Origin of Regular Satellites
Angioletta Coradini
1
Outline
What are the characteristics of satellites to
be considered to formulate a theory
A brief review of the existing models
A description of a 3 D hydrodynamical
model in the framework of nucleated
instability
2
What Kind of bodies we are studying?
Regular Satellites
Jupiter has 4 large (>1500 km) moons, Saturn 1, and Uranus and
Neptune none. Neptune appears to be moon-poor in general.
All are synchronous, except Hyperion (chaotic)
Densities are all close to 1 g/cm3, suggesting mainly volatile ices.
Uranian satellites are denser than Saturnian ones
Uranus satellite densities increase (roughly) with distance.
Several of the periods are close to (or actually in) resonance e.g.
Mimas-Tethys, Iapetus-Titan. May have had significant effects earlier in
history.
Uranian system has no resonances (at present day)
Irregular Satellites
Possibly captured
3
Volcanism,
Oceans, Magnetic
Fields were
discovered on
different satellites
4
Enceladus by VIMS
Hyperion
Titan
Phoebe
Titan
Iapetus by CIRS
Iapetus by CIRS
5
The kind of observations
Imaging
Overall geological/geophysical history
Large Scale processes characterizing the surface
Figure
Spectroscopy
Composition
Mineralogy
Gas emission
Theor
interaction with ionized particles
Magnetometer/Plasma analyzers
Internal and external magnetic fields
Radio Science
Internal structure
6
What satellites tell?
Ice becomes a new important component of the
satellites in Jupiter system and is dominating the
Saturn System
There may have been initial variations in composition and
structure due to lateral nebular gradients
New heating mechanism are dominating these
satellites High volatility materials can reduce the
ice melting point Enceladus
However the quantity and quality of radiogenic
element shall be carefully assumed
Organic chemistry have surely played an important
role
How this information can be used in a general scheme of
formation?
7
Origin
Satellite formation can be a natural byproduct of planet formation.
Two formation mechanisms are believed responsible for the majority of the
large planetary satellites:
Co-formation
The Galilean satellites are a key example of a satellite system that is
believed to have co-formed with its parent planet, with satellites
accumulating within a circumplanetary accretion disk that existed during
the final stages of the planets own growth.
Impact
Our own Moon is thought to have resulted from what was perhaps the
largest impact of Earths accretion, and the giant impact hypothesis is
favored because could explain dynamical and physical attributes of the
Earth-Moon system.
Co-existence of both Mechanisms
Saturn System could have been affected by intense bombarding but at
least Titan origin shold be linked to Saturn formation
8
Working Hypothesis: Co-formation
We consider a scenario in which the
regular satellites form within
circumplanetary accretion disks
produced during the final stages of
gas accretion (e.g.,Coradini et
al1981, Magni and Coradini, 2003,
Lubow et al. 1999; D'Angelo et al.
2002, Canup and Ward, 2002)).
For a given inflow rate M of gas and
solids, a quasi steady-state
circumplanetary gas disk is
produced through a balance of the
inflow supply and the disk's
internal viscous evolution,
assuming that the disk viscous
spreading time is short compared
to the timescale over which the
inflow changes.
Minimum mass subnebulae for the Jupiter and Saturn
satellite systems (from Pollack & Consolmagno 1984).
9
Satellite -disk models
The -disk (Coradini et al. 1989) assumes viscous evolution of an accretion disk formed via
nebula mass inflow into circum-jovian orbit. The steady-state disk conditions were using the
Lynden-Bell & Pringle (1974) formalism.
The disk was conceived to be highly convective with a strong turbulence viscosity parameter
=0.1 in the inner satellite region, and a mass accretion rate of 0.1 solar masses per year
New models have been recently proposed that try to remueve this difficulty by carefully
evaluation mass accretion rate and viscosity (Mousis et al. 2002a,b; Mousis & Gautier 2003,
Makalkin et al. 1999, Makalkin et al. 2006 ).
Basic difficulties:
difficulties the disk is too hot, accretion too fast, satellite
lifetimes against decay in short time due to friction with the gas
10
Alternative model: Slow-inflow accretion disk
Canup and Ward 2002
Gas & solids delivered during final stages of Jovian accretion
~10-2 MJ is minimum mass that was processed through satellite disk, but not
necessarily in disk all at one time
Gas maintains quasi steady-state; solids accrete and buildup in disk with time
Result: prolonged satellite formation over >105 years in a cool, gas-starved
disk
Consistent with incompletely differentiated Callisto, icy outer satellites,
satellite survival against viscous decay
Regular satellites of giants formed during final slow accretion of gas
and solids to planets
Inward orbital migration of large satellites likely
Differences in final satellites systems can result from similar conditions,
depending of stopping inflow
11
Some key open issues for the Canup and Ward
2002 Model
1) Character of late inflow onto Jupiter/Saturn?
Flow dynamics within Hill sphere
Specific angular momentum on inflow
Dust/Ice Ratio unknown
2) Disk viscosity: magnitude & character?
Turbulence due to inflow (e.g., Cassen &
Moosman)
General turbulence associated with Keplerian
disks (e.g., Klahr & Bodenheimer)
12
Hydro-dynamical model
The planet accretion has
been treated assuming an
annular region to mimic
the planet feeding zone.
This region is centered on
the Sun and has a
thickness comparable
with the height of the
protosolar nebula at the
same distance.
In the case treated here, at
the Jupiter distance, the
annular region has a
thickness of about 10 a.u.
and at the Saturn distance
of about 15 a.u.
The reference system is
rigidly rotating with an
angular velocity equal to
the Keplerian one.
13
A new model
In the equation of hydrodynamics the viscosity term has
been included .
The viscosity tensor has been evaluated as a perturbative
term following Landau and Lifchitz, approach.
The thermal evolution of the disk has been improved
We are now able to follow the thermal evolution of the disk
due to radiative losses, since the time dependent
radiation equation has been solved.
14
The central cell
we have introduced quasi-stationary equilibrium structure
for the central body and in each time step we have verified
if the gas accretion rate is compatible with the assumption
that the central body is in hydrodynamic equilibrium.
YES
Gas can freely enter in the
Central cell
NO
Structure is
relaxed
15
The grids
91*91*17 and 121*121*19
(140777 e 278179 mesh points)
16
The effect of turbulent viscosity (1)
Saturn accretion: influence of turbulent viscosity
100
Mesh 1
M(SN) = 0.016 M(Sun)
Mass of the growing planet (earth masses)
90
r(accr) = 9.54 AU
80
alfa=0
70
alfa=0.1
60
50
40
30
20
10
0
200
400
600
800 1000 1200
time (years)
1400
1600
1800
2000
The accretion time scale of Saturn increase due to the extra pressure related to the turbulence effects: this shall
be considered as a timescale, since in this calculation we are not yet considering the effect of the gap.
17
The effect of turbulent viscosity(2)
Radius of the disk orbiting Saturn when viscosity is present ( blue ) is smaller then
the one inviscid ( black). This is due to the dissipative effects characterizing the
turbulent fluid.
18
Jupiter and Saturn disks
10.00
5.00
0.00
-5.00
-10.00
-10.00 -8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
-10.00
-5.00
0.00
5.00
10.00
19
Surface density in the central plane of SN at the end of
the accretion ( exploded view)
JUPITER final disk log sigma (gr/cm**2)
final SATURN DISK - log sigma (gr/cm**2)
5.70
10.00
5.60
9.90
5.50
9.80
5.40
9.70
5.30
Y (AU)
Y (AU)
9.60
9.50
5.20
5.10
9.40
5.00
9.30
4.90
9.20
4.80
9.10
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
X (AU)
0.10
0.20
0.30
0.40
0.50
4.70
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
X (AU)
20
Area where the gas has prograde
motion Accretion disk
JUPITER final disk Vrot/Vkep (prograde region)
final SATURN disk - vrot/vkep (prograde region)
5.70
10.00
5.60
9.90
5.50
9.80
5.40
9.70
Y (AU)
5.30
9.60
5.20
9.50
5.10
9.40
5.00
9.30
4.90
9.20
4.80
4.70
-0.50
9.10
-0.40
-0.30
-0.20
-0.10
0.00
X (AU)
0.10
0.20
0.30
0.40
0.50
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
21
4
2
JF4
JF2
log <Rd(Kepl)>/R(Jup)
0
JF1
-2
-4
-6
-8
-10
0.5
1
1.5
2
2.5
3
3.5
log r/R(Jup)
The region that we can call disk is deeply imbedded in the feeding zone and much
smaller than the Hill sphere.
Moreover is characterized by the fact that the gas motion from being prograde
becomes retrograde in the planet reference system.
In Figure are depicted the regions where the gas is in Keplerian motion
22
Jupiter and it surrounding nebula
evolution
23
Temperature profiles:
Jupiter
5
M(SN)=0.01 M(Sun)
4.5
4
convective
3.5
log T (K)
The planet is characterized by the
presence of a large inner
convective zone divided by a
radiative region from the external
convecting layer.
3
radiative
2.5
2
convective
Mp=0.3 M(Jup)
1.5
Mp=0.1 M(Jup)
1
0
100
200
300
400
500
600
700
r/R(Jup)
The two profiles correspond to the
p lanet s m asses 0.1and 0.3 Ju piter
masses. The external envelope of
the planet covers a very large
region of more than 700 RJ
24
2
1.8
log Rp/R(Jup)
1.6
Ca
1.4
1.2
Ga
1
Eu
0.8
0.6
Io
4
4.5
5
5.5
6
6.5
7
log Accretion timescale (yr)
During the slow contraction phase the planet recedes from the region
where presently satellite are located. The formation region of Callisto is in
100.000 years emptied, but 10 millions of years aren t sufficient to clear up the
formation region of Io.
The planet luminosity evolves from values ranging from about 1.1 10-6 1.1
10-5 -after 10.000 years of evolution to about 1.1 10-6 after about 107 .
25
2.6
2.4
<R(keplerian region)>
2.2
2
log R/R(Jup)
1.8
Radius!!!
1.6
R(protoplanet)
1.4
Ca
1.2
Ga
1
Eu
0.8
0.6
Io
4
4.5
5
5.5
6
6.5
7
log Accretion timescale (yr)
Protoplanet radius and external radius of the protosatellitary disk versus
accretion timescale for the growing planet in its final evolution phases.
At right are plotted the distances of the Galilean satellites
26
1
0
Io
Europa
Ganymede
Callisto
log Psat(H2O)/P(r=Rp)
-1
-2
-3
-4
-5
-6
0.6
0.8
1
1.2
1.4
1.6
1.8
2
log Rp/R(Jup)
Only at Callisto distance ice is always present
27
Saturn and its surrounding nebula
evolution
28
Saturn System: Accretion
4
accretion time
time (yr)
Here is shown the
accretion time as
function of the mass
present in the
feeding zone.
Obviously the
smaller the mass in
the feeding zone the
longer the accretion
time.
Saturn reaches a value
of 90% of its
mass
4
in about 10 y
Here the presence of
the gap has been
considered
10
3
10
final accretion timescale
2
10
0
10
1
10
M(feed.zone)/M(Saturn)
2
10
29
Effective radius of the envelpe
1200
0.0272
1000
Hill lobe limit
0.0133
R(protoplanet)/R(Saturn)
The effective radius of the envelope upper part
compared with the radius of the core.
However it should be taken into account that the
envelope, at least at the beginning of the
accretion fill the Hill lobe. The material is also
rapidly accreted
The central part increases in mass and density
and gradually becomes separated from the
envelope.
However for a large part of the initial history core
and envelope can be hardly distinguished.
Also the boundary with the PSN isn t sharp and
frequent mass exchange between the nebula
and the envelope are present.
Also a kind of disk is formed.
The planet assumes its identity only in the final
phases, when the accretion is very slow and
the gas amount in the PSN decreases.
0.0067
800
M(SN)/M(Sun)=0.0035
600
400
200
140777 mesh points
0
0
1000
2000
3000
time (yr)
4000
5000
6000
30
S aturn acc retion
4
m es h 91*91*15
Rp/R(Saturn), Rd/R(Saturn), Md/M(Titan)
10
R (final prot oplanet)
3
10
R(final ac c r. disk )
2
10
1
10
0
10
M(final ac c r. dis k )
-1
10
-2
10
3
3. 5
4
4.5
5
5.5
log ac c retion times c ale (y r)
6
6.5
7
The time evolution of the mass of the accretion disk gives us a constraint on the timing
of the formation of the regular satellites
31
Angular Momentum at the end of the
accretion
18
10
Saturn accretion M(SN)=0.019 M(Sun)
core+envelope
17
planet+rec.disk
16
10
central cell
18
10
15
10
core+envelope
planet+rec.disk
14
10
13
10
12
10
278179 mesh points
blue: turbulent SN alfa=0.003
black: nonturbulent SN
11
10
0
200
400
600
800
time (yr)
1000
1200
1400
specific angular momentum (cm**2/s)
specific angular momentum (cm**2/s)
10
3
central cell
16
2
3,2
10
1
1
14
1 alfa=0.1
2 alfa=0.01
3 alfa=0.0
10
12
Jupiter accretion M(SN)=0.017 M(Sun)
10
278179 mesh points
10
10
0
500
1000
1500
time (yr)
32
Saturn accretion: orbital migration of the growing planet
7
decay timescale (years)
10
6
10
tidal interaction
with SN
radial momentum
capture
5
10
angular momentum
capture
4
10
0
200
400
600
800
1000
time (years)
1200
1400
1600
1800
33
2
10
1
Mass and temperature of the final disk
0
10
-1
10
-2
10
-3
10
Saturn accretion: M(SN)=0.02 M(Sun) Mp=M(Saturn)
2.5
averaged values
-4
10
3
3.5
4
4.5
5
5.5
6
6.5
log accretion timescale (years)
7
7.5
8
2.4
2.3
log Tdisk (K)
convolute disk mass (Titan masses)
10
2.2
2.1
2
1.9
1.8
1.6
1.8
2
2.2
2.4
log r/R(Saturn)
2.6
2.8
3
34
Saturn formation: M(SN) = 0.016 M(Sun)
600
Saturn accretion: M(SN)=0.02 M(Sun) Mp=M(Saturn)
2.5
D(centr.cell)=0.02 AU
averaged values
550
2.4
450
2.3
central cell
log Tdisk (K)
400
350
300
250
200
2.2
2.1
2
150
growing planet photosphere
100
0
500
1.9
1000
1500
time (years)
1.8
1.6
1.8
2
Saturn accretion: M(SN)=0.02 M(Sun) Mp=M(Saturn)
1
2.2
2.4
log r/R(Saturn)
2.6
2.8
3
0
-1
log Psat(H20)/P
effective temperature (K)
500
-2
-3
-4
averaged values
-5
1.6
1.7
1.8
1.9
2
2.1
log r/R(Saturn)
2.2
2.3
2.4
2.5
35
10.5
Small Particles have shorter decay time
than accreted particles
Protoplanet boundary
10
log Mcrit(particle) (gr)
Ca
Ga
9.5
Eu
Decay Time 104 years
Critical decay time: 10**4 yr
9
4.5
5
5.5
6
6.5
7
log accretion time (yr)
13.5
In the disk accreted particles can
survive to the viscous drift and to
the disk dissipation!
Protoplanet boundary
13
log Mcrit(particle) (gr)
Ca
Ga
12.5
Eu
Critical decay time: 10**6 yr
12
4.5
5
5.5
6
6.5
7
Decay Time 106 years
log accretion time (yr)
36
Conclusions
3-D hydrodynamical models reconcile the -disk
and the starved disk approach
The thermodynamical condition of the evolving
disk in which satellite started their formation
changed.
The dust survives most of these changes, evolves
gradually and accumulate in time.
Chemistry of the different satellites should reflect
these complex processes .
37
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