaneous radiant power at a given frequency, per unit area is defined as
the change in radiant power can be described as,
68
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
^ = —Iua + S
as
(4.19)
where s is the path, a is the attenuation over the path, and S is the emission over the path.
Scattering effects may be folded into the emission and attenuation terms without loss of
generality (Janssen, 1993). These effects can be neglected in Jovian atmospheres for fre­
quencies less than 300 GHz (Joiner, 1991). This significantly simplifies the development
of the model by limiting emission contributions to local thermal emission and attenuation
contributions to local absorption. By invoking local thermodynamic equilibrium, and as­
suming black body radiation (Ulaby et al., 1981), the source term may be related to B v, the
Planck function, by the relation,
S = etBv{T).
(4.20)
The Planck function, which is in units of energy per unit solid angle per unit frequency,
relates the intensity of the source emission to the equivalent thermal emission of a blackbody emitter,
B ( T ) = — ___ -_______________________________ (4->L)
'
c2 eheikr _ i — c2
1 1
where h is Planck’s constant, T is the physical temperature, v is frequency, c is the speed
of light, and k is Boltzman’s constant. The approximation in equation 4.21 is for lowfrequency (microwave) cases where hu
k T and is known as the Rayleigh-Jeans ap­
proximation. With this approximation the true thermal temperature of the black body T
69
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
is replaced with the effective brightness temperature Tb. The relation between the thermal
temperature and the brightness temperature is,
T) = — = 2kTl>2— \— = — ( ehL,tkT - l )
] ~ Tb
c2 B ,(T )
hv T
V ’
(4 22)
which becomes unity in the Rayleigh-Jeans limit (hv <C k T ). The brightness temperature
of the black body can then be directly related to the radiation intensity,
TM =
(4.23)
If equation 4.19 is integrated over the path s, it becomes,
SQ
1,(0) = I„(so )e-T(*o) + J B ,( T ) e - T(s)ads
(4.24)
o
where the first term on the right is the intensity at the boundary of the integration and rep­
resents contributions to emission from sources other than those over the path of integration,
such as background or surface emission, and r is the optical depth defined by,
3
t„( s )
=
J
a ^ d s '.
(4.25)
o
For the gaseous giant outer planets, the surface term I u(so)e~T(io) can be neglected. By
replacing the intensity with the brightness temperature (equation 4.23) and the Planck func­
tion with the thermal temperature (equation 4.21) the equation of transfer (equation 4.24)
becomes,
(4'26)
70
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Finally, in the Rayleigh-Jeans limit, 3? becomes unity and the radiative transfer equation is
approximated by,
Sq
Tb(v) =
J T{s)e~T{s)ads.
(4.27)
o
The resulting equation yields a microwave brightness temperature, in units of Kel­
vin, over a given bandwidth. With the omission of scattering, equation 4.27 is simply the
integration of the emission and absorption of energy contributions over each infinitesimal
layer of the atmosphere in the observation path.
The discrete form of equation 4.27 (Butler et al., 2001) is simply,
N
Tatm(x ,y ) = £ 7 -( 7 i,4n) (1 - e~T'-')e~T,+l-y
(4.28)
i= i
where, i is thecurrent layer, T* is the physical temperature in Kelvin of the layer, and
Tb,c
isthe opacity of the layer (see equation 4.29). Note, the physical temperature of the
layer Tt may be a function of planetary longitude (7 i) and latitude (0 J , as in Butler (2001).
This is reflected in equation 4.28, and may be implemented to map spatial variations in
atmospheric emission. In this work, the individual layers are homogeneous.
The opacity term (r) for the ith layer,
77,
in equation 4.28, is calculated as the
integral of the absorption from all absorbers over the layer. The opacity term r for the in­
tegrated absorption from all atmospheric layers above the ilh layer attenuates the emission
from this layer. This opacity term is calculated as,
C
n,c = ^ T a,
(4.29)
a=b
where b is the index of the layer above i or / +
1,
c is the highest atmospheric layer of
71
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calculation, and r'a is the opacity term for a single layer. The difference in the functions be­
tween the two opacity terms is often confusing, but is central to understanding the equation
of transfer. Recall that the emission / from a layer can be related directly to the layer ab­
sorption
(a),
(equation 4.20), that the emission may be related to the physical temperature
of the layer, (equation 4.21), and that the brightness temperature is related to the physical
temperature, (equation 4.22). Therefore, the emission from a given layer i is related to
the opacity of that layer and this opacity is represented by the term riyi in equation 4.28.
This emission is attenuated by the opacity of every layer of atmosphere between itself and
the highest atmospheric layer. This is the r I+l ;v term in equation 4.28, and is calculated
numerically as in equation 4.29.
It is useful to know how each portion of the atmosphere affects the brightness tem­
perature, this can be found through calculation of the weighting function,
Wi = (1 - e -T,,')e “r,+l-v .
(4.30)
In ground based radio telescope measurements of the outer planets the disk of the
planet is often unresolved and the disk average brightness temperature need only be cal­
culated. Since planetary bodies are more correctly defined as oblate spheroids and are not
perfect spheres, the disk averaging must be integrated over the spheroid. To simplify the
calculation of disk averaged radiative transfer a spherical approximation may be employed
with an error of less than 1% for 1.5 GHz (DeBoer, 1995) and for wavelengths between 1
mm (300 GHz) and 10 cm (3 GHz) (Joiner, 1991).
Typically the radiative transfer equation is integrated over the disk o f the planet to
72
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Local normal to
isobaric surface
z
Observer
Isobaric atmospheric layers
0: zenith angl
Figure 4.1: Geometry of the radiative transfer model.
73
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
find the disk-averaged brightness. The geometry for this integration is shown in Figure 4.1.
The angle between the line-of-sight to the observed location and the local surface normal
is defined as the zenith angle (6) and a zenith angle of zero is referred to as nadir (or nadir
looking) from the point of view of the observer. The path-length though a layer (s) is greater
for off-nadir observations by a factor of ^ = tycos (0 )and the total brightness observed in
equation 4.27 is dependent on this path length. With the assumptions of a spherical planet
and an observer located very far from the planet {e.g. on the Earth) the disk-averaged
brightness can be calculated by,
2n R
f f Tb(r, iii)rdrdip
•
<«»
where Tb is the brightness temperature at a position on the planetary disk, (r,i/>), and R is
the radius of the projected disk of the planet.
4.5
Localized Radiative Transfer Model
The assumptions made in deriving equation 4.31 will not be valid for the upcoming CassiniSatum observations. At closest approach Cassini’s instruments will be observing Saturn
from a distance of six Saturn radii, therefore, the assumption that the observer is at great
distance is invalid. The proximity of the observation also complicates the calculation of
zenith angle. In order to overcome these difficulties a ray-tracing based radiative transfer
model has been implemented. In the following sections a ray-tracing based elliptical-shell
radiative transfer model is developed and applied to Saturn.
74
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The ray-tracing RTM is adapted from the technique described by Butler (2001),
which makes use of computer graphics algorithms (Haines, 1989; Heckbert, 1989). Haines
(1989) describes a ray-sphere intersection technique intended for graphic operations (i.e.
shading, reflections) that determines the intersection of a discrete light-ray and a spherical
surface. To handle highly oblate planets, such as Saturn, an adaptation of this technique to
ellipsoids is developed. Also, a vector technique for Snell’s law, developed by Heckbert
(1989), is used to calculate the refractive bending through the atmosphere.
To facilitate development of the ray-tracing technique definitions for possibly am­
biguous terms are first provided. A ray is a straight line segment, defined by vector coordi­
nates (origin,direction), in cartesian space, which represents a single spatial sample of the
antenna pattern. The boresight ray (or simply boresight) is a ray that represents a spatial
sample of the center of the antenna pattern. A beamsample is any given spatial sample of
the antenna pattern. An incident ray is the ray that is projected from a given origin and
intersects an atmospheric layer. A transmitted ray is the resulting ray through a layer after
Snell’s law has been applied to the incident ray. An atmospheric layer (or layer) is an
isobaric ellipsoidal shell, the properties of which have been calculated by the thermochem­
ical model. The surface of a layer is the outermost (innermost) ellipsoid describing the
atmospheric layer as a ray approaches from the upper (lower) layers.
The purpose of the ray-tracing is to calculate the path of the ray though the layers
of the atmosphere. As can be seen in equation 4.27 the distance through each layer must
be determined in order to calculate the emission and the attenuation o f energy in that layer.
75
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In a planar stratified model, this is accomplished simply by multiplying the thickness of
the layer by cos(9) where 9 is the zenith angle. In the ray-tracing technique the pathlength
is calculated as the distance a ray must travel from its origin to its intersection with the
ellipsoidal layer. First, a qualitative discussion of the technique is provided, followed by
the mathematical development.
4.5.1
Ray-tracing Described
For most radio observations of the planets, emitted rays originating deep in the atmosphere
are measured as they emerge outward toward an orbiting spacecraft or earth. However, for
modeling purposes it is easier to model ray-paths originating at the spacecraft and pene­
trating the planet’s atmosphere. These are equivalent by reciprocity.
Thus, the initial origin of the rays is the location of the spacecraft, in cartesian
space, where the origin of the space is defined as the center of the planet. Figure 4.2 depicts
an example of an off-nadir observation (left-hand side), and a limb sounding observation
(right-hand side). Refer to Figure 4.2 for the following discussion. The initial ray direction
is set as the pointing direction of the spacecraft antenna. First, the boresight ray-path is
calculated. If the boresight does not intersect the first ellipsoid, the antenna is not pointed
toward the planet. Once the ray intersects the first layer, which is depicted in the figure as
layer 1, the vector location of this intersection is recorded. From this, the local normal, and
thus the zenith angle, can be calculated. The distance to the planet is labeled as di in the
figure. The incidence angle is found and Snell’s law is applied to find the vector direction
76
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z
A
Initial
intersection
Spacecraft
Case 1: Off-nadir
Spacecraft
Case 2: Limb sounding
Figure 4.2: A two dimensional graphic example of the ray-tracing process. An off-nadir
(left) and a limb sounding case (right) are shown. Two possible outcomes for the limbsounding case are shown, d 3 shows the ray exiting the atmosphere, while dc shows critical
refraction (total internal reflection).
77
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of the ray transmitted through the layer. This is depicted in the figure as the new vector
originating at the intersection of ray dx and layer 1, which is labeled as
Once the vector
direction of the ray is determined, the vector origin of the ray-segment is set as the initial
intersection. A new ellipsoid is defined by the next (deeper) layer (layer 2). The ray-ellipse
intersection algorithm is applied with these inputs and returns the distance (di) to this next
layer from the ray origin. The distance is recorded. The origin of the next vector is set as
the intersection of d x with the outer boundary of layer 2. The direction is again determined
by application of Snell’s law. The distance through layer 2 is labeled in the figure as d2The remaining layers are handled in the same manner until the preceding layers provided
by the thermochemical model become so opaque that no significant ray transmission occurs
(case I), or the ray passes out the back of the planet (case 2 , ray d3).
Case 2 occurs when the ray does not intersect the next (deeper) layer, as in limb
sounding. If this occurs, the next layer is redefined to be the current layer, which is the
ellipsoid where the origin of the current ray is located. The ray-ellipse algorithm is applied,
but in this case the ray can be envisioned to be inside of the elliptical shell heading outward.
This makes no difference to the application of the algorithm, but requires the index of the
layers to be decremented. This continues until the ray has left the outermost atmospheric
layer.
Another possible outcome of case 2, occurs is when the decreasing refractive index
of the next layer causes critical refraction. This is where the ray is totally internally re­
fracted, as depicted as ray dc. In this case the layer where critical refraction occurs returns
78
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
a pathlength of infinity, which sets the brightness temperature of that layer to the thermal
temperature. The emission from this layer is then attenuated by the layers above.
4.5.2
Ray-tracing Algorithm Mathematics
The mathematical foundation for the ray-tracing component of the RTM is developed in
this section. The ray-ellipsoid intersection test used in the RTM is adapted from a raysphere intersection test described by Haines (1989). The ray-sphere intersection algorithm
begins with definition of the parametric equation for a ray. A ray is defined as,
X 0 Y0 Z 0
R origin — R q —
(4.32)
R direction — R d —
x d Yd Zd
where
X 2d+ Y 2 + Z 2 =
(4.33)
1
which defines a ray as a set of points described by the equation for a line,
(4.34)
R — R q + R d x f,
where t > 0. The sphere is defined by,
•Scenter — *^c —
X c Yc Z c
(4.35)
Sradius — *Sr
*surface —
X,
Ys Z ,
where
(X s - X c T + (Y 3 - Ycf + (Z s - Z c)2 =
s2
79
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(4.36)
To find the intersection the equation for the ray is expressed as,
X = X 0 + X dt
Y = Y0 + Ydt
Z =
Zq
(4 -37)
+ Z dt
and is substituted for the vector describing the surface of the sphere,
X a Ya Z a , in
equation 4.36, resulting in,
(.Vo +
X dt -
X c)2 + (Yo
+
Ydt
-
Yc)2 + (Z q + Zdt - Z c)2 = S 2.
(4.38)
This can be simplified into a quadratic equation,
.4f2 + B t + C = 0
(4.39)
where,
.4 =
X 2 + Y2 + Z2
B
2 ((.Yo -
=
C =
(.Yo -
,YC)
=
1
Xd+
X c)2 + (Yo
(Vo -
-
V'c)
K )2 +
Yd + (Z q - Z e)Z d)
(ZQ -
Fc)2 -
(4 -4 0 >
S 2.
The solutions to this equation are the standard quadratic solutions,
_ - B - y /B 't- A A C
t(J —
2.4
(4 -4 l)
. _ —B + y/B 2—AAC
2.4
~
where the t's (solutions) are the distance to the intersection point from the ray ori­
gin. If the discriminant of these equations is negative, the ray misses the sphere. For the
purposes of the RTM this is the case when either the antenna is not properly pointed, where
the miss occurs during the first intersection test, or when the ray begins to pass out the
80
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backside of the planet. The smallest positive t is the correct solution. Once t is found, the
vector location of the intersection is,
Hnt —
—
X 0 + Xdt
Xi yt Zi
Vq
+ Ydt Z q 4- Zdt
(4.42)
and the unit vector normal at the surface is then,
fnorm al —
—
(tI,-Y c)
Sr
(x,-A'c)
Sr
(x ,- Z c )
S,
(4.43)
In terms of the RTM, the solution to the quadratic equation (r) is the distance the
ray travels through a given layer. The origin of the transmitted ray is set at the intersection
location rmt and the direction of the transmitted ray is calculated from the intersection, r in(,
and the surface normal, r norma/, using Snell’s law.
The vector form of Snell’s law is also taken from a computer graphics algorithm.
Heckbert’s method (Heckbert, 1989) uses a vector approach to solve for the transmission
angle for a ray transmitted through an interface between mediums with different refractive
indexes. Referring to Figure 4.3 the angle between the two known quantities, the incident
ray vector (I) and the local surface normal (N), is calculated,
cos (0i) =
- I
•N.
(4.44)
From Snell’s law, the relative index of refraction (rj) is,
tj =
sin (0 2) /sin (0 t ) =
771/ 772.
(4.45)
The angle of the transmitted ray (02) can be computed from known quantities,
cos (0 2 ) =
- sin2 (02)) = y j( 1 —r?2sin2 (0t )) = y /{ l - t)2 (1 - cos2 (0i))).
(4.46)
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R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Figure 4.3: Vector implementation of Snell’s Law using Heckbert’s method (1989).
82
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
The vector direction of the transmitted ray is then computed as,
T = r)l + (77cos (Oi) - cos (02)) N .
(4.47)
Using these algorithms and the technique described in section 4.5.1 the path through
each layer is calculated for use in the RTM.
4.5.3
Ellipsoid Ray-Tracing
Saturn’s equatorial and polar radii, at the 1 bar isobar, as determined by the Voyager radio
occultation experiment (Lindal et a i, 1985), are 60268 km and 54364 km, respectively.
DeBoer (1995) showed that for the disk averaging case, the error in the brightness temper­
ature calculated using the spherical approximation is less than 1% at 1.5G H z. However, in
using the ray tracing local radiative transfer model, the errors due to assuming a spherical
planet could be extremely large. The worst case scenario would be if Saturn was approx­
imated as a sphere the size of Saturn’s mean radius and the antenna was pointed near the
limb of Satum, the model may return the erroneous result that the boresight missed the
planet. Less extreme cases would occur as the boresight is positioned closer to nadir.
Typically Satum is modeled as a Darwin de Sitter spheroid (Zharkov and Trubitsyn,
1978), but this geometry is too complicated for straightforward adaptation of the ray-sphere
intersection test. Approximating Satum as an ellipsoid allows for a more tenable adaptation
of the ray-sphere intersection test and has precedence (see eg. (Grossman, 1990)). The
maximum local error between the radius of an oblate Satum approximated by a Darwin de
Sitter spheroid and its radius approximated as an ellipsoid is less than 0.85% and occurs
83
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at 45° (planetocentric) latitude (see Figure 4.4). With this approximation the ray-sphere
intersection test, described in section 4.5.2, is adapted for use with oblate planets.
For the ellipsoidal approximation the equation for the sphere (equation 4.35) is
replaced by the equation for an ellipsoid,
where a, b, and c are the vertices of the x, y, and z axes of the ellipse. By setting the center
of the planet (ellipsoid) at the origin of cartesian space, and using equation 4.48, equation
4.36, in section 4.5.2 becomes,
( ^ ± ^ ) 2+ ( l i ± ^ ) 2+ (
^
)
2 = 1.
(4.49)
Equation 4.39 is still valid, but A, B, and C must be modified,
.4
=
AX] +
rvj + K Z]
B = 2 {A X 0X d + T Y 0Yd + K Z QZ d)
(4 -50)
C = A X 02 + TV'02 + K Z * - 1
where,
A = i,
T = £,
K = J, ■
< «1>
With these changes the algorithm developed in section 4.5.2 is valid for ellipsoidal volumes,
with the exception of the calculation o f the local surface normal. To find the local surface
normal at thelocation of
the intersection, the gradient of the surface
is calculated.If the
function defining the surface of the ellipsoid volume (equation 4.48) is denoted as G, the
84
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
90
1
120
0.8
0.6
150
0.4
0.2
180
330
210
240
300
270
Figure 4.4: Comparison of approximations to oblate spheroidal volumes. A 2D projection
of a Darwin de Sitter spheroid is compared to 2D projection of an ellipsoid. Both are
normalized to a maximum extent of unity at the equator. A unity-radius circle is provided
for reference. Note that no difference between the two results is clearly discernible.
85
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
local surface normal is,
f normal — tl —
VG
|V G |’
(4.52)
where,
(4.53)
and.
(4.54)
4.5.4
Beam-forming
Since the ray-tracing algorithm assumes an infinitely narrow beam (or ray) it is necessary
to form spatial samples of the main beam in order to estimate properly the emergent flux
of the atmosphere incident on the antenna. This is accomplished by generating a set of
vectors, which were defined earlier as beamsamples, where each vector describes a ray that
is offset from the direction of the boresight ray. The boresight may take on any arbitrary
direction and this unnecessarily complicates the generation of the beamsamples, therefore
the beamsamples are first generated at the origin of the coordinate system, then rotated and
translated to the origin of the antenna.
Using the geometry shown in Figure 4.5, the antenna pattern is sampled over N
concentric circles. This facilitates the weighting of the model result to approximate the
affect of gain reduction off boresight. This reduction is approximated by a Gaussian beam,
beamweight(&<f)) = e( 276x (b w h u )
86
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
(4.55)
where A d>is the angle between the beamsample and the boresight, and B W H M is
the 3d B beamwidth of the antenna’s main beam. The beamsamples in a given concentric
ring are evenly spaced in 0 and increase in number for concentric rings with larger A0. To
maintain equal areas throughout the rings, the number of samples in a given ring increase
with radius. With a given half-power beamwidth and the constraint of an equal area per
sample, two free parameters remain, the number of concentric rings N c, and the number
of samples in the initial ring nQ. The free parameters could alternatively be defined as
the spatial sampling rate in 9, which defines the number of rings, and the initial spatial
sampling rate in <p, which defines the number of samples in the primary ring. In either case,
once the two free parameters are chosen, the number of beamsamples in each ring may be
found by,
;V (A:) = N (1) x (2k — 1),
(4.56)
where N is the number of samples and k is the integer multiple of the ring spacing in terms
of radius. For example, if a ring spacing of 1/3 of the half-power beamwidth is chosen,
then there will be three concentric rings sampling the beam. If the first ring is sampled
at 90° per sample, there will be four beamsamples in the first ring. To enforce the equalarea-per-sample the number of samples needed for the secondary beam, from Eq. 4.56,
is twelve, spaced 30° apart. The final ring will be at the half-power beamwidth and have
twenty samples, spaced 18° apart. This scenario yields 37 beamsamples, which includes
the boresight sample.
The spatial resolution of the beamsampling may be increased and is limited only
87
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
250
200
150
100
E
-50
-100
-150
-200
-250
100
150
200
250
Z (km)
Figure 4.5: Top view of synthetic beamsampled antenna pattem.The axes indicate the de­
flection from boresight as would occur for a Nadir-look with the spacecraft aligned with
the x-axis at a distance of 6 Satum radii from the surface of the planet (360,000 km).
88
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
x 104
300
200
300
100
200
100
-100
-100
-200
Y (km)
-200
-300
-300
Figure 4.6: Side view of the synthetic beamsampled antenna pattern. The axes indicate the
deflection from boresight as would occur for a Nadir-look with the spacecraft aligned with
the x-axis at a distance of 6 Satum radii from the surface of the planet (360,(XX) km).
89
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
by the memory of the computer used and the patience of the user. The scenario of 37
beamsamples is used in all of the local RTM applications discussed in this work and the
resulting beamsamples are depicted in Figures 4.5 and 4.6. The error incurred by spatial
sampling will be greatest near the limb and doubling the spatial sampling to 73 ((36 x 2) +
1) changes the resulting brightness at the limb by less then 0.01%. The pattern of the
Cassini main antenna is well characterized down to the —30d B level (Janssen, private
communication). This antenna pattern could easily be incorporated into the model in the
future if interpretations of the Cassini observations warrant.
Once the vectors describing the antenna pattern are computed, the resulting vectors
must be rotated and translated to the origin of the spacecraft antenna represented by the
boresight origin. This is depicted graphically, for a two-dimensional case, in Figure 4.7
Rotations in 3-space are not necessarily unique so the rotational matrices must be applied
in a specified order. It is helpful to note that the order of matrix multiplication is dependent
on the handedness of the coordinate system (Shames, 1980) and the choice of rotational
matrices. The right-hand rotational matrices for the given axes are as follows,
90
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
1. Generate Beam-pattem
\\l
\ /
\
2. Rotate to
observation
orientation
3. Translate
to spacecraft
position
Figure 4.7: A two dimensional graphic example of rotating and translating the beamsam­
ples. Once the beam-pattem is generated (with the z-axis as its axis o f symmetry), the
beamsamples are then rotated to the orientation of the boresight of the spacecraft antenna.
The origin of the beamsamples, which originally was the origin of the coordinate system,
is translated to the origin of the spacecraft antenna.
91
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0
1
0 cos q
—sin q
0 sin q
cos a
cos a
Ry =
0 sin a
0
1
- sin a
Rz =
where
a
0
(4.57)
0
0 cos a
cos a
— sin a
0
sin a
cos a
0
0
0
1
is the angle between the respective axis to be rotated and the arbitrary vector,
which is the boresight vector. The rotation matrices are applied to rotate the primary axis
of the beamsamples (the z-axis) to align with the boresight vector,
B e a m s a m p le s r o ta u d
= (R x x R y
R:
* R ^ v x R ~l x {Beamsamplesoriginal))
(4.58)
The resulting vectors, which are originally radiating from the cartesian origin, are
then translated to the location of the spacecraft antenna by replacing the origin of the orig­
inal beamsamples with the location of the spacecraft boresight vector.
92
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
4.6
Application of the Radiative Transfer Models
4.6.1 Disk-average Saturn Radiative Transfer Results
By using a disk-averaged radiative transfer model, similar to that described in section 4.4,
an ammonia mixing ratio of 2x solar matches the emission spectrum of Satum well, except
in the spectral region near the 6 cm wavelength (Briggs and Sackett, 1989b). Briggs and
Sackett (1989) state that a reduction of ammonia abundance to one-half ( x l O -5) solar at
about 1.5 bar matches the 6 cm observation, but this requires additional absorbers in the
deep atmosphere to match the observed spectrum at longer wavelengths. A model with 3a>
solar abundance ammonia in the deep atmosphere and one-half solar above 1.5 bars was
found to be more consistent with observations. Matching observations at 6 cm requires a
removal process for ammonia in Saturn’s upper atmosphere (Briggs and Sackett, 1989b).
Since hydrogen sulfide reacts with ammonia in equal amounts to form an ammonium hy­
drosulfide cloud (NHtSH) (see, (Lewis and Prinn, 1980) and (Gulkis et a i, 1978)), it
effectively depletes ammonia, allowing models to match better the 6 cm emission and the
rest of Saturn’s spectrum simultaneously. Large amounts of H 2S are required (10 —14x) to
remove sufficient amounts of ammonia to match observations (see eg. (Briggs and Sackett,
1989b; Grossman, 1990)).
In many of these works the possibility of another microwave absorber, including
phosphine, was postulated. However, two factors detracted from the attractiveness of in­
voking phosphine to account for excess microwave absorption. First, as discussed earlier in
93
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
this work, previous models of phosphine microwave opacity grossly underestimated phos­
phine absorption at wavelengths greater than a few centimeters. Also, the very presence of
phosphine in the outer planets, at detectable levels, was in doubt on the basis of thermody­
namic equilibrium calculations. Prinn and Lewis (1975) conclude that P i / 3 is not chemi­
cally stable at the temperatures found in outer planet upper atmospheres (T < 500K ) and
Borunov et al. (1995) argued that P / / 3 should be removed as precipitate for temperatures
below 150A'. Also, as discussed in detail in Orton et al. (2000), models of the tropospheric
chemistry of P P 3 (Prinn and Lewis, L975) (Fegley and Prinn, 1985) (Fegley and Lodders, 1994) predict P H 3 reacts with H 20 to form P^Oq. For the case of thermodynamic
equilibrium this reaction would effectively remove phosphine as a candidate for significant
microwave absorption.
Phosphine was first postulated as a major influence on Saturn’s (infrared) spectrum
by Gillett and Forrest (1974) more than a decade before its first spectroscopic detection
(Bregman et al., 1985). Since the work of Briggs and Sackett (1989) and Grossman (1990),
detections of phosphine at Satum have been accumulating and are reasonably consistent
to within the stated errors. Noll and Larson (1990) detected a phosphine abundance of
7(+3, - 2 ) x 10-6 at pressures greater than 400 millibar. Weisstein and Serabyn (1994a)
detected a phosphine abundance of 3 ± 1 x 10~6 at about the one bar pressure level, and
Orton et al. (2000) detected a phosphine mixing ratio of approximately 4.1 x 10~7 at the
150 millibar pressure level to 1.2 x 10-5 at the 645 millibar level. Orton et al. (2000)
released a Corrigendum, or correction, (Orton et al., 2001) increasing the 150 millibar
94
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
value to 4.3 x 10-7 and reducing the 645 millibar value to 7.4 x 10-6 and state that the
deep atmospheric mixing ratio of P H 3 must be at least 8 x 10-6 .
Comparisons of disk-average RTM results for Satum are presented with observa­
tions (see eg. (der Tak et al., 1999; Grossman, 1990)) below. A listing of observations is
provided in Table 4.2 for reference. The resulting spectra are compared in the following,
and an atmosphere with solar abundances is provided for reference. A listing of the models
is provided in Table 4.3. Note that all models were calculated including deep mixing ratios
of 4.2 x 10-3 C H a (Courtin et al., 1984) and 1.0 x 10-6 water v apor. The model proposed
by Briggs and Sackett (1989) included a water vapor abundance of 6.9 x 10-3 , however,
this large abundance of water vapor, coupled with the high levels of H 2S seriously deplete
ammonia when the DeBoer and Steffes (1996) thermo-chemical model is used. The De­
Boer and Steffes model incorporates a model for the aqueous cloud developed by Romani
(1989), which differs from the model used by Briggs and Sackett (Weidenschilling and
Lewis, 1973). Since Briggs and Sackett include ammonia and hydrogen sulfide in sim­
ilar amounts, when the DeBoer and Steffes thermo-chemical model is used the Romani
(1989) aqueous cloud model depletes enough ammonia that the abundance of hydrogen
sulfide is slightly greater than that of ammonia, below the N H AS H cloud. At the base of
the N H + SH cloud gaseous ammonia and hydrogen sulfide are depleted in equal amounts,
leaving an upper atmosphere dominated by hydrogen sulfide. This is not consistent with
Satum observations. To obtain synthetic brightness spectrum results, using the abundances
reported by Briggs and Sackett (1989), and the DeBoer and Steffes (1996) thermo-chemical
95
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 4.2: Listing of observations compiled from van Der Tak et al. 1999, Grossman
(1990), de Pater and Dickel (1982) and Briggs and Sackett (1989).
Frequency
GHz
1.45
1.46
1.46
1.49
4.86
4.89
4.89
4.89
4.89
4.89
4.89
4.89
5
8.14
8.43
8.5
14.93
15
15.00
15.00
15.00
15.08
22.56
23.08
23.08
88.24
88.24
90.91
97.1
111.1
111.1
141.1
150
195
214.3
214.3
214.3
227.3
295
300.00
309.9
Tb
K
219
225.7
230.5
230.9
176.4
173.6
172.3
174
177.4
171.8
168.6
180.5
185
173.6
161.1
161.4
140.1
168
142.9
139.7
158.9
136.1
132.5
130.2
106
150
157.8
149.3
148
156
137.3
164
137
139
143
188
194
140
148
145
134.5
±TB
K
11
12
15
11.5
8.8
8.7
7
8
8
9
8.4
18
30
8.7
8.1
8.05
7
30
10
10
7.9
6.8
13.3
15
25
9
31.6
14.9
11
7.8
6.85
12
11
14
17
18.8
21
7
15
14.5
6.7
96
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Table 4.3: Listing of models discussed in text, f Model F includes a 10% super-saturation
of ammonia, f t Model G includes a 20% super-saturation of ammonia.
Model
nh3
(ppm)
ph3
(ppm)
H 2S
(ppm)
A
A2
A3
A4
B
B2
B3
C
C2
C3
C4
D
E
F
G
520
520
520
520
468
468
468
412.5
412.5
412.5
412.5
281
468
468f
468ft
0
6.2
12.4
3.1
12.4
6.2
3.1
9.3
9.3
12.4
6.2
9.3
6.2
12.4
12.4
410
410
410
410
30.8
30.8
30.8
308
154
308
308
30.8
0.0
30.8
30.8
model, that are similar to the Briggs and Sackett (1989) brightness spectrum results, the wa­
ter vapor mixing ratio must be reduced. This reduction in water vapor content presents no
significant difficulties in comparing the interpretation of these models since water vapor
content does not directly affect the brightness temperature results in the microwave region
( / > 1 GHz). The effect that water vapor content has in this spectral region is seen through
its depletion of ammonia. Also, subsequent to the work of Briggs and Sackett (1989), a
water vapor mixing ratio of only 2 x 10-7 below the 3-bar level has been inferred from
observations (Graauw et al., 1997).
Comparisons of the model atmospheres examined in this section are shown in Fig­
ure 4.8. Our first model (model (A)) uses the deep abundance reported by Briggs and
97
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Sackett (1989) and is representative of previous Satum models that require a large abun­
dance of deep atmospheric N H 3 (3 —4x solar), to match the brightness temperature of the
6 - 20 cm wavelength region and a large abundance of H 2S (11 - 14x solar) to deplete am­
monia, by way of an N H ^ S H cloud, to match emission at wavelengths shortward of 6 cm.
To illustrate the effect of including the observed abundance of phosphine on the the Briggs
and Sackett model (A), models (A2) and (A3) include 10 and 20-solar abundances of phos­
phine, respectively. Model (B) includes a 20-times solar abundance of phosphine,which
allows for the reduction of ammonia to 2 —2.5 times solar and the reduction of hydrogen
sulfide to one solar abundance. Models (B2) and (B3) illustrate the effect of phosphine
abundance on model atmospheres with one-solar abundance of hydrogen sulfide. Model
(C) is the model that best fits model (A) (Briggs and Sackett) with the inclusion of a 15times solar abundance of phosphine. In order to maintain a comparable spectrum with the
introduction of phosphine, ammonia is reduced to 2.25-times its solar abundance, which re­
duces the need for hydrogen sulfide to 10-times its solar abundance. Model (C2) shows the
effect of reducing hydrogen sulfide in model (C) to 5-times its solar abundance. Model (D)
provides a best fit to the observations at 1.5,4.89, and 8.14 GHz without requiring a large
deep abundance of hydrogen sulfide. Model (E) is 2.5-times solar N H 3, 10-times solar
P H 3 and no H 2S , which shows the effect of hydrogen sulfide on the 13.78 GHz spectrum.
Note that, with the exception of the absorption signature of phosphine’s first ro­
tational line at 266.9 GHz, no significant difference between these synthetic spectra can
be discerned in this figure at frequencies greater than 10 GHz. Therefore, comparisons
98
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
300
Solar
250
3
CO
h.
0Q}.
E
03
H
200
150
100
1.E+00
1.E+01
1.E+02
Frequency (GHz)
1.E+03
Figure 4.8: Synthetic disk-average emission spectra for Satum. A solar model is provided
as reference. For composition of other models, see text.
99
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0.1
XC*Q
0)
a
in
in
0k ).
Q.
Model A
Model B
100
0
100
300
200
400
500
600
Temperature (K)
Figure 4.9: Temperature/Pressure profiles for models (A) and (B).
between disk-averaged results from these model atmospheres will be made only for 1-10
GHz. All models in this work that include phosphine show the strong absorption due to
phosphine's first rotational line at 266.9 GHz. This absorption feature is prominent in
Saturn’s emission spectrum and has been examined in detail to infer deep phosphine abun­
dance (Orton et al., 2000). The temperature/pressure (TP) profiles of models (A) and (B)
are illustrated in Figure 4.9. The TP profile for the remaining models are not significantly
different from that of models (A) and (B).
100
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
300
Solar
250
©
D
200
0
Q.
E
®
150
100
1.E+01
1.E+00
Frequency (GHz)
Figure 4.10: Synthetic disk-average emission spectra results from models A (thick-line),
A2 (dash-line), and A3 (thin-line). Model (A) is taken from the best-fit model by Briggs
and Sackett (1989).
101
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Pressure (bar)
NH.
H2S
100 -----1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
Mixing Ratio
Figure 4.11: Vertical mixing ratio for model (A).
102
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
0.1
Weighting Function: 75 degrees
1
Weighting Function:
Nadir
10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Cloud Density [g/cm3]
Figure 4.12: Cloud structure for model (A). The 13.78 GHz weighting functions are shown
for Nadir and 72-degree zenith angles.
103
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Briggs and Sackett (1989) (BS) required a deep abundance of over 500 ppm of
ammonia to match 1.5 GHz observations, and a reduction in ammonia in the upper at­
mosphere to match 4.89 and 8.14 GHz observations. To deplete the deep abundance of
ammonia at higher altitudes, BS included a deep abundance of over 400 ppm of hydrogen
sulfide, which reacts with ammonia to form the N H +SH cloud (Romani et al., 1989). It
is difficult to match simultaneously the 1.5 GHz observations and the 4.89/8.14 GHz ob­
servations, even with the inclusion of H2S as an ammonia depletion agent. The synthetic
brightness spectrum from (A) (thick-line) is compared with observations and models (A2)
(dash-line) and (A3) (thin-line), which include ten and twenty-solar abundances of phos­
phine, in Figure 4.10. The inclusion of phosphine in atmospheric models, illustrated by
models (A2) and (A3), improves the match between the synthetic emission spectra based
on model (A) and observations at 1.5 GHz, by reducing the 1.5 GHz brightness spectrum
emission. The vertical mixing ratio profile for model (A) is shown in Figure 4.11, and the
cloud structure for model (A) is shown in Figure 4.12 along with the 13.78 GHZ weighting
functions for nadir and 75-degree zenith angle observations.
The increase in opacity due to the inclusion of phosphine allows for consideration
of models with reduced ammonia and hydrogen sulfide. Models (B) and (B3) are compared
in Figure 4.13. Model (B2) falls between models (B) and (B3) and is not plotted to maintain
clarity. These models illustrate the resulting emission spectra for models with only a solar
abundance of H 2S. H2S has yet to be detected at Satum and an upper bound of 2 x 10-7
HoS has been estimated from measurement attempts (Owen et al., 1977; Caldwell, 1977).
104
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
300
2 200
100
1.E+00
1.E+01
Frequency (GHz)
Figure 4.13: Synthetic disk-average emission spectra results from models B (thick-line)
and B3 (dash-line).
105
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Pressure (bar)
0.1
nh3
H2S
\
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
Mixing Ratio
Figure 4.14: Vertical mixing ratio for model (B).
106
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Weighting Function: 75 degrees
3u
-a
n h 4s h
u
Weighting Function:
Nadir
Aqueous Solution
100
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Cloud Density [g/cm3]
Figure 4.15: Cloud structure for model (B). The 13.78 GHz weighting functions are shown
for Nadir and 72-degree zenith angles.
107
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Therefore, the large deep abundance of hydrogen sulfide (410 x 10-6 ) required by model
(A) is problematic. With the addition of 1.2 x 10~6 phosphine the low gigahertz spectral
region ( / < 7 GHz) is lowered by approximately 6 Kelvin; This allows for the reduction
of ammonia from that in model (A) (520 x 10~6) to 463 x 10~6. Figure 4.13 shows that
models with reduced ammonia and a solar abundance of hydrogen sulfide yield good fits
to 1.5 GHz observations, but are at the lowest range of the error bar for the 4.89 GHz
observation, and are slightly below the error bar for the 8.14 GHz observation. The vertical
mixing ratio profile for model (B) is shown in Figure 4.11, and the cloud structure for
model (B) is shown in Figure 4.12 along with the 13.78 GHZ weighting functions for nadir
and 75-degree zenith angle observations.
By invoking increased amounts of hydrogen sulfide, as in model (A), the modeled
emission spectrum may be increased. Figure 4.16 illustrates models with reduced ammonia
(412.5 x 10-6), 15-times solar abundance of phosphine, and hydrogen sulfide abundances
of 154 (thick-line) and 308 (thin-line) ppm (5-10 solar abundance). Model (C) matches
the Briggs and Sackett (1989) model atmosphere (A) very closely. Results from model (A)
(dash-line) are provided in Figure 4.16 for comparison. Reducing the hydrogen sulfide to
5-times its solar abundance (model C2) results in an emission spectrum that is an excellent
match with the 1.5 GHz observations, and is consistent with the 4.89 GHz observations,
but is slightly lower than observations at 8 GHz. The vertical mixing ratio profile for model
(C) is depicted in Figure 4.17
As shown in Figure 4.18, model (D) (dashed-line) compares well with observations
108
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300
Solar
250
CD
3
« 200
Q.
E
o
H
150
100
1.E+00
1.E+01
Frequency (GHz)
Figure 4.16: Synthetic disk-average emission spectra results from models C (thin-line) and
C2 (thick-line). Model (A) (dash-line) is provided for comparison.
109
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Pressure (bar)
PH-
1
NH.
H2S
10
100 -----
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
Mixing Ratio
Figure 4.17: Vertical mixing ratio for model (C).
110
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300
Solar
250
co 200
0Q9.
E
09
I-
150
100
1.E+00
1.E+01
Frequency (GHz)
Figure 4.18: Synthetic disk-average emission spectra results from model D (dash-line).
Model (A) (thick-line) is provided for comparison.
Ill
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
Pressure (bar)
0.1
1
NH;
HZS
10
100 ----1.0E-06
1.0E-04
1.0E-05
1.0E-03
Mixing Ratio
Figure 4.19: Vertical mixing ratio profile for model (D).
112
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at 1.5 and 4.89 GHz, and is within the error of the 8.14 GHz observation. The result of
this model at 1.5 GHz is similar to that of model (A) (thick-line), which is plotted for
comparison. The vertical mixing ratio profile for model (D) is shown in Figure 4.19.
The results of these comparisons show that the results of previous model atmo­
spheres of Saturn, such as the Briggs and Sackett (A), may be reproduced closely, in light
of the phosphine detections and the new phosphine formalism, with a reduction in ammo­
nia from 520 ppm to 412.5 ppm and a reduction in hydrogen sulfide from 410 ppm to 308
ppm. This is with a phosphine abundance of 15-times its solar value (model C). Other
variations in ammonia and hydrogen sulfide abundance (models B,C) compare reasonably
well with observations but fall on the lower edge of observational uncertainty. Note that
while some of the models that include only a single solar abundance of hydrogen sulfide
compare to observations as well as model (A), specifically models (D) and (C2), all of these
models result in lower emission spectra over the 1-5 GHz frequency range. In fact, while
model (C2) results in an emission spectrum that is at the lowest extent of the observation
errors at the 4.89 and 8.14 GHz observation results, it produces a superior fit to the 1.5 GHz
observation, as compared with model (A).
Model (C) compares well with the Briggs and Sackett model (model (A)), and both
compare favorably to observations. Without corroborating evidence both models appear
equally valid, however, with the positive detections of large amounts of phosphine (Orton
et al., 2000; Weisstein and Serabyn, 1994a; Noll and Larson, 1990), model (C) appears
superior. Model (D) produces an emission similar to model (A) at 1.5 GHZ, and is lower at
113
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
the 5-8 GHz spectral region, but still within the observation error. Model (C2) produces a
superior fit to the 1.5 GHz observation. Model (B) should be considered as an approximate
upper bound of phosphine abundance (20x) and model (B2) an approximate lower bound.
Models with 10-20 solar abundance of phosphine are also consistent with the reinterpreta­
tion of Voyager results, as discussed in section 3.3.1.
Recall Figure 3.7, the computed opacity profile for an atmosphere with a saturated
abundance of ammonia, over the pressure levels sensed by the Voyager radio occultation
experiment, and no phosphine, such as model (A), does not match the opacity profile in­
ferred by the occultation experiment. The effect of including a 5, 10, and 20-times solar
abundance of phosphine to an atmosphere with saturated ammonia is examined in figure
4.20. The inclusion of phosphine allows one to match the opacity profile inferred from the
Voyager radio occultation experiment (Lindal et al., 1985). Since the ammonia abundance
is set by its saturation curve, an increase in ammonia will not affect this profile. An at­
mosphere including a saturation abundance of ammonia and 5 to 20 times solar abundance
of phosphine fits the observations of the Voyager radio occultation experiments. The most
recent detection of phosphine at Saturn is consistent with a deep mixing ratio of phosphine
of approximately 8 ppm (Orton et al., 2000). Therefore, a phosphine abundance between
6.22
x
10-6 and 12.44 x 10-6 at altitudes below the 0.7 bar pressure level is supported both
by the abundance inferred in this work from Voyager radio occultation experiments and by
sub-millimeter-wavelength observations.
With the statistical spread in observation measurements and lack of reliable ob-
114
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0.7
0.8
X -B and
0.9
cc
.a
0
i_
3
CO
CO
01 _
CL
S -B an d
0
0.01
0.005
0.015
Absorption (dB/km)
Figure 4.20: Comparison of the vertical opacity profile inferred from the Voyager radio
occultation experiments at Satum (Lindal, 1985), with calculated opacity profile assuming
an atmosphere including a saturation abundance of ammonia and a range of deep phosphine
abundances (5,10,20-times solar). Phosphine is modeled to decay with altitude to match
the decay rate observed by Orton et al. (2000).
115
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servations in the 2-4 GHz region of Saturn’s emission spectrum, it is difficult to endorse
a single best model. The competing models may be grouped into two major categories,
namely the solar hydrogen sulfide abundance models (B,B2,B3, and D) and the super-solar
hydrogen sulfide abundance models (A,A2,A3,C,C2). While model (C) closely matches
the results from model (A), model (C2) obtains a superior fit at the 1.5 GHz observation
frequency, therefore, it is chosen as the best fit of the super-solar hydrogen sulfide models.
In general, these models fit the 4.89 and 8.14 GHz frequencies well, but result in emis­
sion that is at the upper limit of the 1.5 GHz observations. In the solar hydrogen sulfide
abundance category the primary difficulty is in matching both the 1.5 GHz observation and
the 4.89/8.14 GHz observation. This problem is the same as encountered by Briggs and
Sackett (1989) and others (See eg. Grossman (1990)). With the addition of phosphine, the
difficulties are reduced but not completely ameliorated. Still, these models are attractive
as they do not require a super solar abundance of hydrogen sulfide, which has yet to be
positively detected in Saturn’s atmosphere. Model (D) produces an slightly better fit to
observations at 4.89/8.14 GHz than does model (B), but suffers from emission at 1.5 GHz
that is at the extreme upper bound of the observation error. It should be noted, however,
that this high emission at 1.5 GHz is comparable to that of the Briggs and Sacket preferred
model (model (A)). The best fit for the solar hydrogen sulfide abundance models is there­
fore chosen to be model (B). This model included a 20-times solar abundance of phosphine,
and as previously mentioned the most recent reported phosphine detection at Saturn (Orton
et al., 2000) has been reduced from a deep abundance of 12 ppm (20x solar) to 8 ppm ( «
116
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13x solar) in a recent correction (Orton et al., 2001). A model similar to model (B) with
a 13-times solar deep abundance of phosphine would result in an emission spectrum that
is roughly between model (B) and its 10-times solar abundance derivative model, model
(B2).
Models (B) (468 ppm NH $, 12.4 ppm PH$, 30.8 ppm H2S ) and (C2) (412.5 ppm
.V//•}, 9.3 ppm PHz, 154 ppm H2S) represent the best-fit models for solar and super­
solar H2S atmospheres, respectively. Since H 2S has never been positively detected in
the atmosphere of Saturn, model (B), requiring only one-solar abundance of H2S, is an
attractive choice. However, H2S had never been detected in Jupiter’s atmosphere either,
until the in situ measurements of the Galileo Probe Mass Spectrometer (Niemann et al.,
1998), which estimates the deep (P ^ 16 bar) H2S abundance to be 77 ppm. In light of
this fact, it is reasonable to conclude that Saturn’s atmosphere may include an abundance of
H2S that is greater than one solar abundance. Also, since model (C2) produces an emission
spectrum that is a better fit to observations, as compared to model (B), this model is chosen
as the best-fit model. It is also superior to previous super-solar H 2S models, which required
an H2S abundance of 10-times solar (or more), in both its ability to match observations and
its lower required (5-times solar) H2S abundance.
Measurements of Saturn’s emission spectrum in the frequency range of 2-4 GHz
would significantly improve the discrimination between the super-solar and solar hydrogen
sulfide models. The synthetic emission sprectra results for models (B) and (C2) differ by
as much as 16 Kelvin at 2GHz.
117
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4.6.2
Saturn Local RTM: Will Cassini See Phosphine?
The Cassini radar experiment is a synthetic aperture radar (SAR) designed to make highresolution radar maps of the surface of Saturn’s moon Titan. However, the RADAR instru­
ment can also be operated as a passive 13.78 GHz radiometer/receiver capable of measuring
microwave noise radiated by Saturn’s atmosphere.
The local radiative transfer model described in section 4.5 can be used to investi­
gate the ability of the Cassini spacecraft 13.78 GHz RADAR/radiometer (CRR) to detect
phosphine. The local RTM developed is extremely versatile, but the following constraints
have been imposed both to model the conditions of the Cassini instrument and to simplify
the analysis. On its closest approach (planned) Cassini will observe Satum from a distance
of 6 Satum radii (360,000 km). The observer for the local RTM, is therefore set to this
distance. The beamwidth of the radiometer is approximately 0.33 degree (Janssen, per­
sonal communication), and this value is used for beamsampling. The recently measured
rms sensitivity of the radiometer is reported to be on the order of 0.05 Kelvin (Janssen,
personal communication), but a conservative rms sensitivity of 0.1 Kelvin is adopted in
this work. The last constraint placed on the local RTM is the observer is placed on the xy
plane, given z is aligned with the axis of Saturn’s rotation. This is simply for convenience
and consistency.
With these constraints a number of observation conditions are examined in an effort
to characterize the ability of the Cassini radiometer to infer phosphine profiles. The general
cloud structure representative of these models is presented in Figure 4.21. The solid-line
118
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0.1
u
C3
£
Weighting Function:
75 degrees
1
O
u
Weighting Function:
.. _ . Nadir
H20-lce
s
Vi
Vi 10
a>
u
&
Aqueous Solution
100
—
1.E-09
1.E-07
1.E-05
1.E-03
Mixing Ratio
Figure 4.21: Solid-line: Cloud structure as generated from the thermochemical model for
solar abundance. Dashed-line: 2 x solar. Weighting functions for nadir and 75 degree zenith
angle observations are provided.
119
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structure is for the solar reference model shown in Figure 4.21 and the dashed-line structure
depicts the effect on cloud structure of increasing the constituents by a factor of two. The
purpose of this figure is to show the general atmospheric structure in the region sensed by
the local RTM. To that end, the 13.78 GHz weighting functions are shown for the local
RTM at results at nadir and at a zenith angle of 75 degrees. Extensive studies on the
atmospheric cloud structure of the outer planets is ongoing (see eg. (Atreya et al., 1999))
and beyond the scope of this work.
Figure 4.22 shows the weighting functions for the nadir (dashed) and 75 degree
or limb (dotted) cases superimposed over the opacity contributions from ammonia and
phosphine for an upper atmosphere including the saturated abundance of ammonia and a
twenty-times solar abundance of phosphine that decays as per observations (Orton et al.,
2000). Note that phosphine opacity dominates at pressures less approximately 0.6 bar.
Also, note that the weighting function for the limb case is cut-off at the knee of the ammonia
contribution in the region of the ammonia-ice cloud. If the weighting function could be
pushed a little higher, the brightness temperature should be significantly more sensitive to
phosphine variations.
The weighting functions for the Cassini RADAR/Radiometer (CRR) at nadir and
75 degrees are super-imposed to indicate the pressure range of importance. As expected
the weighting function moves upward, in altitude, as the CRR is pointed limb-ward. Un­
fortunately for prospects of detecting phosphine, in both cases the weighting function falls
largely over the region dominated by ammonia. Note that the weighting function for the
120
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-4
NH
-10
PH
.-*2
-1 4
-1 6
P ressure (Bar)
Figure 4.22: Relative contributions to opacity from ammonia and phosphine for nadir and
75 degrees zenith angle.
121
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10'2
- to
,-'2
-1 4
-1 6
10'2
P ressure (Bar)
Figure 4.23: Relative contributions to opacity from ammonia and phosphine for models
(B) and (B3)
122
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limb case is cut-off at the knee of the ammonia contribution. Phosphine is seen to begin
dominating at pressures below the 0.5 to 0.7 bar level. It is interesting to note that this is
the lowest pressure level at which opacity was sensed by the Voyager-Satum radio occul­
tation experiment (Lindal et al., 1985). Also note, as depicted in Figure 4.21, the region
visible to the CRR is in region where ammonia should follow its saturation vapor pressure.
Therefore, assuming ammonia is following its saturation curve, the CRR will be mostly
insensitive to changes in the deep abundance of ammonia. Since phosphine has a signif­
icantly higher saturation vapor pressure (Orton and Kaminski, 1989), it is not similarly
limited. The phosphine removal shown follows the observed reductions reported (Orton
et al.. 2000). Figure 4.23 depicts similar results given a deep phosphine abundance of only
5-times solar. The models including 10 and 15-times solar abundances of phosphine fall
between the 5 and 20-times solar abundances of phosphine shown in these figures. Also,
since ammonia has reached its saturation abundance in the pressure region of interest, the
profiles in these figures apply to all o f the other models.
Many of the models examined in the following were defined, discussed and labeled
in the previous section, in order to avoid confusion the model labels (A,B,C,D,E) previously
defined will remain and derivative models are numbered. For example, model (B2) is
identical to (B) except for a reduction in phosphine to 10-times solar. Due to the very
recent Corrigendum (Orton et al., 2001) model comparisons will be made primarily to
models with phosphine abundances of 6.2 ppm (lOx-solar) or 9.3 ppm (15x-solar), rather
than 12.4 ppm (20x-solar). The synthetic brightness temperatures at 13.78 GHz resulting
123
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Table 4.4: Model Brightness Temperature Results for disk-average, nadir and 75 degrees
zenith angle.
Model
Disk Avg
Nadir
75°
A
A2
A3
A4
B
B2
B3
C
C2
C3
C4
D
E
F
G
145.03
144.26
143.51
144.64
143.18
143.96
144.36
143.90
143.80
143.52
144.28
143.90
143.96
n/a
n/a
146.68
146.54
146.28
146.68
145.89
146.13
146.27
146.43
146.13
146.30
146.56
146.18
145.90
145.40
144.75
139.58
139.24
138.62
139.58
138.45
139.06
139.42
138.91
138.89
138.60
139.23
138.90
138.63
138.04
137.51
from the local RTM are listed in Table 4.4 for observations at nadir and at a zenith angle
of approximately 75 degrees, along with the disk-average result. The choice of a zenith
angle of 75 degrees is motivated by projection of the beamwidth of the radiometer on the
planetary disk. Recall that the zenith angle in this work is defined at the boresight of the
beam. A zenith angle of 75 degrees avoids the cases where the beam spills over into cold
space.
It can be inferred from these nadir results, and the reported Cassini radiometer sen­
sitivity (less than 0.1 K), that the Cassini radiometer will be able to discriminate between
different mixing ratios of phosphine on the order of one to two times the solar phosphine
abundance. As expected from examining the weighting functions depicted in Figure 4.22,
124
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-4
-10
-1 2
-1 6
P ressure (Bar)
Figure 4.24: Relative contributions to opacity from ammonia and phosphine for nadir ob­
servations of models (B) and (G).
CRR’s discrimination is improved by limb-ward observations. From the 75 degree observa­
tions in Table 4.4, it can be inferred that CRR will be able to discriminate between different
mixing ratios of phosphine on the order of five times the solar phosphine abundance.
It should be noted that calculation of these values assumes perfect knowledge of
opacity formalisms, temperature-pressure profiles, and of the other constituent abundance
profiles.
125
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-4
cm
I
-1 0
-1 2
-16
P ressure (Bar)
Figure 4.25: Relative contributions to opacity from ammonia and phosphine for 75 degree
zenith angle observations of models (B) and (G).
126
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The effect of uncertainty due to hydrogen sulfide on the 13.78 GHz brightness is
examined through comparison of model (B2) and model (E). Model (B2) is model (B) with
10-times solar phosphine and model (E) is model (B2) without H 2S. The results of these
models show that H 2S abundance has no significant effect on 13.78 GHz emission. The
direct effect of H2S is negligible due to its relatively small deep abundance, its removal
through formation of the N H 4S H cloud, and its low absorption at 13.78 GHz. The in­
direct effect of H 2S , through its removal of NH $, is also negligible since ammonia is in
saturation in this region. Model (D) differs from (B2) in that it has a deep ammonia abun­
dance of 1.5-times solar. The resulting difference is negligible due to ammonia saturation.
Therefore, to investigate the effect on brightness from uncertainties in the abundance of
the ammonia abundance in the local RTM was forced to be 10% and 25% greater
than the calculated saturation abundance. This over-abundance could be caused by some
combination of super-saturation, dynamic processes (see eg. (Atreya et al., 1996), (Atreya
et al., 1997)), and uncertainty in the temperature and pressure. The relative contributions
and weighting functions of the 25 percent case are depicted in Figures 4.24 and 4.25, re­
spectively. Therefore, to determine phosphine abundance at the sensitivity described in
the previous paragraph, the contributions to opacity from ammonia abundance must be
determined to within, approximately, two percent. A ten-percent uncertainty in the con­
tribution to opacity from saturated ammonia abundance will mask a differential phosphine
abundance of approximately 15-times solar.
The results of Table 4.4 show that phosphine detection is likely whether the atmo-
127
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sphere includes a super-solar abundance of hydrogen sulfide with an ammonia abundance
on the order of 510 ppm, or a single solar abundance of hydrogen sulfide and a reduced am­
monia abundance (281-468 ppm). These results also indicate that the possibility of phos­
phine detection and discrimination is primarily influenced by the abundance of phosphine
and the proper characterization of ammonia’s saturation vapor pressure over the pressure
levels of observation.
This result illustrates the need for accurate estimates of the saturated abundance of
ammonia, on temporal and spatial scales of the radiometer measurement. Cassini radio
occultation experiments may be employed to infer the ammonia abundance required for
accurate interpretation of the phosphine abundance. As a disequilibrium species, accurate
measurements of the vertical profile of phosphine abundance will yield information on the
vertical mixing rate of Saturn’s atmosphere (Fegley and Prinn, 1985; Orton et al., 2000).
With the high spatial resolution of the CRR, and the numerous orbits planned, an accurate
temporal and spatial map of vertical mixing may be inferred from these measurements.
As seen from the various weighting functions, phosphine discrimination will be sig­
nificantly improved if the weighting function can be pushed above, in altitude, the 0.6 bar
region. At the frequency of the CRR (13.78 GHz) this can only be accomplished with limbsounding cases in which only a portion of the antenna pattern is incident with the planet. It
is difficult to discern between true brightness variations and beam coupling effects for the
case of the radiometer pointed only partially at the planetary disk. The observation may be
deconvolved if adequate knowledge of the beamcoupling is available (Jenkins et al., 2001).
128
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Since the current local RTM models only the main beam, as the real contributions from the
unmodeled side-lobes become increasingly important as less of the beam is incident on the
planetary disk, the model becomes more inaccurate. Since the Cassini RADAR/radiometer
beam pattern is known down to the 30 dB level, the deconvolution technique can be used
and the local RTM can be adapted to model the real antenna pattern more precisely.
4.6.3
Disk-average Neptune RTM
As discussed in section 3.3.2, the opacity inferred from the Voyager-Neptune radio occulta­
tion experiment was attributed solely to ammonia (Lindal, 1992). However, models based
on laboratory measurements and observations made since Lindal’s attempts to interpret
the Voyager results cast doubt upon a Neptune troposphere dominated by gaseous ammo­
nia. For instance, the ground-based observations of the 1-20 cm emission from Neptune is
much higher (or brighter) than would occur for the ammonia abundance required by Lindal.
Since Neptune’s microwave emission spectrum cannot be matched well with an ammo­
nia predominant atmosphere, dePater (1991) investigated the likelihood of an atmosphere
dominated by hydrogen sulfide (H2S), but was hampered by uncertainty in H 2S absorp­
tion. This prompted DeBoer and Steffes (1996a) to conduct laboratory measurements of
H2S and with a better understanding of the opacity of H 2S revisited the likelihood of an at­
mosphere dominated by hydrogen sulfide. To obtain a reasonable match between modeled
and observed emission, DeBoer and Steffes required a 40 times solar abundance of H2S
and the addition of phosphine at levels ten to twenty times its solar value. With the new
129
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
400
o VLA
350
a Single Dish • • 10x Solar H2S —
20x Solar H2S
Both Models: 0.5x Solar N H 3,4x PH3
300
<
d
3 250
C
O
u.
S. 200
E
C
D
I- 150
100
1.E+00
1.E+01
1.E+02
Frequency (GHz)
1.E+03
Figure 4.26: Measured and synthetic emission spectrum (models) of Neptune. The discrete
circles and squares with error-bars arc VLA and single-dish measurements, respectively. A
listing of these observations may be found in de Pater and Richmond (1989). The synthetic
emission spectrum is based on the DeBoer and Steffes (1996a) Neptune model using the
new measurement-based phosphine opacity model detailed in this paper. Both models
include 0.5x solar ammonia, 4x solar phosphine. The upper dash-line model shown is for
lOx solar, while the lower (darker) solid-line model is for 20x solar.
130
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formalism for phosphine microwave opacity detailed in this paper, the required abundance
of phosphine is reduced to four to five times solar and a model yielding a superior match to
observations is obtained. The results of this model, shown in Figure 4.26, requires a 10-20
times solar abundance of H2S, a 4-5x solar abundance of PH3, and a 0.5x solar abundance
of NH3. The phosphine abundance is in agreement with that derived from application of
the new phosphine microwave formalism to Voyager radio science results, as described in
section 3.3.2. The result is an emission spectrum with an excellent fit to observational data,
which is also consistent with Voyager radio science results.
131
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132
CHAPTER 5
Summary and Conclusions
5.1
Centimeter Wavelength Absorption of Phosphine
From laboratory measurements, phosphine opacity has been shown to exceed that predicted
by the most complete theoretical phosphine absorption models available by more than an
order of magnitude in the centimeter wavelength region. This result also illustrates the
gross inadequacy of approximating the centimeter wavelength spectrum of phosphine by
including only the contribution from phosphine’s first rotational line (J = 1 -> 0) at 266.9
GHz. The centimeter wavelength opacity of phosphine has been found to be more opaque
than ammonia, on a per-molecule comparison, at frequencies less than ss 7 GHz. This has
serious implications for radio scientific studies o f the outer planets
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
5.2
Conclusions Regarding the Re-interpretations of Voy­
ager Radio Occultation Experiments
The re-interpretations of Voyager radio occultation experiment (VRO) results at Saturn and
Neptune have illustrated that phosphine is likely responsible for some significant portion
of the microwave opacity inferred from the occultation experiments. At Saturn, application
of the new phosphine formalism allows one to replace the previous interpretation, which
requires a super-saturation of ammonia, with a more physically appealing scenario of an
atmosphere with a saturation abundance of ammonia and a ten to twenty-solar abundance
of phosphine, which is corroborated by independent observations.
At Neptune the problems of matching a hydrogen sulfide dominant atmosphere to
VRO results are ameliorated with the inclusion of approximately a 4-times solar abundance
of phosphine.
5.3
Application of the Local Radiative Transfer Model to
the Cassini RADAR/Radiometer at Saturn
An analysis of the results from the local radiative transfer model developed in this work
indicate that the Cassini RADAR/Radiometer will detect phosphine at Saturn and that,
given sufficient accuracy of the measurement of the saturation abundance of ammonia, the
Cassini radiometer will be able to discriminate phosphine abundance on the order of 0.6-
133
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1 .2
ppm.
This result emphasizes the strict requirements o f accurately measuring the ammonia
saturation levels in the regions of interest using other measurement techniques (ie. radio
occultation experiments).
5.4
Directions for Future Studies
5.4.1 Laboratory Studies
The laboratory measurements in this work have illustrated quite clearly the need for the
verification and improvement of theoretical absorption models for important atmospheric
constituents. As the laboratory measurements in this work extend from 1.5 to 27 GHz, the
absorption spectrum of phosphine is still uncertain above this range. The results of this
work indicate a nearly zero slope in phosphine’s absorption spectrum extending to 32 GHz.
While the characterization of phosphine’s spectrum in this region is of general importance
to planetary science and should be investigated upon those merits alone, the planned 32
GHz radio occultation experiments by the Cassini spacecraft at Saturn significantly elevate
the importance and immediacy of these laboratory measurements.
The estimated vertical opacity profile of a Satumian atmosphere with a saturation
abundance of ammonia and mixing ratios of 10 and 20-times solar phosphine is illustrated
for the 9.3 mm wavelength (32 GHz) in Figure 5.1. The vertical mixing ratio of phosphine
follows that of the Orton et al. (2000) detections.
134
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0.2
20x PH
0.4
0.6
Ox PH
03 0.8
.Q
,-4
>'3
10"Z
1 0 ''
Absorption (dB/km)
Figure 5.1: Predicted 9.3 mm (32 GHz) vertical opacity profile of a Satumian atmosphere
dominated by a saturation abundance of ammonia and phosphine. The vertical mixing ratio
profile of phosphine follows that of the Orton et al. (2000) detections, with a deep mixing
ratio of 0, 10 and 20-solar.
135
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5.4.2
Ground Based Observations
Accurate ground based observations of Saturn’s emission spectrum in the frequency range
2-4 GHz would significantly aid in determining the atmospheric composition of Saturn’s
atmosphere. As discussed in the text, the tradeoffs in matching synthetic emission spectra
of super-solar and single-solar hydrogen sulfide atmospheric models are subtle. The ap­
proximately 16 Kelvin difference in synthetic emission at 15 cm between these two classes
of models can be exploited to reject definitively one class of models, if accurate measure­
ments are conducted of Saturn’s emission spectrum in this frequency region.
5.4.3
Improvements to the Localized Radiative Transfer Model
The localized radiative transfer model developed and described in this work may be im­
proved to aide in future interpretations of Cassini radio science at Saturn. This model has
been developed with applications to measurements from the the 13.78 GHz radiometer on
the Cassini spacecraft. To increase the utility of this model, a latitude-dependent thermo­
chemical model may be used to replace the homogeneous shell thermo-chemical model.
This would allow for the interpretation of the banded structure of Saturn’s atmosphere.
Also, the more complete model of the antenna pattern, as measured by the Jet Propulsion
Laboratory (JPL), may replace the theoretical model used in this work. The JPL antenna
pattern model includes the side-lobes of the antenna pattern out to -30 dB, while the model
used in this work models only the main lobe down to 3 dB. This would allow for better
characterization of the results, especially at the limb of the planet.
136
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5.5
Uniqueness and Contributions
The primary goals of this work have been to measure accurately the microwave (centimeter
wavelength) opacity of phosphine under conditions of the outer planet atmospheres, to
derive a physically-based formalism of phosphine absorption, and to illustrate the impact
of the new phosphine formalism on issues in planetary science.
5.5.1 Laboratory Work
For the first time, laboratory measurements of the centimeter wavelength opacity of phos­
phine have been conducted. The handling of phosphine gas mixtures presented unique
challenges. The Occupational Safety and Health Administration (OSHA) places an upper
limit on phosphine exposure to 300 ppb and 600 ppb for long term and short term exposure,
respectively. This presented difficulties in the safe handling of phosphine during and after
measurements. During the measurements, the low leak rates required by safety standards
far exceeded those required for measurement stability, and were increasingly difficult to
maintain under the high pressures and low temperatures of the measurements. After the
measurements, a system had to be designed to remove phosphine from the measurement
apparatus safely. Increased usage of phosphine in industry has led to the manufacture of
new products for the safe handling of this poisonous gas. A new gas handling system was
devised that included phosphine scrubbers, which removed all phosphine from the waste
gas down to our detection level of 20 ppb. This new system will allow the safe handling of
phosphine mixtures for future laboratory measurements.
137
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The first laboratory measurement-based centimeter wavelength phosphine opacity
formalism has been developed as part of this work. This new formalism represents a greater
than an order of magnitude improvement over current theoretically-derived models. The
application of this formalism to outstanding issues in planetary science has illustrated that
unaccounted-for phosphine opacity is likely responsible for difficulties in interpreting the
Voyager radio occultation experiment results at Saturn and Neptune.
For the first time, the errors introduced by uncertainties in transmissivity and mis­
matched dieletric loading have been estimated and included in the reported total measure­
ment error.
5.5.2
Applications
This work has shown that the vertical mixing ratio profile of ammonia, as inferred from the
Voyager radio occultation experiment (VRO), at Saturn (Lindal el al., 1985) requires an
abundance of ammonia that is super-saturated. Furthermore, this work has shown that with
the inclusion of phosphine, at mixing ratios supported by independent observations, the
opacity profiles derived from the VRO experiments are matched with a saturated abundance
of ammonia.
At Neptune the vertical mixing ratio profile of ammonia inferred from the VRO
experiment was inconsistent with a hydrogen sulfide dominant atmosphere, which has been
indicated (see eg. (de Pater et al., 1991)). With the application of the phosphine formalism
derived in this work, it has been shown that an upper atmosphere depleted of ammonia
138
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(hydrogen sulfide dominant) is consistent with the opacity profile inferred from the VRO if
phosphine opacity is taken into account.
For both Saturn and Neptune, the effects of including phosphine in atmospheric
models have been shown to be consistent with observations and VRO results.
A new ray-tracing based localized radiative transfer model with ellipsoidal shell at­
mospheric layers has been developed for this work. This model has been applied to inves­
tigate the ability of the Cassini RADAR/Radiometer to detect and discriminate phosphine
opacity in the atmosphere of Saturn. These results represent the first quantitative evidence
that phosphine will be detectable by the Cassini RADAR/Radiometer.
5.6
Publications and Presentations
Publications
Hoffman, J. H. and P. G. Steffes, and D. R. DeBoer 2001. Laboratory measurements
of the microwave opacity of phosphine: application to the atmospheres of the outer planets.
Icarus, in press.
Hoffman, J. H. and P. G. Steffes, 1999. Laboratory measurements of phosphine’s
microwave opacity: implications for planetary radio science. Icarus, 140, 235-238.
139
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Presentations
Hoffman, J.P. and P.G. Steffes, 2001. Laboratory measurements of the microwave
opacity of phosphine: Opacity formalism and applications to the atmospheres of the Outer
Planets. Georgia Tech Student Paper Competition, Science Applications International Cor­
poration (SAIC). Awarded SAIC Technical Paper Prize, April 26, 2001.
Hoffman, J.P. and P.G. Steffes, 2001. Laboratory measurements of the microwave
opacity of phosphine: Opacity formalism and applications to the atmospheres of the Outer
Planets. Presented at the National Radio Science Meeting, Boulder, CO, January 9, 2001.
Awarded F irst Prize in the student paper competition.
Hoffman, J.P., P.G. Steffes and D. R. DeBoer, 2000. Laboratory measurements
of the microwave opacity of phosphine: Opacity formalism and applications to the atmo­
spheres of the Outer Planets. Bulletin o f the American Astronomical Society, vol. 32, no. 3,
2000. P, 1110. Presented at the 32st Annual Meeting of the Division for Planetary Sciences
of the American Astronomical Society, Pasadena, California, October 26,2000.
Hoffman, J.P. and P.G. Steffes 1999. Low Temperature Laboratory Measurements
of the Centimeter Wavelength Properties of Phosphine Under Simulated Outer Planet Con­
ditions, Bulletin o f the American Astronomical Society, vol. 31, no. 4, 1999. P, 1169.
Presented at the 31st Annual Meeting of the Division for Planetary Sciences of the Ameri­
can Astronomical Society, Padova, Italy, October 14,1999.
Hoffman, J. P. and P. G. Steffes, 1999. Preliminary Results of Laboratory Measure­
ments of the Centimeter Wavelength Properties of Phosphine under Simulated Conditions
140
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
for the Outer Planets, International Union o f Radio Science Programs and Abstracts: 1999
National Radio Science Meeting, p. 286, Jan. 1999. Presented at the National Radio
Science Meeting, Boulder, CO, January 7,1999.
Hoffman J. P., P.G. Steffes, and D. R. DeBoer 1998. Preliminary Results of Labora­
tory Measurements of the Centimeter Wavelength Properties of Phosphine under Simulated
Conditions for the Outer Planets, Bulletin o f the American Astronomical Society, vol. 30
no. 3, 1998. p. 1102. Presented at the 30th Annual Meeting of the Division for Planetary
Sciences of the American Astronomical Society, Madison, WI, October 16,1998.
141
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142
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Vita
James Patrick Hoffman was bom on February 12, 1972 in Levittown, Long Island in the
state of New York. After graduating from the Island Trees High School, he attended the
State University of New York at Buffalo where he interned at Motorola and was inducted
into Eta Kappa Nu and Tau Beta Pi. He graduated magna cum laude in June of 1996 with a
bachelor’s degree in Electrical Engineering and a minor in English Literature. He obtained
his Master’s degree in Electrical Engineering from the Georgia Institute of Technology in
1999, followed by a doctorate in 2001, also from Georgia Tech.
As a Ph.D. student, James Hoffman conducted research in the field of planetary re­
mote sensing. In particular, his dissertation focused on the microwave laboratory measure­
ments of gaseous phosphine opacity under simulated outer planet conditions, and radiative
transfer modeling. For this work he won F irst Prize at the 2001 National Radio Science
Meeting (URSI) Student Paper Competition and was awarded the Technical P aper Prize in
the Science Applications International Corporation’s (SAIC) Georgia Tech Student Paper
Competition.
Currently a Ph.D. candidate, James Hoffman plans to join the Advanced Radar
Technology and Implementation Group of the Radar Science and Engineering Section at
NASA’s Jet Propulsion Laboratory in Pasadena, California.
R e p r o d u c e d w ith p e r m i s s i o n o f t h e c o p y r i g h t o w n e r . F u r t h e r r e p r o d u c t i o n p r o h i b i t e d w i t h o u t p e r m i s s i o n .
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