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Icarus 305 (2018) 186–197
Contents lists available at ScienceDirect
Icarus
journal homepage: www.elsevier.com/locate/icarus
Energy deposition and ion production from thermal oxygen ion
precipitation during Cassini’s T57 flyby
Darci Snowden∗, Michael Smith, Theodore Jimson, Alex Higgins
Department of Physics, Central Washington University, 400 E. University Way, Ellensburg, WA 98926, United States
a r t i c l e
i n f o
Article history:
Received 24 January 2017
Revised 7 June 2017
Accepted 10 January 2018
Available online 11 January 2018
Keywords:
Titan
Atmosphere
Aeronomy
a b s t r a c t
Cassini’s Radio Science Investigation (RSS) and Langmuir Probe observed abnormally high electron densities in Titan’s ionosphere during Cassini’s T57 flyby. We have developed a three-dimensional model to
investigate how the precipitation of thermal magnetospheric O+ may have contributed to enhanced ion
production in Titan’s ionosphere. The three-dimensional model builds on previous work because it calculates both the flux of oxygen through Titan’s exobase and the energy deposition and ion production
rates in Titan’s atmosphere. We find that energy deposition rates and ion production rates due to thermal O+ precipitation have a similar magnitude to the rates from magnetospheric electron precipitation
and that the simulated ionization rates are sufficient to explain the abnormally high electron densities
observed by RSS and Cassini’s Langmuir Probe. Globally, thermal O+ deposits less energy in Titan’s atmosphere than solar EUV, suggesting it has a smaller impact on the thermal structure of Titan’s neutral
atmosphere. However, our results indicate that thermal O+ precipitation can have a significant impact on
Titan’s ionosphere.
© 2018 Elsevier Inc. All rights reserved.
1. Introduction
Cassini has discovered that most of the O+ and other water group ions (e.g. H2 O+ , OH+ ) in Saturn’s magnetosphere originate from the plumes of Enceladus. Once ionized, these particles
are confined to a region near Saturn’s magnetic equator known
as the plasma sheet. Eventually, the water group ions are transported to Saturn’s outer magnetosphere where Titan orbits. Near
Titan, Saturn’s plasma sheet is only a few Saturn radii thick and
the tilt of Saturn’s magnetic axis causes the plasma sheet to be
morphed into a bowl shape by the pressure of the solar wind.
Therefore, depending on the season, the average position of the
plasma sheet is above or below Titan’s orbital plane. However,
the plasma sheet does not stay in its average position, rather it
is highly dynamic and is observed oscillate with a period similar
to Saturn’s rotational period (around 10.7 h). The motion of the
plasma sheet causes it to periodically move past Titan, exposing
Titan’s atmosphere to the water group ions that are confined there
(Arridge et al., 2008). Hörst et al. (2008) showed that the oxygen
containing ions that originated from Enceladus’s interior have a
significant and lasting impact on the chemistry and composition
∗
Corresponding author.
E-mail address: darci.snowden@cwu.com (D. Snowden).
https://doi.org/10.1016/j.icarus.2018.01.014
0019-1035/© 2018 Elsevier Inc. All rights reserved.
of Titan’s atmosphere. Despite this, there are relatively few studies
that quantify how thermal O+ precipitation affects Titan’s thermosphere and ionosphere.
We have developed a three-dimensional ion precipitation
model to quantify the flux of magnetospheric thermal (1 eV to
10 keV) O+ into Titan’s atmosphere. We use this model to investigate how precipitating oxygen affects Titan’s thermosphere
and ionosphere by calculating global ionization and energy deposition rates. In particular, we examine the O+ precipitation during
Cassini’s T57 flyby. Titan was observed to be in Saturn’s plasma
sheet both before and after T57 (Rymer et al., 2009; Nemeth et al.,
2011); therefore, Titan’s atmosphere should have been exposed to
thermal O+ precipitation while Cassini was making in situ measurements. Also, during T57, Cassini’s Radio Science Investigation
(RSS) and Langmuir Probe observed abnormally high electron densities in Titan’s ionosphere near 1200 km altitude suggesting enhanced ionization from thermal ions or electrons from Saturn’s
magnetosphere (Kliore et al., 2011; Richard et al., 2015).
The flux of oxygen through Titan’s exobase calculated here is
in agreement with other recent simulations of O+ precipitation at
Titan (e.g. Sillanpaa and Johnson, 2015); however, our model is
unique in that we also calculate how this flux affects Titan’s atmosphere. We find that, in limited regions, ionization rates from
magnetospheric O+ in the thermal energy range are high enough
to explain ionospheric density enhancements on the order of
D. Snowden et al. / Icarus 305 (2018) 186–197
187
2. Cassini’s T57 flyby
Cassini’s T57 flyby took place at 18:32 UT on 2009 June 22.
Fig. 1 shows the trajectory of the flyby and the solar zenith angles traversed in Titan’s atmosphere. Cassini entered Titan’s atmosphere on the anti-Saturn/night side, downstream of the corotational magnetospheric ram direction. Cassini then traveled toward the ram direction and exited on the day side of Titan’s ionosphere. During T57, Titan was on the night side of Saturn’s magnetosphere at 22 h Saturn local time.
The average ambient magnetic field was [2.27, 4.77, −1.05] nT
and the By component of the magnetic field indicates that Titan
was below Saturn’s magnetic equator (Simon et al., 2010). Moments derived from Cassini Plasma Spectrometer (CAPS) data show
that the upstream density, temperature, and velocity was variable
for several hours before T57 (see Fig. 2). Rymer et al. (2009) and
Nemeth et al. (2011) have classified this flyby as a mix of bi-modal
and plasma sheet types. A bi-modal classification means that the
oxygen ions have a higher density and are colder than what is typically observed in the plasma sheet and is most likely correlated
with Titan passing through Saturn’s current sheet. Finally, as previously discussed, occultation data has been used to calculate the
electron density during this flyby and Kliore et al. (2011) showed
that it was abnormally high compared to previously observed densities on the solar limb. The peak electron density measured by the
Langmuir Probe was also high for Titan’s nightside ionosphere at
1380 cm−3 (Snowden and Yelle, 2014b; Richard et al., 2015; Agren
et al., 2009). Both observation suggest significant ionization from
magnetospheric particles.
0.1
W + Temperature (eV)
0.05
W + Velocity (km s -1)
10 0 0 cm−3 . The precipitation of O+ into Titan’s atmosphere occurs over a limited region of Titan’s ionosphere. For a magnetic
field configuration similar to the T57 flyby, we find that the region of enhanced ionization is close to but does not overlap with
the area where RSS observed enhanced densities in Titan’s ionosphere. However, high ionization rates do overlap with the area
that Cassini’s Langmuir Probe measured enhanced densities. Our
results suggest that both thermal O+ precipitation and thermal
magnetospheric electron precipitation can be important ionization
sources in Titan’s atmosphere above 10 0 0 km. We find that the energy deposited by thermal O+ is similar to the energy deposited by
other magnetospheric particles, but less than the energy deposited
by solar EUV.
W + Density (cm -3)
Fig. 1. The trajectory during Cassini’s T57 flyby as seen from above the equatorial plane and looking toward Saturn. Cassini’s altitude (dashed) and solar zenith angle (solid)
versus altitude. Results are displayed in the TIIS coordinate system with the x-axis pointing in the nominal magnetospheric flow direction, the y-axis pointing toward Saturn,
and the z-axis completing the right handed system. The arrow labeled T57 shows the average upstream magnetic field direction.
0
15:30:00
16:00:00
16:30:00
17:00:00
15:30:00
16:00:00
16:30:00
17:00:00
15:30:00
16:00:00
16:30:00
17:00:00
500
400
300
200
100
200
150
100
50
Time (UTC)
Fig. 2. Ion moments derived from CAPS/IMS (ion mass spectrometer) data taken
before closest approach during the T57 flyby (Young et al., 2004). The top panel
shows W+ ion density, which is an ion group that includes the density of H2 O+ ,
OH+ , and O+ . The center panel shows W+ group temperature and the bottom panel
shows W+ bulk velocity.
3. Model
3.1. 3D model of Titan’s plasma interaction
Titan does not have an intrinsic magnetic field and the plasma
and electromagnetic fields that make up Saturn’s magnetosphere
interact directly with Titan’s atmosphere. In Saturn’s outer magnetosphere, where Titan orbits, the plasma densities vary between
about 0.01 and 0.1 cm−3 depending on the relative location of
Saturn’s plasma sheet. The bulk magnetospheric plasma velocity
is about 100 km/s and the direction can vary significantly from
corotation (Thomsen et al., 2010). The magnetic field near Titan
has a strength of about 5 nT and the convective electric field,
which nominally points away from Saturn, has a strength of about
0.3 mV/m (Arridge et al., 2011a; Arridge et al., 2011b). The slowing
of the magnetospheric plasma causes a pile-up and enhancement
of the magnetic field upstream of Titan. The perturbation of the
magnetic and electric field near Titan’s atmosphere affects the cy-
188
D. Snowden et al. / Icarus 305 (2018) 186–197
Fig. 3. Results of two-dimensional particle tracing simulations. The background magnetic field is 5 nT into the page and the electric field is 0.5 mV/m in the negative ydirection. The magnetic field around a circular obstacle increases with a cosine function with maximum magnitudes of either 10 nT (a, c) or 20 nT (b, d). Colored lines show
the trajectories of 16 amu ions with a bulk velocity of 100 km/s and thermal energies of 100 eV (green), 1,000 eV (red), and 10,000 eV (cyan). (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of this article.)
cloidal trajectory of oxygen ions with gyroradii that are on the order of the scale size of the gradients in the magnetic field (about
one Titan radius, RT = 2575 km) or in the thermal energy range below about 10,0 0 0 eV. If a southward ambient magnetic field is assumed, the draping and enhancement of the magnetic field tends
to prevent oxygen ions from impacting the anti-Saturn and wake
sides of Titan’s atmosphere. In other regions, oxygen ions are not
completely deflected and can reach altitudes near Titan’s exobase
where neutral collisions begin to dominate.
Results from simple two-dimensional simulations that illustrate
how the magnetic pile-up region upstream of Titan might affect
the trajectories of oxygen ions with different energies are shown
in Fig. 3. In each simulation, the magnetic field is 5 nT in the negative z-direction (into the page) except in a torus region where
the magnetic field strength is either doubled or quadrupled over
a region of 1 or 3 RT . In the center of each region of enhanced
magnetic field is a circular obstacle (or “atmosphere”) with a radius of 4075 km (1.58 RT ), where particles are absorbed. Particles
with energies of 10, 10 0 0, and 10,0 0 0 eV (with gyroradii equal to
0.46, 1.5, and 4.6 RT , respectively) are injected with a drift velocity
of 100 km/s at the left hand boundary. In Fig. 3(a) all of the ions
directly upstream of Titan’s atmosphere are absorbed, as evident
by the empty wake region behind Titan. In this case, the magnetic
enhancement is so weak and spatially limited it does not have a
strong effect on the O+ trajectories. In Fig. 3(b), the stronger enhancement of the magnetic field means that the trajectory of all
ions is affected. The shrinking of the O+ gyroradii in the region of
enhanced fields causes the ions to drift around the atmosphere.
This prevents some ions from impacting the anti-Saturn side of
the atmosphere and more ions populate Titan’s wake. Fig. 3(c) and
(d) shows the effect of expanding the region of enhanced magnetic field. Increasing the spatial scale of the gradient in the mag-
D. Snowden et al. / Icarus 305 (2018) 186–197
netic field strongly affects the trajectories of the 10,0 0 0 eV ions.
About the same number of 100 eV and 10 0 0 eV particles hit the
atmosphere in panels (a) and (c), but more 10,0 0 0 eV particles are
deflected in panel (c). Panel (d) shows that enhancing the field
strength means that many more 10,0 0 0 eV particles are deflected
around the atmosphere.
The possible deflection of thermal magnetospheric oxygen ions
due to the enhanced magnetic field near Titan means that a threedimensional model that includes realistic electromagnetic fields
and plasma flow near Titan is needed to calculate the flux of ions
crossing Titan’s exobase. Here we used a three-dimensional multifluid model of Titan’s interaction with Saturn’s magnetosphere to
calculate magnetic and electric fields near Titan. Previously, the results of this model were shown to be in good agreement with observations from Cassini’s TA, TB, T3, and T55 flybys (Snowden et al.,
2007; Snowden and Winglee, 2013). The multifluid model solves
the generalized Ohm’s law, the induction equation, and the continuity, energy, and momentum equations for 4 ion fluids (1 amu,
16 amu, 28 amu and 52 amu) and an electron fluid, assuming
isotropic temperatures and quasi-neutrality. Ionospheric ions are
produced by photoionization, photoelectron ionization, and lost
through dissociative recombination. Equations are solved on a 3D
rectangular nested Cartesian grid with five boxes and the total simulation size is 44 × 35 × 35 RT . In this study, we used the electric
and magnetic field calculated by the multifluid model to form a
10 × 10 × 10 RT data grid with a maximum resolution of 120 km
near Titan. A more detailed description of this model can be found
in Snowden and Winglee (2013).
Many previous studies have shown that the plasma density,
magnetic field, and plasma velocity are highly variable near Titan (e.g. Rymer et al., 2009; Nemeth et al., 2011). The variability means that the properties of induced fields around Titan, and
their affect on the precipitation of magnetospheric particles, is also
highly variable. In this study, we are trying to reproduce the ion
precipitation for T57; therefore, the upstream parameters of the
model have been selected to be in agreement with the upstream
parameters observed by Cassini. Fig. 5 shows the magnetic field
observed before and after the flyby. The W+ velocity, temperature,
and density observed by CAPS/IMS are shown in Fig. 2. We do not
show H+ /H+
density and temperature but H+ /H+
CAPS/IMS mo2
2
ments exhibit similar variability with densities between ∼ 0.005
and 0.2 cm−3 and temperatures between ∼ 100 and 1,0 0 0 eV over
the same time period.
In the multifluid simulations, the magnetospheric plasma was
initialized upstream of Titan and was assumed to be composed of
H+ (1 amu) and O+ (16 amu). Two simulations were run, the first
“nominal flux” simulation represents average magnetospheric values measured near Titan. The second “high flux” simulation represents the maximum density and velocity observed. The nominal
flux simulation had the following upstream parameters: H+ density of 0.05 cm−3 , O+ density of 0.05 cm−3 , upstream velocity of
[90, 0, −30] km/s, upstream ion temperature of 500 eV, and upstream magnetic field of [2, 4, −2] nT. The high flux simulation
had the following upstream parameters: H+ density of 0.09 cm−3 ,
O+ density of 0.09 cm−3 , upstream velocity of [150, 0, 0] km/s, upstream ion temperature of 500 eV, and upstream magnetic field of
[2, 4, −2] nT.
Fig. 4 shows the total simulated magnetic and electric field
in the equatorial plane. In both simulations, the magnetic field
strength is enhanced in a region roughly 5–7 RT upstream of Titan. The maximum field strength in the pile-up region is about
5 nT greater in the high flux simulation due to the greater upstream density and flow speed. The magnetic and electric field in
this simulation also have a bow wave upstream because magnetospheric plasma flow is super-alfvénic, whereas the flow in the
nominal flux simulation is sub-alfvénic.
189
We verify the results of the model by comparing the magnetic
field from our nominal simulation to that measured by Cassini
and Fig. 5 shows a comparison between the simulated magnetic
field and the magnetic field measured by Cassini’s magnetometer. This figure also shows the tilt of the flow-induced magnetosphere due to the significant y-component of the upstream magnetic field, which is not apparent in Fig. 4. The magnetic field simulated by the nominal simulation along the T57 trajectory is similar to the measured magnetic field; however, the model does not
accurately reproduce the data before closest approach. The magnetometer data indicates that the ambient magnetic field was variable before this flyby and it is likely that at least some of the disagreement between the simulation and the data is due to fossilized
remnants from a different ambient magnetic field.
3.2. Ion precipitation model
We use a particle tracking model to study the precipitation
of thermal (1–10,0 0 0 eV) O+ into Titan’s upper atmosphere. The
model has two parts. First, the trajectory of 16 amu superparticles
in Saturn’s magnetosphere are calculated by solving the Lorentz
equation of motion, m ddtv = q(E + v × B ) using the Boris method
with a fixed time step of 0.1 s (Boris, 1970). The model interpolates
the E and B fields from the three-dimensional multifluid simulation
to the position of the particle. Fig. 5 shows a few of the two million cycloidal trajectories simulated. Only a small fraction (4932 or
0.25%) of the initialized particles intercepted Titan’s atmosphere,
and we show the trajectory of a few intercepting particles in red.
Nearly all the particles that intercepted Titan’s atmosphere were
initialized nearly directly upstream of Titan in a similar region as
these particles.
Around 1600 km altitude, the collision frequency between O+
and N2 becomes comparable to the gyrofrequency of an oxygen
ion with energy less than 10 keV. If a superparticle reached this
altitude, we assumed that it continued to move through Titan’s atmosphere along a straight path as shown in Fig. 6. This figure indicates that most particles hit Titan’s exobase at a grazing angle
and traveled horizontally through the atmosphere relative to the
surface. Fig. 7 shows that the incidence angles, measured from the
1600 km surface normal, follow a smooth distribution centered on
60°. Therefore, it is not appropriate to assume that magnetospheric
ions penetrate the atmosphere with a normal angle relative to the
exobase, as is often done in one-dimensional models.
The range and energy deposition rates of the particles were calculated using the continuous loss approximation, i.e.:
dE
∼ −2n(Sn + Se ),
dx
(1)
where n is the neutral gas density and Sn and Se are the nuclear and electronic stopping loss cross sections for O+ interacting with N gas, respectively. The factor of 2 accounts for the fact
we are modeling the interaction with N2 rather than N. The nuclear cross sections were calculated using the universal potential
(Johnson, 1990) and the electronic stopping cross sections are from
the mstar program (Paul and Schinner, 2001) and both are shown
in Fig. 8. We only included collision with N2 because it is by far the
most dominant molecule below the exobase and assumed a spherical shape for Titan’s atmosphere. We used the N2 density profile
from Strobel (2012), which is an average of the density measured
by Cassini’s ion neutral mass spectrometer (INMS). Using an average N2 density profile introduces some error; however, the INMS
density from T57 does not accurately describe the neutral density all latitudes and longitudes. Snowden and Yelle (2014b) also
used this method to estimate the energy deposition rates of magnetospheric ions in Titan’s ‘plasma sheet’ and ‘bi-modal/heavy-rich’
plasma environments. However, the model used here is different
190
D. Snowden et al. / Icarus 305 (2018) 186–197
Fig. 4. The total magnetic field and electric field calculated by the multifluid simulation in Titan’s equatorial plane. The two left panels show results from the nominal flux
simulation and the two right panels show results from the high flux simulation.
from the model in Snowden and Yelle (2014b) because that model
did not take into account how the field structure near Titan affects
the energy flux, incidence angle, or the spatial distribution of precipitating O+ at the exobase.
The continuous slowing down approximation is a macroscopic
approach to simulating the effect of ion precipitation on the atmosphere. The nuclear and electronic stopping loss cross sections can
be used to calculate the energy lost by an ion moving through a
gas due to the collective effect of elastic collisions and various inelastic collisions, respectively. Continuous loss calculations are not
as precise as a Direct Monte Carlo (DSCM) models (Michael and
Johnson, 2005; Michael et al., 2005; Shah et al., 2009) or twostream/multi-stream ion transport models (e.g. Michael and Johnson, 2005; Shah et al., 2009; Luhmann and Kozyra, 1991). For example, DSCM simulations account for both the angular scattering
of particles after collisions and the partitioning of energy between
internal heat and kinetic energy. This can be particularly important near Titan’s exobase because a significant amount of the energy deposited by precipitating ions with energies of several keV is
lost due to sputtering (Michael and Johnson, 2005). The continuous
loss approximation also assumes that precipitating particles follow
a linear trajectory. Measurements of O+ collision cross sections at
the energies we are considering (10’s to several keV) indicate that
the collisions are forward scattering (Schafer et al., 1987). However,
this method still overestimates the penetration depth of the particle to some degree. Despite these drawbacks, the continuous loss
calculations are informative and comparisons between continuous
loss calculations and Monte-Carlo calculations at other planets (e.g.
Kallio and Barabash, 20 0 0) show that the two different methods
result in only small differences in the energy deposition rates or
ionization rates. We also report the global O+ flux and the distribution of incidence angles at the exobase so these results could
be used in more sophisticated models to precisely quantify energy
deposition and sputtering rates.
Fig. 9 shows the range or depth of penetration in Titan’s atmosphere versus the oxygen ion’s energy when it crosses the exobase.
As expected, higher energy ions have a larger range and ions with
larger incident angles have a shorter range. This figure also shows
that nearly all the thermal O+ incident on Titan’s atmosphere are
stopped above 1100 km altitude. This figure does not show that a
D. Snowden et al. / Icarus 305 (2018) 186–197
191
Fig. 5. The total magnetic field calculated by the nominal flux multifluid simulation. The trajectory of several of the simulated superparticles are also shown and the
red trajectories show particles that hit Titan’s atmosphere. The straight red line indicates the T57 trajectory. The right panel shows the components of the magnetic field
calculated by the multifluid simulation (green) compared with Cassini magnetometer data (blue). (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
Fig. 6. The simulated trajectory of thermal O+ that cross Titan’s exobase. The shading of the lines corresponds to the incident energy of the particles, with darker shades of
blue corresponding to higher energy particles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Since we are focused on thermal magnetospheric O+ nearly all
of the ions that hit the atmosphere had energies less than 5 keV.
In this energy range both charge exchange and ionization reactions are relevant, with the latter becoming more important at
larger energies and the former being dominant at low energies.
We used average total ion production cross sections, which includes both dissociative and non-dissociative impact ionization and
charge exchange, (σ ion ) and charge exchange cross sections (σ cx )
from Shah et al. (2009). At each altitude level, the fraction of the
incident ion flux that remained in the charged state was tracked
using,
Fion =
σion (E ) − σcx (E )
σion (E )
(2)
The ion fraction is used to reduce the flux of ions entering the next
atmospheric layer,
(E, zi ) = (E, zi−1 )Fion ,
Fig. 7. A histogram showing the distribution of incident angles of thermal O+ crossing a surface at 1600 km altitude. The angle is measured from the surface normal.
significant number of ions that entered Titan’s atmosphere with
high incidence angles exited the atmosphere before being stopped.
(3)
where i indicates the altitude level starting from the top of the atmosphere. This reduced flux was used to calculate ionization rates
in subsequent layers; however, the full flux of oxygen particles
(now assumed to be a mix of ions and energetic neutrals) was used
to determine the energy deposition rates and the range of the oxygen atoms in Titan’s atmosphere.
192
D. Snowden et al. / Icarus 305 (2018) 186–197
Table 1
Magnetospheric parameters used to weight the simulated O+ superparticles and
the resulting energy and number fluxes through a surface at 1600 km.
Simulation
High flux
Nominal flux
Magnetospheric O+ density (cm−3 )
Magnetospheric O+ bulk velocity (km s−1 )
Magnetospheric O+ temperature (eV)
Magnetospheric O+ energy flux (GeV cm−2 s−1 )
Total number flux (s−1 )
Average number flux (cm−2 s−1 )
Max number flux (cm−2 s−1 )
Total power (MW)
Average energy flux (MeV cm−2 s−1 )
Max energy flux (MeV cm−2 s−1 )
0.09
150
200
145
1.4 × 1024
4.7 × 105
4.8 × 106
516
1010
1300
0.05
110
200
24
2.7 × 1023
9.0 × 104
8.7 × 105
76
160
1800
3.3. Initialization and weighting of particles in the ion precipitation
simulation
We injected two million superparticles into the simulation at
random locations along a half-sphere 8 RT upstream of Titan. The
particles were started with a drifting Maxwellian distribution on a
discrete energy grid from 10 to 10,0 0 0 eV with smoothly varying
logarithmic spacing. The number of particles in a given energy bin
is given by the integral
N ( E ) = 4π
v1
v2
f ( v )v2 d v,
where
f (v ) =
Fig. 8. (top) The nuclear (Sn ) and electronic (Se ) stopping loss cross sections for
O+ interacting with N. (bottom) Total ion production and charge exchange cross
sections due to O+ impacting N2 . The total cross sections are a sum of several dissociative and non-dissociative reactions, see Shah et al. (2009) for details.
1450
exp −
( v − vb )2 .
v2
(5)
J
,
N (E )/A
(6)
where N(E) is the number of particles initialized in each energy bin
and A is the area of the surface that we initialized the particles on,
in this case a half-sphere with a radius of 8 RT . The value of w(E)
varies with energy but was on the order of 1023 particles/s.
80
1400
( π v )
2 3/2
The bulk velocity of each particle was initialed with the same magnitude and direction as the oxygen fluid at that location in the
multifluid simulation, and we assigned a random thermal velocity according to the particles temperature. By assigning a random
thermal velocity we are also assumed a uniform pitch angle distribution.
For atmospheric calculations, we weighted the superparticles by
comparing the initialized energy spectrum to a differential particle
2
flux distribution, J = vm f, computed with CAPS/IMS moments derived before the T57 flyby. The particle flux distribution was discretized on the same energy grid used to inject the particles. The
weight for each superparticle, with units of particles/seconds, was
determined by
w (E ) =
1500
n
(4)
70
1350
50
1250
40
1200
30
1150
1100
20
1050
10
1000
0
1000
2000
3000
4000
5000
Incident Energy (eV)
Fig. 9. The range of thermal O+ in Titan’s atmosphere.
Incident Angle (deg)
Altitude (km)
60
1300
4. Results
As shown in Fig. 2, ion moments calculated from the CAPS
data before T57 were variable. Therefore, we report results from
a high flux case and a nominal flux case to show the range
of how oxygen ion precipitation might affect Titan’s atmosphere.
Table 1 summarizes the parameters used to weight the superparticles and the resulting fluxes at 1600 km altitude. In the high
flux simulation, we weighted the particles using a differential energy spectrum similar to what CAPS observed at 16:50 UT (Fig. 2).
The O+ energy distribution was assumed to be a Maxwellian
with a density of 0.09 cm−3 , a temperature of 200 eV, and a
velocity of 150 km/s, giving a total magnetospheric energy flux
of 1.5 × 1011 eV cm−2 s−1 . Titan would be exposed to an energy flux this high in a bi-modal environment or when there is
D. Snowden et al. / Icarus 305 (2018) 186–197
Fig. 10. The number of superparticles hitting Titan’s exobase versus the energy of
the ion when it is injected into the simulation.
an unusually high density of O+ and an exceptionally large flow
velocity. In the nominal simulation, the O+ energy distribution was
assumed to be Maxwellian with a density of 0.05 cm−3 , a temperature of 200 eV, and a velocity of 110 km/s giving a total magnetospheric energy flux of 2.4 × 1010 eV cm−2 s−1 . This energy flux is
closer to the average value observed upstream during T57 or similar to what was seen by CAPS at 15:45 UT (Fig. 2). It representative
of Titan being in Saturn’s plasma sheet with a relatively high density of O+ ions (Nemeth et al., 2011), but not as high as in the high
flux simulation.
Ledvina et al. (2005) showed that strong gradients in the magnetic field near Titan shield low energy O+ ions from entering Titan’s atmosphere similar to what was shown in Fig. 3; however,
our results indicate this is not always the case. Fig. 10 shows the
number of ions that hit Titan’s exobase versus the energy each
ion was injected into the simulation with. Qualitatively, this distribution is very similar to the energy distribution initialized 8 RT
upstream. Most of the ions that hit Titan’s atmosphere had energies near 1 keV. Few ions with high energies ( > 5 eV) hit Titan’s atmosphere, simply because very few of these high energy
ions were injected into the simulation.Therefore, unlike the simulation of Ledvina et al. (2005), we do not see a significant shielding
of ions below energies of 2 keV. The lack of shielding is probably due to differences in upstream parameters used in the threedimensional multifluid simulation that calculated the electric and
magnetic fields. Compared to earlier work that used upstream parameters that were similar to those observed by Voyager 1, the
plasma environment during T57 results in a smaller increase in
the magnetic field strength in the draping region resulting in less
effective shielding. Therefore, it is not always appropriate to assume that lower energy oxygen ions, with energies less than about
2 keV, will be deflected away from Titan before precipitating into
the atmosphere as was done in Snowden and Yelle (2014b).
However, in agreement with earlier work (Ledvina et al., 2005;
Sillanpää et al., 2007; Regoli et al., 2016), we find that the energy
flux incident is not spatially uniform. This can be seen in Fig. 11,
which shows the inward energy flux and the inward particle flux
at 1600 km altitude. Most of the O+ ions hit the ram side of Titan’s
atmosphere (between 135° and 225°) with a slight shift toward the
Saturn-facing side (between 225° and 315°). The fluxes are qualitatively similar in both the nominal and high flux simulation. This
indicates that the direction of the magnetic field, which was the
same in both simulations, strongly determines where ions cross Titan’s exobase. Table 1 lists the total power; average and max en-
193
ergy flux; and the total, average, and max particle flux across the
1600 km surface calculated by each simulation.
The model continued to track the particles as they moved
through Titan’s atmosphere and to determine ionization, energy
deposition, and charge exchange rates. Fig. 12 shows the globally
average altitude profiles and the altitude profiles for the ram (longitudes between 135° and 225° with the sub-ram point at 180°),
anti-Saturn (between 45° and 135°), wake (between 315° and 360°
and 0° and 45°), and Saturn-facing (between 225° and 315°) sides
of Titan’s atmosphere. The profiles have the form of a Chapman
production function, although they are not as smooth as what
would be theoretically predicted due to poor statistics in some regions. The profiles are especially discontinuous on the wake side,
where few particles entered the atmosphere. Running the simulation with fewer or more particles changes how smooth the curves
appear, but does not significantly change the values. It is worth
noting that injecting particles downstream of Titan does not increase the energy deposition and ion production rates on the wake
side because the ions drift downstream before they impact Titan’s
atmosphere.
As expected, energy deposition rates and ion production rates
are highest in the ram quadrant of Titan’s atmosphere. They are
also significantly greater in the high flux simulation compared to
the nominal simulation. Ion production is dominated by charge exchange for O+ atoms with energies less than 5 keV; therefore, the
ion production curves shown are almost entirely due to charge exchange reactions. In either simulation, the peak rates occur near
1150 km altitude. Table 2 show the results of fitting the Chapman
production function to globally averaged and ram side profiles and
an example of one fit is shown in Fig. 13.
Fig. 14 shows the ionization rate calculated at 1150 km for the
high flux simulation. For the upstream parameters assumed here,
we find that the ionization rates peak in a limited region centered at about 0° latitude and 200° longitude. The area of peak
ionization shifts depending on the magnetospheric flow direction
and the upstream magnetic field. In this case, the counterclockwise
tilt of the region of high ionization is due to the y-component of
the upstream magnetic field (By > 0) used in the three-dimensional
multifluid simulation. The cycloidal drift motion of the ions is parallel to the convective electric field and a significant By tilts the
convective electric field out of the equatorial plane, which affects
which ions impact Titan’s exobase. As Fig. 9 shows, most of the
particles that reach 1150 km altitude had a small incident angle;
therefore, the region of maximum ionization looks similar to the
area of maximum particle flux at the 1600 km altitude surface. At
higher altitudes, the ionization rates are smaller but more spread
out due to the horizontal motion of the particles.
5. Discussion
5.1. Comparison to T57
The peak electron density measured on the nightside of Titan’s ionosphere during the inbound portion of T57 was abnormally high at about 1380 cm−3 near 1100 km (Snowden and Yelle,
2014b; Richard et al., 2015). A similar enhancement in the solar limb electron density above 10 0 0 km altitude was observed
in the RSS data (Kliore et al., 2011). Richard et al. (2015) and
Sagnières et al. (2015) used a chemical model based on CH+
densi3
ties to derive ion production rates for N+
directly
from
INMS
taken
2
during T57. Their results imply that the ion production rates along
the inbound portion of Cassini’s trajectory were close to 1 cm−3 s−1
near the peak of the ionosphere.
Fig. 1 shows the orientation of T57 relative to the dayside
of Titan’s ionosphere. Cassini traveled through the peak of the
ionosphere around −30◦ latitude and 170° longitude at altitudes
194
D. Snowden et al. / Icarus 305 (2018) 186–197
Fig. 11. The inward energy flux (left panels) and number flux (right panels) of O+ ions hitting a surface at 1600 km altitude for the high and nominal flux simulations. The
sub-ram point is at 180° and the Saturn-facing point is at 270°. The subsolar point is at 300°.
Table 2
Chapman production function fit to average and ram-facing altitude profiles shown in
Fig. 12.
High flux simulation
Fit of Qe
1−
z−z0
H
−e
−
z−z0
H
Nominal flux simulation
to
Global average energy deposition
Ram energy deposition
Global average ion production rate
Ram ion production rate
Q
z0
H
Q
z0
H
75
212
0.83
2.3
1170
1157
1188
1177
72
65
78
74
10
23
0.10
0.21
1196
1178
1210
1193
74
67
80
74
near 1100 km, which is near where we calculated high ionization rates from precipitating O+ . In the high flux simulation,
we find that the ion production rates, including ionization and
charge exchange, can be as high as 2 cm−3 s−1 . Ionization rates
at 1150 km in the nominal simulation look qualitatively similar to
Fig. 14 but the rates are lower, with a maximum total ion production rate around 0.4 cm−3 s−1 . Therefore, O+ impact ionization rates
could be similar to those calcuated by Richard et al. (2015) and
Sagnières et al. (2015) (∼1 cm−3 s−1 ) at mid-latitudes on the ram
side of Titan’s atmosphere for upstream energy fluxes between our
nominal and high flux simulation.
RSS observed high electron densities around 76° latitude and
280° longitude, which is close to but does not overlap the area
where we calculate high ionization rates. However, it is possible
that the region of high ionization rates shifted due to changes in
the upstream flow direction or magnetic field direction. As we discuss in the next section, the enhanced ionospheric densities may
also be caused by magnetospheric electron precipitation suggested
by Kliore et al. (2011) and Richard et al. (2015).
5.2. Comparison to previous work
The results of this model can be compared to previous calculations of ionization and energy deposition from thermal O+ precipitation in Titan’s upper atmosphere. Sillanpää et al. (2007) used
a hybrid model to calculate the energy and number flux of O+
ions across Titan’s exobase. For Voyager 1 conditions, they calculated a global power input of 310 MW measured at an altitude of
1625 km and an average energy flux of 2 GeV cm−2 s−1 . This model
has been updated to include ion-neutral interactions near Titan’s
exobase and more recently Sillanpaa and Johnson (2015) calculated
the energy and particle flux for upstream parameters observed
during Cassini’s T15 flyby. They found that including ion-neutral
interactions below 20 0 0 km had a significant effect on the energy
and particle flux measured at 1400 km altitude. In the simulation
that included slowing of particles approximated by stopping power
cross sections and the possible removal of particles through inelastic collisions, they calculated a global energy input of 61 MW and
a particle flux of 1.95 × 1023 ions s−1 at an altitude of 1400 km.
In the high flux simulation, we calculate a total power of
516 MW and an average energy flux of 1010 MeV cm−2 s−1 incident on a surface at 1600 km altitude. For the nominal case, the total power was significantly smaller at 76 MW with a global energy
flux of 160 MeV cm−2 s−1 . The particle flux for the high and nominal simulations were 1.4 × 1024 ions s−1 and 2.7 × 1023 ions s−1 ,
respectively. Therefore, for our high flux case, we find that the energy incident on Titan’s atmosphere is higher than that calculated
in previous work. This simulation used an abnormally high magnetospheric energy flux distribution near Titan. As Fig. 2 shows, Titan
was exposed to this high energy flux for less than 10 minutes at
a time. The nominal flux simulation uses an upstream flux that
is more typical of Titan’s environment in Saturn’s plasma sheet.
The energy and particle flux calculated by this simulation are in
good agreement with the most recent result of Sillanpaa and Johnson (2015), especially since we report the total power at an alti-
D. Snowden et al. / Icarus 305 (2018) 186–197
195
Globally Averaged Energy Depostion Rate (cm
-3
-1
s )
Fig. 12. The energy deposition and total ion production rates averaged over the globe or over the Saturn-facing, ram, anti-Saturn-facing, or wake side of Titan’s atmosphere.
Left panels show results from the high flux simulation and right panels show the results from the nominal flux simulation.
70
60
50
40
30
Fig. 14. The ionization rate calculated in the high flux simulation at 1150 km altitude.
20
10
1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550
Altitude (km)
Fig. 13. The globally average energy deposition profile for the high flux case fit
with the Chapman production function. The results for this fit and others can be
found in Table 2.
tude of 1600 km rather than 1400 km, where ion-neutral collisions
significantly slow the plasma.
The total power and energy flux resulting from thermal magnetospheric O+ precipitation can also be compared to other relevant energy sources in Titan’s upper atmosphere. The total power
from solar EUV during the 20 07–20 09 time period was about
1 GW (Woods, 2005), which is greater than what we calculate
196
D. Snowden et al. / Icarus 305 (2018) 186–197
for thermal O+ even in our high flux simulation. The energy
flux from thermal O+ is similar to other magnetospheric particles. Shah et al. (2009) found that large fluxes of high energy
O+ (∼200k) resulted in energy fluxes at Titan’s exobase around
6 GeV cm−2 s−1 . Brandt et al. (2012) found that precipitating energetic neutral atoms, with energies between 24 and 55 keV, resulted
in energy fluxes at Titan’s exobase around 5 GeV cm−2 s−1 . In
Snowden and Yelle (2014a), the global energy input from magnetospheric electrons was found to be between about 13 and 150 MW.
Locally, we calculate maximum energy deposition rates in Titan’s atmosphere as high as 200 eV cm−3 s−1 for our high flux
simulation and 10 eV cm−3 s−1 for our nominal flux simulation.
These energy deposition rates correspond to total ion production
rates around 2 cm−3 s−1 and 0.4 cm−3 s−1 , respectively. Energy
deposition rates were highest around 1150 km, which is near the
solar EUV peak. The local energy deposition rates reported here
are within the range of those calculated by Shah et al. (2009) for
higher energy O+ ( > 10 keV) ions. However, O+ with energies
greater than 10 keV deposit most of their energy below 10 0 0 km,
where they would have less of an impact on Titan’s atmosphere
due to the higher neutral density. Similarly, the ionization rates
calculated in our high flux case are close to the ionization rates
that Regoli et al. (2016) calculated for O+ precipitation with energies greater than 10 keV. However, again they found that the
peak ionization rate of about 4 cm−3 s−1 occurred at altitudes below 10 0 0 km.
The temperature of Titan’s upper atmosphere is highly variable
(Westlake et al., 2011; Snowden and Yelle, 2014b) and it is possible that some of the variability is due to heating from magnetospheric particle precipitation. Results of various thermal models
(e.g. Westlake et al., 2011; Bell et al., 2011; Snowden and Yelle,
2014b) suggest that heating rates on the order of 20 to 40 eV cm−3
s−1 result in 10 to 20 K increases in the temperature of Titan’s atmosphere. If we assume a 50% heating efficiency, the results here
imply that heating rates due to thermal O+ precipitation over limited areas of Titan’s atmosphere vary between about 5 and 100 eV
cm−3 s−1 when Titan is in Saturn’s plasma sheet, with the more
common value being closer to 5 eV cm−3 s−1 . Heating rates near
100 eV cm−3 s−1 imply that O+ precipitation may have a significant effect on the temperature in regions experiencing O+ precipitation. However, the thermal inertia of Titan’s atmosphere means
that Titan must be exposed to the O+ precipitation for at least several Earth days and Cassini data indicates that Titan is only periodically exposed to Saturn’s plasma sheet for tens of minutes to
hours.
Relatively short periods of enhanced ion precipitation can have
a significant effect on the density of Titan’s ionosphere. In fact,
Edberg et al. (2015) found that, on average, the density of Titan’s
ionosphere was enhanced by a factor of 1.4 when Titan was observed in Saturn’s plasma sheet where it would be exposed to
thermal magnetospheric particle precipitation. For example, T5 is
another flyby that occurred when Titan was in Saturn’s plasma
sheet and ionization rates from magnetospheric particle precipitation rates were large. This flyby occurred on the night side
of Titan’s ionosphere, near 135° solar zenith angle and the electron density observed in Titan’s ionosphere was around 10 0 0 cm−3 .
Similar to T57, Cravens et al. (2009) showed that you could explain the nightside ionospheric density with ionization rates between 1 and 2 cm−3 s−1 in agreement with the more recent work
of Richard et al. (2015) and Sagnières et al. (2015) who used chemical models to determine ionization rates from CH+
measured by
3
Cassin’s Ion Neutral Mass Spectrometer.
Magnetospheric electrons are usually assumed to be the dominant ionization source in Titan’s night side. For example, both
Kliore et al. (2011) and Richard et al. (2015) invoked magnetospheric electron ionization to explain the enhanced densities ob-
served during T57. However, there is a lot of uncertainty in simulations of magnetospheric electron ionization rates in Titan’s atmosphere due to assumption about the magnetic field line configuration. In addition, Snowden et al. (2013) has shown that the
inward flux of electrons should be reduced overtime because Titan’s atmosphere depletes the electrons in Saturn’s flux tubes.
Sagnières et al. (2015) avoids these complications by calculating
the electron ionization rates from the electron spectrum measured
by CAPS at the same altitude. They calculated ionization rates due
to magnetospheric electrons and compared them to the ionization
rates derived from a chemical model for T5, T50, T57, and T59 and
found that the electron impact ionization rates are 2 to 3 times too
small to explain the observed electron density. The results of our
model suggest that some of the discrepancy could be explained by
including thermal O+ precipitation.
Determining which magnetospheric particle is responsible for
enhanced densities in Titan’s ionosphere is challenging because
both electron and ion impact ionization is non-uniform and depends on the configuration of Titan’s induced magnetosphere. In
general, the results of this global ion precipitation model and the
global electron precipitation model in Snowden and Yelle (2014a)
suggest that ion impact ionization and energy deposition is largest
on Titan’s ram-side, while magnetospheric electron impacts dominate the wake-side or in regions closer to the ‘poles’ of Titan’s
induced magnetosphere.
6. Conclusion
We present results of three-dimensional simulations of thermal
magnetospheric O+ precipitation into Titan’s upper atmosphere.
The three-dimensional model builds on previous work because it
calculates both the flux of oxygen through Titan’s exobase and the
energy deposition and ionization in Titan’s atmosphere.
Here we have simulated upstream conditions similar to those
observed during Cassini’s T57 flyby. We find that thermal O+ precipitation results in ionization and energy deposition rates that are
quantitatively similar to thermal magnetospheric electrons when
Titan is in Saturn’s plasma sheet. The highest ionization and energy deposition rates occur on the ram side of Titan’s atmosphere
but will shift depending on the upstream flow direction and magnetic field direction. Overall, the total power deposited by magnetospheric O+ is lower than that contributed by solar EUV even during T57, which occurred when Titan was in a relatively dense part
of Saturn’s plasma sheet. Therefore, we expect the precipitation of
thermal O+ to have a smaller impact on the energetics of Titan’s
neutral atmosphere.
We compare simulation results to ionization rates derived from
the electron density observed by Cassini. We find that the simulated ionization rates are sufficient to explain the abnormally high
electron densities observed by RSS and Cassini’s Langmuir Probe
during T57. The electron densities observed during T57 are some of
the highest ever observed on the night side of Titan’s ionosphere
for at least the first 10 years of Cassini’s mission (Kliore et al.,
2011); therefore, our results indicate the energy and particle fluxes
we have calculated represent the upper range of thermal O+ fluxes
incident on Titan.
Acknowledgments
This research was supported by NASA under grant
NNX14AH81G. Dr. Snowden would like to thank her undergraduate coauthors (Mike Smith, Theo Jimson, and Alex Higgins)
for their hard work developing this model and the McNair Scholars
program for partially funding their research.
D. Snowden et al. / Icarus 305 (2018) 186–197
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