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glcw_2_01_dunaeva_report

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A COMPARISON OF INTERNAL STRUCTURE
OF GANYMEDE AND TITAN.
Dunaeva A.N., Kronrod V.A., Kuskov O.L.
Vernadsky Institute of Geochemistry and Analytical Chemistry,
Russian Academy of Sciences,
Moscow, Russia
Ganymede
Titan
Ganymede and Titan:
пѓ�are the two largest satellites in the Solar System;
пѓ�were formed in the outer zones of their central planets (Jupiter and Saturn);
пѓ�are regular satellites (their orbits and rotation are the same as the rotation of
associated central planets);
пѓ� satellites rotation is synchronous with their orbits;
пѓ� low density of the satellites suggests that they could contain remarkable
amounts of H2O.
The main differences between Ganymede and Titan
"Galileo", "Voyager" and "Cassini-Huygens" spacecraft missions to Jupiter and Saturn showed
that Ganymede and Titan are different both external and internally:
Ganymede Titan
Atmosphere
пѓ�
Trace oxygen atmosphere
Dense nitrogen atmosphere (~400 km):
– N2 - 98.4%, CH4 and Ar - 1.6%,
– CO2 and other trace organics.
– Free oxygen is absent.
Magnetic field
пѓ�
A relatively strong intrinsic magnetic field and
magnetosphere.
Intrinsic magnetic field is absent.
Climate
пѓ�
Exogenous
climatic
processes
(evaporation,
condensation, precipitation, cycle of substances,
seasons) are not available.
The seasonal weather patterns are similar to Earth,
but governed by methane cycle (including winds,
rains, seasons change, etc.).
Surface features
Two types of terrain:
– Very old, highly cratered, dark regions;
– Younger (but still ancient), lighter regions marked
with an extensive array of grooves and ridges;
Criovolcanism insignificant but important in the
formation of the bright terrain.
The surface is "complex, fluid-processed, and
geologically young" (c):
– Ridges, valleys, riverbeds, dunes, stable lakes of
liquid hydrocarbons;
– Minor amounts of relatively young impact
craters;
– Clearly defined criovolcanism.
Models of Ganymede and Titan.
Titan:
Ganymede:
Mitri et al., 2009
Sohl F. et al., 2003
Grasset et al., 2005
Ganymede’s general
image from NASA, JPL
Sohl F., 2010
Titan’s general image from NASA
Phase diagram of water and the temperature distribution
in the Ganymede’s and Titan’s icy crust.
325
T, K
50
50
300
100
150
250
200
300
350
400
450
500
H , km
25
L
T ,o C
275
0
250
III
V
Ih
225
200
175
150
125
100
75
550
II
VI
H I h = 8 0 k m -2 5
H L= 310 k m
-5 0
H Ih = 95 k m
H L= 230 k m
-7 5
H Ih = 1 5 0 -1 6 0 k m
-1 0 0
( m o d e ls w it h o u t
in t e r n a l o c e a n )
-1 2 5
-1 5 0
Straight thin lines - conductive temperature profiles through the
G a n y m e d e 's
external (ice-Ih) crust.
s u r f a c e c o n d it io n s s
-1 7
T ita n 's
Dashed lines – adiabatic convective heat transfer
in5 the water
subcrustal ocean and in high-pressure ices.
H, HIh, HL - the distance from the satellite's surface (depth), the
P, kb
2
4 thickness of the6 external ice-Ih crust
8 and of the inner
1 0liquid
ocean respectively.
Calculation of the Ganymede's and Titan’s heat flux
F(mW/m2) = [пЃЈo(RSat - РќIh) /(Рќ Ih RSat)]ln[T2 /Рў1]
F ,m W /m 2
400
20
350
300 250 200 150
100 50
0
пЃЈo = 567 W/m - thermal conductivity
of ice Ih,
H w, km
RSat – satellite’s radius,
15
НIh – thickness of the icy crust,
Т1 – satellite's surface temperature,
M e lt in g p o in ts L - I h
10
T r ip le p o in t
F = 7 m W /m 2 [ 2 ]
5
F = 3 .3 m W /m 2
L -Ih -III
2 5 1 .1 5 K / 2 .0 7 k b a r
F = 5 m W /m 2 [ 1 ]
Т2 – the temperature at the ice-Ih liquid phase boundary,
Hw - the thickness of internal ocean,
F – heat flux.
F = 2 .9 m W /m 2
0
20
40
60
80
100
120
140
160
ГЌ Ih , k m
The thickness of the icy crust and internal ocean of
Ganymede (blue) and Titan (black) via the heat
flow through the satellites ice-Ih crust.
[1] Bland, M.T., et al., 2009
[2] Mitri G., Showman A., 2008
Initinal data for modeling, problem setting and methods of solution
Physical characteristics of the satellites
Ganymede
Titan
Pressure at the surface, P[bar]
1.0e-06
1.467
Temperature at the surface, T [K]
110.0
93.0
Gravity acceleration, g пЂЁ R пЂ© [m/s2];
1.428
1.35486
Radius, R [km]
2634.0
2575.0
Average density, g/cm3
1.936
1.88202
Mass, M [kg]
0.14819e24
0.1346e24
Normalized moment of inertia, I/MR2
0.3105
0.3419
Models of the satellites internal structure described by the system of following equations:
пѓ� Equations of hydrostatic equilibrium:
dP
dR
пЂЅ пЂ­ пЃІ пЂЁR пЂ© пѓ— g пЂЁR пЂ© ,
dg
dR
пЂЅ пЂ­ 4пЃ° пѓ— G пѓ— пЃІ пЂЁ R пЂ© пЂ­ 2 g пЂЁ R пЂ© R
пѓ� The equations of the satellites mass and moment of inertia:
n
n
4
3
3
8
5
5
I пЂЅ
   R i  R i 1 , M     R i  R i 1
i
i
3
15
пЂЁ
пЂЁ
пЂ©
iпЂЅ0
пЂ©
iпЂЅ0
  R   density of the
water-ice shell,
пЃІ ice , m
пЃІ Fe пЂ­ Si
пѓ� The equation for calculating ice component concentration in mantle:
C ice пЂЅ
пЃІ ice , m пЂЁ пЃІ Fe пЂ­ Si пЂ­ пЃІ m пЂ©
пЃІ m пЂЁ пЃІ Fe пЂ­ Si пЂ­ пЃІ ice , m пЂ©
пЃІ Fe пЂ­ Si = 3.15 - 3.62 g/cm3 (LL-chondrites)
пѓ�High-pressure water ices equations of state.
пЃІm
 average density of
ice in mantle,
 density of the
rock–iron
component,
 average density of
mantle
G a n y m e d e 's s u r fa c e
2500
Ih (~ 95 km )
~230 km
V (~ 55 km )
liq u id o c e a n
~465 km
~530 km VI
1500
пЃІ c o re = 5.1 5 g /c m 3
F e -S i m a n tle
пЃІ c o re = 5.7 g /c m 3
пЃІ co re = 6 .5 g /c m 3
500
F e -F e S c o r e
820
840
860
880
900
0 .3 8 8
0 .3 9 2
0 .3 9 6
I /M R 2 fo r r o c k – ir o n c o r e
3 .5
3 .5 5
3 .6
3 .6 5
M a n tle d e n sity , g /c m 3
T it a n 's s u r f a c e
2500
Ih (8 0 k m )
liq u id o c e a n ( ~ 3 1 0 k m )
V + V I (~ 1 2 0 k m )
1500
r o c k - ic e m a n t le
500
r o c k - ir o n c o r e
400
440
480
520
T h ic k n e s s o f th e w a te r -ic y s h e ll, k m
T h ic k n e s s o f th e w a te r -ic y sh e ll, k m
0 .3 8 4
D is ta n c e fr o m T ita n 's c e n t e r , k m
D is t a n c e f r o m G a n im e d e 's c e n te r , k m
The internal structure of Ganymede and Titan.
0 .4
In general three-layer models of satellites including the outer
water-ice shell, mantle (rock or rock-ice) and the inner core (Fe-Si
or Fe-FeS) can be made.
Moreover, two-layer models (without inner core) could be realized.
In this case satellite has significant large outer water-icy shell, but
a ) its inner core not forms.
On this model the maximum possible thickness of the water-ice
shell is about 900 km and 500 km for Ganymede and Titan
respectively.
Water content and density gradients in large icy satellites of
Jupiter and Saturn.
3 .6
60
Io
3 .2
G anym ede
E u ro p a
C a llis to
H 2O , w t %
d e n s ity , g /c m 3
T ita n
40
20
2 .8
2 .4
T ita n
G anym ede
2
C a llis to
E u ro p a
Io
1 .6
0
5
10
15
20
25
O rb ital d istan ce (in R p lan et )
30
5
10
15
20
25
O rb ital d istan ce (in R p lan et )
The total water content in Ganymede is 46-48% , in Titan - 45-52% .
30
Conclusion.
Ganymede and Titan are the similar in size and chemical composition: the density of
the satellites’ rock material is typical for the hydrated L/LL chondrites.
The satellites do not differ in terms of bulk water content which in average is about
50 wt.% (water/rock ratio is close to 1).
Ganymede and Titan both may have subsurface oceans.
– Internal ocean in the satellites not forms when the heat fluxes less than 3.3
mW/m2 and 2.9 mW/m2 for Titan and Ganymede respectively.
Internal structure of the satellites can differ fundamentally:
– Ganymede is a completely differentiated body, with the inner region formed by
separating of the original L/LL-chondritic substance into the silicate mantle
and metallic core.
– Titan is differentiated only partially: its inner areas are represented by a
mixture of rock and ice components.
 Equal content of bulk H2O and the same density of the satellites’ rock material allow
to have assumption that Ganymede and Titan could have been formed from the
planetesimals with similar composition corresponding to the ordinary L/LLchondrites. Different conditions of the satellites’ formation from accretion disks led to
major differences in their internal structure.
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