Formation of The Jovian and SaturnianSatellite Systems

Takanori Sasaki, Shigeru Ida (Tokyo Tech)Glen R. Stewart (U. Colorado)

Jovian System v.s. Saturnian System

Titan

Io Europa Ganymede Callisto

rocky rocky icy icy, undiff.

icy, undiff.

mutual mean motion resonances (MMR)

only one big body

www.sciencemag.org SCIENCE VOL 327 12 MARCH 2010 1339

PERSPECTIVES

Interesting Times for Marine N2O

OCEANS

Louis A. Codispoti

Changes in ocean chemistry could exacerbate

global warming by raising the atmospheric

concentration of nitrous oxide, a potent

greenhouse gas.

Although present in minute concentra-tions in Earth’s atmosphere, nitrous oxide (N

2O) is a highly potent green-

house gas ( 1). It is also becoming a key factor in stratospheric ozone destruction ( 2). For the past ~400,000 years, changes in atmospheric N

2O appear to have roughly paralleled changes

in CO2 and to have had modest impacts on cli-

mate ( 1), but this may change. Human activi-ties may be causing an unprecedented rise in the terrestrial N

2O source ( 2). Marine N

2O

production may also rise substantially as a result of eutrophication, warming, and ocean acidification. Because the marine environ-ment is a net producer of N

2O, much of this

production will be lost to the atmosphere, thus further intensifying N

2O’s climatic impact.

Crucial to this discussion are the relation-ships between dissolved oxygen levels and their variability, and the production of N

2O.

Under well-oxygenated conditions, microbes produce N

2O at low rates as a side product

during the fi rst step of nitrifi cation (NH4+→

NO2

−). At low oxygen concentrations, nitri-fi ers may also reduce NO

2− to N

2O, a pro-

cess referred to as nitrifier denitrification ( 3). Overall, the fraction of N

2O produced by

nitrifi ers relative to NO2− increases as oxygen

concentrations decrease, such that the yield at ~1% oxygen saturation is ~20 times greater than at 100% saturation ( 4).

These relationships favor high N2O pro-

duction by nitrification in hypoxic waters (O

2 1% and 30% saturation). Under sub-

oxic conditions (O2 1% saturation), deni-

trifying bacteria that use oxidized nitrogen to support respiration can be net producers or net consumers of N

2O. N

2O concentrations

are high at the boundaries and low in the cen-ter of quasi-stable suboxic zones ( 5). These zones account for 0.1 to 0.2% of the ocean volume ( 3), but are surrounded by much larger volumes of hypoxic waters (~10% of the ocean volume). Studies of N

2O produc-

tion in regions containing suboxic waters suggest that these regions are strong net pro-ducers ( 5, 6).

Generally, then, N2O yields are high when

O2 concentrations are low. N

2O production

rates should be particularly high in shallow suboxic and hypoxic waters, because respira-tion and biological turnover rates are higher near the sunlit waters where phytoplankton produce the fuel for respiration.

When denitrifiers switch from oxic to nitrogen respiration, they experience a lag in their ability to reduce N

2O to N

2. Con-

ditions are thus particularly favorable for N

2O production when suboxia occurs close

University of Maryland Center for Environmental Science, Horn Point Laboratory, Cambridge, MD 21613, USA. E-mail: codispot@umces.eduC

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dial ice-rock mixtures may display distinct degrees of internal differentiation. Impact-induced melting and/or intense tidal heating of Ganymede, locked in orbital resonances with the inner neighboring satellites Io and Europa, may have triggered runaway differ-entiation, but Callisto farther out from Jupiter remained unaffected ( 11). Titan’s interior must have stayed relatively cold and less dissipative to avoid tidal heating and damping of Titan’s notable orbital eccentricity ( 12). Prolonged accretion times farther away from their prima-

ries and gradual unmixing of ice and rock may also play a role for incomplete differentiation of icy satellites.

References and Notes

1. L. Iess et al., Science 327, 1367 (2010). 2. R. Jaumann et al., in Titan from Cassini-Huygens, R.H.

Brown, J.-P. Lebreton, J. Hunter Waite, Eds. (Springer, New York, 2009), pp. 75–140.

3. R. M. C. Lopes et al., Icarus 186, 395 (2007). 4. J. Lunine et al., in Titan from Cassini-Huygens,

R. H. Brown, J.-P. Lebreton, J. Hunter Waite, Eds. (Springer, New York, 2009), pp. 35–59.

5. G. Tobie et al., Nature 440, 61 (2006). 6. G. Schubert et al., in Jupiter, F. Bagenal, T. Dowling,

W. McKinnon, Eds. (Cambridge Univ. Press, Cambridge, 2004), pp. 281–306.

7. F. Sohl et al., J. Geophys. Res. 108, 5130 (2003). 8. A. D. Fortes et al., Icarus 188, 139 (2007). 9. O. Grasset et al., Planet. Space Sci. 48, 617 (2000). 10. H. A. Zebker et al., Science 324, 921 (2009). 11. A. C. Barr, R. M. Canup, Nat. Geosci. 3, 164 (2010). 12. F. Sohl et al., Icarus 115, 278 (1995). 13. Supported by the Helmholtz Association through the

research alliance “Planetary Evolution and Life.” I am grateful to M. Weiland and R. Ziethe for technical support and additional computations supplementing construction of the fi gure.

Inside Titan. Global gravity fi eld and shape data suggest that rock and ice are incom-

pletely separated within Titan’s deep interior, overlain by a water ice/liquid shell that

may contain a cold water-ammonia ocean (blue), sandwiched between high-pressure

water ice below (gray) and a fl oating ice/clathrate shell above (white). The three smaller

images show that the extent of separation of rock from ice would depend on the rock

density that is predominantly affected by the amount of silicate hydration.

10.1126/science.1186255

Published by AAAS

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Circum-planetary disk models

Actively-Supplied Accretion Disk

49

Figure 2. An inflow-produced accretion disk. Inflowing gas and solids initially achieve centrifugal force balance across a region extending from the surface of the planet out to distance ro, and solids accrete into satellites throughout this region. The gas spreads viscously onto the planet and outward to a removal distance, rd, with rd >> ro. The half-thickness of the gas disk is H ~ c/Ω, where c is gas sound speed and Ω is orbital frequency, with H/r ~ 0.1. After Canup and Ward, (2002).

rd

ν = αcH

Inflow (gas + small solids)

ro

H

RP

Figure 8: Left: Idealization of the initial ! and assumed photospheric T profiles for the circumjoviansubnebula. The re-constituted mass of Io, Europa, and Ganymede determine the mass of the opticallythick inner disk, while the mass of Callisto is spread out over the optically thin outer disk. Ganymede lies

just inside the centrifugal radius rc, while Callisto lies outside a transition region that separates the innerand outer disks. The transition region between in the inner and outer disks is assumed (see text). Thetemperature is set to agree with the compositional constraints of the Galilean satellites (e.g., Lunine and

Stevenson, 1982; Mosqueira and Estrada, 2003a,b), which implies a Jovian luminosity of ! 10!5 L", fora planetary radius of ! 1.5 " 2 RJ consistent with planet formation models (Hubickyj et al., 2005; Fig.

1a). Upper left: Critical mass at which migration stalls as a function of Jupiter radii for various !-profilesusing both vertically thermally stratified (solid and dotted curves), and vertically isothermal models (bolddashed curve). Gas drag is included. The solid curve corresponds to the minimum mass model, while the

dotted and dashed curves correspond to the SEMM model. The short-dashed curve is a constant ! andT model. Lower right: Migration and growth models for proto-Ganymede. The full sized Ganymede is

evolved backward in time from the location where it opens a gap to the point where it reaches embryosize (! 1000 km) for a SEMM disk. Two models for growth are used. Solid curve: linear growth model.Dotted curve: growth rate proportional to the disk surface density. Growth is consistent with the limited

migration of Ganymede. See Mosqueira and Estrada, 2003b for detailed descriptions.

in the local solar nebula.Once a significant fraction of the solids in the disk have aggregated into objects large enough to

decouple from the gas (radii R ! 10"100 m) and settle to the disk midplane, they drift inward dueto gas drag at di!erent rates, leading to further “drift-augmented” accretion. In the weak turbulenceregime, the ratio of the sweepup time (which assumes most of mass of the disk is initially in smallparticles entrained in the gas) to gas drag is

!sweep

!gas#

4"sR

3"p"v/

4"sRvK

3CD"("v)2! CD#

"

"p< 1, (7)

quite generally in the inner (and outer) disk. Here, "p is the average solids density in the midplane,

30

“Minimum Mass” Disk[Canup & Ward, 2002] [Mosqueira & Estrada, 2003]

Msatellites/Mplanet ~ 10-4

[Canup & Ward, 2006]

Difference b/w Jovian and Saturnian satellite systems

[Sasaki et al., 2010; Ogihara et al., 2012]

× Only for Jovian system

× Unrealistic initial conditions[Tanigawa et al., 2012 JpGU]

× Difficult to make satellites(?)[Miguel, Sasaki & Ida, in prep.];

Circum-planetary disk models

Actively-Supplied Accretion Disk

49

Figure 2. An inflow-produced accretion disk. Inflowing gas and solids initially achieve centrifugal force balance across a region extending from the surface of the planet out to distance ro, and solids accrete into satellites throughout this region. The gas spreads viscously onto the planet and outward to a removal distance, rd, with rd >> ro. The half-thickness of the gas disk is H ~ c/Ω, where c is gas sound speed and Ω is orbital frequency, with H/r ~ 0.1. After Canup and Ward, (2002).

rd

ν = αcH

Inflow (gas + small solids)

ro

H

RP

“Minimum Mass” Disk[Canup & Ward, 2002] [Mosqueira & Estrada, 2003]

Msatellites/Mplanet ~ 10-4

[Canup & Ward, 2006]

Difference b/w Jovian and Saturnian satellite systems

[Sasaki et al., 2010; Ogihara et al., 2012]

× Only for Jovian system

× Unrealistic initial conditions[Tanigawa et al., 2012 JpGU]

× Difficult to make satellites(?)[Miguel, Sasaki & Ida, in prep.];

Canup & Ward (2002, 2006)

Actively-Supplied Accretion Disk Uniform mass infall Fin from the circum-stellar disk Infall regions: rin < r < rc (rc ~ 30Rp) Diffuse out at outer edge: rd ~ 150Rp Infall rate decays exponentially with time Temperature: balance of viscous heating and blackbody radiation Viscosity: α model

49

Figure 2. An inflow-produced accretion disk. Inflowing gas and solids initially achieve centrifugal force balance across a region extending from the surface of the planet out to distance ro, and solids accrete into satellites throughout this region. The gas spreads viscously onto the planet and outward to a removal distance, rd, with rd >> ro. The half-thickness of the gas disk is H ~ c/Ω, where c is gas sound speed and Ω is orbital frequency, with H/r ~ 0.1. After Canup and Ward, (2002).

rd

ν = αcH

Inflow (gas + small solids)

ro

H

RP

Overview of Sasaki et al. (2010)

Circum-Planetary Disk Satellite Formation

Difference of Jovian/Saturnian systems is naturally reproduced.

Adding New Ideas　　Disk boundary conditions

Canup & Ward, 2002, 2006Satellites formed in c.-p. diskActively-supplied accretion diskSupplied from circum-stellar disk→ Analytical solution for T, Σ

Ida & Lin, 2004, 2008, 2010Analytical solution for

accretion timescaletype I migration timescaletrapping condition in MMR

The New Ideas

Jupiter

Saturn

Difference of “inner cavity” is from Königl (1991) and Stevenson (1974)Difference of gap conditions is from Ida & Lin (2004)

inner cavity

no cavity

opened up gap in c.-s. disk　→ infall to c.-p. disk stop abruptly

did not open up gap in c.-s. disk → c.-p. disk decay with c.-s. disk

Jovian System

inner cavity@corotation radius

outer proto-satellitegrow faster & migrate earlier

Because the infall mass flux per unit area is constant,the total mass flux to satellite feeding zones is larger in outer regions.

Jovian System

Type I migration ishalted near the inner edge

The outer most satellite migrates and sweeps upthe inner small satellites.

Jovian System

Proto-satellites grow & migrate repeatedlyThey are trapped in MMR with the innermost satellite

MMR

Jovian System

Total mass of the trapped satellites > Disk mass→ the halting mechanism is not effective

　　　 → innermost satellite is released to the host planet

Jovian System

after the gap opening → c.-p. disk deplete quickly

Saturnian System

No inner cavity outer proto-satellitegrow faster & migrate earlier

Saturnian System

Large proto-satellites migrate from the outer regionsand fall to the host planet with inner smaller satellites

fall to Saturn

Saturnian System

c.-p. disk depleted slowly with the decay of c.-s. disk

Monte Carlo Simulation (n=100) Parameters: Disk viscosity (α model) Disk decay timescale Number of “satellite seeds”　

= 103 102

in = 3 106 5 106

N = 10 20

yr

Results: Distribution of the number of large satellites

number of produced satellites

Tota

l cou

nt o

f the

cas

e

Jovian Saturnian

1 20 6543 7 1 20 430

20

40

20

40

60

80

0

Results: Distribution of the number of large satellites

number of produced satellites

Tota

l cou

nt o

f the

cas

e

Jovian Saturnian

1 20 6543 7 1 20 430

20

40

20

40

60

80

0

inner two bodies: rocky& outer two bodies: icy

icy satellite& large enough (~MTitan)

Results: Properties of produced satellite systems

Saturnian

Titan

Jovian

rocky componenticy component

Galilean Satellites

1e-6

a/Rp

Ms/M

p

1e-5

1e-4

1e-3

0 10 20 30 0 10 20 30

Results: Properties of produced satellite systems

Saturnian

Titan

Jovian

rocky componenticy component

Galilean Satellites

1e-6

a/Rp

Ms/M

p

1e-5

1e-4

1e-3

0 10 20 30 0 10 20 30

inner three bodiesare trapped in MMR

the largest satellitehas ~90% of total satellite mass

Summary

• Jovian Satellite System v.s. Saturnian Satellite System Difference of size, number, location, and compositions

• Satellite Accretion/Migration in Circum-Planetary Disk Canup & Ward (2002, 2006) + Ida & Lin (2004, 2008, 2010)

• The Ideas of Disk Boundary Conditions Difference of inner cavity opening and gap opening conditions

• Monte Carlo Simulations Difference of Jovian/Saturnian system are naturally reproduced

[Sasaki, Stewart & Ida (2010) ApJ 714, 1052]