Origin of the Different Architecturesof the Jovian and Saturnian Satellite 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

mutual mean motion resonances (MMR)

only one big body(~95% of total satellite mass)

Questions; Motivation of this study

Satellites’ size, number, and locationJovian: 4 similar mass satellites in MMRSaturnian: only 1 large satellite far from Saturn

Among Galilean satellitesIo & Europa: rocky satelliteGanymede & Callisto: icy satelliteCallisto: undifferentiated

What is the origin of the different architecture?

What is the origin of the satellites’ diversity?

Overview of this study

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

Ida & Lin, 2004, 2008, in prep.Analytical solution for

accretion timescaletype I migration timescaletrapping condition in MMR

Overview of this study

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, in prep.Analytical solution for

accretion timescaletype I migration timescaletrapping condition in MMR

Overview of this study

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

Satellite Formation

Difference of Jovian/Saturnian system is naturally reproduced

Adding New Ideas　　Disk boundary conditions

Ida & Lin, 2004, 2008, in prep.Analytical solution for

accretion timescaletype I migration timescaletrapping in MMR

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

Canup & Ward (2002, 2006) +α

[K]

[g/cm2]

[/years]

[g/cm2]

!

Td "160Mp

MJ

#

$ %

&

' (

1 2

)G5 *106 yrs

#

$ %

&

' (

+1 4r

20RJ

#

$ %

&

' (

+3 4

!

dfd

dt= 0.029

Mp

MJ

"

# $

%

& '

(2 3f

100

"

# $

%

& '

(1)G

5 *106 yrs

"

# $

%

& '

(1r

20RJ

"

# $

%

& '

3 4

Temperature

Gas density

Dust density

Increasing rateof dust density

Inflow flux

!

Fin

= Fin(t = 0)exp "t #

in( ) [g/s]

Overview of this study

Circum-Planetary Disk Satellite Formation

Difference of Jovian/Saturnian system 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, in prep.Analytical solution for

accretion timescaletype I migration timescaletrapping in MMR

Ida & Lin (2004, 2008, in prep.)

Timescales of satellite’s accretion & type I migration

Resonant trapping width of migrating proto-satellites

btrap = 0.16�

mi + mj

M⊕

�1/6 �vmig

vK

�−1/4

rH [m]

[years]

[years]!

" acc =M

˙ M #10

6fd

$1%ice

$1 &

&p

'

( ) )

*

+ , ,

1 3

M

10$4

M p

'

( ) )

*

+ , ,

1 3

M p

MJ

'

( )

*

+ ,

$5 / 6

-

10

'

( )

*

+ ,

2

r

20RJ

'

( )

*

+ ,

5 4

!

"mig =r

˙ r #10

5 1

fg

M

10$4

M p

%

& ' '

(

) * *

$1

M p

MJ

%

& '

(

) *

$1

r

20RJ

%

& '

(

) *

1 2

"G

5 +106

%

& '

(

) *

$1 4

These approximate analytical solutionsare based on the results of N-body simulations

Overview of this study

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, in prep.Analytical solution for

accretion timescaletype I migration timescaletrapping condition in MMR

The 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

Inner Cavity (Analogy with T-Tauri stars)

The rotation period distribution for the 173 stars in NGC 2264that lie within the specified color range appropriate to a spectralclass range of K4–M2 is shown in Figure 6. The 142 stars withperiods detected by Lamm et al. (2005) and appropriate values ofcolor were supplemented by 31 stars of quality 1 from Makidonet al. (2004). Reasons for not using quality 2 stars fromMakidonet al. (2004) are given by Lamm et al. (2005). A double-sidedKolmogorov-Smirnov (K-S) test shows that there is no signifi-cant difference between the distribution shown in Figure 6 andthe period distribution for stars in the same color range chosenonly from the sample of Makidon et al. (2004). It is also quiteclear that the period distributions of the ONC and NGC 2264stars in this mass range are not drawn from the same parentpopulation. A K-S test indicates that they are different at the99.7% confidence limit. While this contradicts the statement inMakidon et al. (2004) that there is no significant difference be-tween ‘‘Orion’’ and NGC 2264, it should be kept in mind that by‘‘Orion’’ those authors are generally not referring to the ONC butto the greater Orion association. In fact, as Figure 7b of Makidonet al. (2004) shows, their period distribution in NGC 2264 doesdiffer from that in the ONC at the 99% confidence limit when aK-S test is applied. Other features of this distribution have beendiscussed by Lamm et al. (2005) and include its bimodality, withpeaks near 1 and 4 days and the extended tail of slowly rotatingstars.

Rotation periods for the three MS clusters are shown inFigure 7. Combined, there are 148 stars, enough to reasonablydefine the distribution in a statistical sense. However, it is notentirely valid to simply combine these three clusters becausethey do not have the same period distributions, as is evident fromthe figures and confirmed by a K-S test. Clearly, ! Per has ahigher proportion of rapid rotators than do the other two clusters.From a strictly empirical point of view, this could be caused byan age difference between the clusters and a general slowdown ofrotation with age expected from wind losses, by mass-dependentrotation properties and a difference in the mass distributionsbetween the clusters, or by some other selection effect. It is easierto explore these issues in the j plane than in the P plane, so wepostpone the task of combining the data until after a discussion ofradii. The combined period distribution shown in the bottom

right panel of Figure 7 is not strictly valid given the real differ-ences between the clusters. However, because these differencesare relatively small and a main feature of the combined plot,namely, its evident bimodal nature, is worth noting, we show thedistribution as a didactic exercise.To summarize, even without correcting for the effects of ra-

dius, a few things are clear about the rotation distributions ofPMS and recently arrived MS stars of solar-like mass. First, thereare indications in Figure 7 that the rotational bimodality observedfor the ONC and NGC 2264 continues into the early MS phase;this becomes more evident when the j distributions are discussedbelow. Second, the period distributions are significantly differentfrom one another at each age step. And third, the trend is for moststars to spin faster as they age, exactly as one would expect ifangular momentum conservation were involved, at least to somedegree. To assess things more physically and quantitatively, weneed to examine j rather thanP. This, in turn, requires that we takeaccount of the stellar radii, a task to which we now turn.

3.2. Stellar Radii

Figure 8 shows the distribution of radii as a function of log TeAfor ONC stars in our periodic sample. As expected, there is awide scatter but no clearly evident trend with temperature. Alldata were taken directly from Hillenbrand (1997). Taken at facevalue, the wide range of radii would indicate stellar ages thatrange from about 0.1 to 10Myr (Palla & Stahler 1999). As notedpreviously, our position is that this scatter is dominated by errorsand that the actual age (and therefore radius) spread in the ONCis probably quite small. Since there is no clear trend of Rwith Teffvisible in the data, we adopt the median radius of R ! 2:09 R"for all stars. This is a more robust value than the mean (2:3# 0:1)because of the outliers at large radius. We show below thatadopting a single value of R ! 2:09 R", as opposed to individualradii, has no effect on the calculated j distribution other than totighten it. Since rotation periods are very accurately determinedand have a large range, while radii are evidently poorly deter-mined but expected to have a very small range, we argue that thisis the most appropriate procedure if the intention is to obtain thebest estimate of the j distribution of a cluster population.

Fig. 6.—Rotation periods for stars in NGC 2264 withR$ I values appropriateto the log TeA range of 3.54–3.67. The periods come from Lamm et al. (2004) for142 stars andMakidon et al. (2004) for 31 additional stars that were not detected asperiodic by Lamm et al. (2004). Only quality 1 stars from Makidon et al. (2004)were used. This distribution differs from the one shown in Fig. 5 for Orion at the99.7% confidence limit according to a K-S test.

Fig. 5.—Rotation periods for stars in the ONC with spectral types (K4–M2)appropriate to the log TeA range of 3.54–3.67. Periods are based on the work ofStassun et al. (1999) and Herbst et al. (2002) as summarized in the latter paper.Effective temperatures are assessed by spectral type, as reported by Hillenbrand(1997), and employ the calibration of Cohen & Kuhi (1979). One star, with aperiod of 35 days, lies outside the boundaries of this figure.

HERBST & MUNDT974 Vol. 633

spin period [day]

num

ber o

f sta

rs

Herbst & Mundt (2005)

Inner Cavity (Analogy with T-Tauri stars)

The rotation period distribution for the 173 stars in NGC 2264that lie within the specified color range appropriate to a spectralclass range of K4–M2 is shown in Figure 6. The 142 stars withperiods detected by Lamm et al. (2005) and appropriate values ofcolor were supplemented by 31 stars of quality 1 from Makidonet al. (2004). Reasons for not using quality 2 stars fromMakidonet al. (2004) are given by Lamm et al. (2005). A double-sidedKolmogorov-Smirnov (K-S) test shows that there is no signifi-cant difference between the distribution shown in Figure 6 andthe period distribution for stars in the same color range chosenonly from the sample of Makidon et al. (2004). It is also quiteclear that the period distributions of the ONC and NGC 2264stars in this mass range are not drawn from the same parentpopulation. A K-S test indicates that they are different at the99.7% confidence limit. While this contradicts the statement inMakidon et al. (2004) that there is no significant difference be-tween ‘‘Orion’’ and NGC 2264, it should be kept in mind that by‘‘Orion’’ those authors are generally not referring to the ONC butto the greater Orion association. In fact, as Figure 7b of Makidonet al. (2004) shows, their period distribution in NGC 2264 doesdiffer from that in the ONC at the 99% confidence limit when aK-S test is applied. Other features of this distribution have beendiscussed by Lamm et al. (2005) and include its bimodality, withpeaks near 1 and 4 days and the extended tail of slowly rotatingstars.

Rotation periods for the three MS clusters are shown inFigure 7. Combined, there are 148 stars, enough to reasonablydefine the distribution in a statistical sense. However, it is notentirely valid to simply combine these three clusters becausethey do not have the same period distributions, as is evident fromthe figures and confirmed by a K-S test. Clearly, ! Per has ahigher proportion of rapid rotators than do the other two clusters.From a strictly empirical point of view, this could be caused byan age difference between the clusters and a general slowdown ofrotation with age expected from wind losses, by mass-dependentrotation properties and a difference in the mass distributionsbetween the clusters, or by some other selection effect. It is easierto explore these issues in the j plane than in the P plane, so wepostpone the task of combining the data until after a discussion ofradii. The combined period distribution shown in the bottom

right panel of Figure 7 is not strictly valid given the real differ-ences between the clusters. However, because these differencesare relatively small and a main feature of the combined plot,namely, its evident bimodal nature, is worth noting, we show thedistribution as a didactic exercise.To summarize, even without correcting for the effects of ra-

dius, a few things are clear about the rotation distributions ofPMS and recently arrived MS stars of solar-like mass. First, thereare indications in Figure 7 that the rotational bimodality observedfor the ONC and NGC 2264 continues into the early MS phase;this becomes more evident when the j distributions are discussedbelow. Second, the period distributions are significantly differentfrom one another at each age step. And third, the trend is for moststars to spin faster as they age, exactly as one would expect ifangular momentum conservation were involved, at least to somedegree. To assess things more physically and quantitatively, weneed to examine j rather thanP. This, in turn, requires that we takeaccount of the stellar radii, a task to which we now turn.

3.2. Stellar Radii

Figure 8 shows the distribution of radii as a function of log TeAfor ONC stars in our periodic sample. As expected, there is awide scatter but no clearly evident trend with temperature. Alldata were taken directly from Hillenbrand (1997). Taken at facevalue, the wide range of radii would indicate stellar ages thatrange from about 0.1 to 10Myr (Palla & Stahler 1999). As notedpreviously, our position is that this scatter is dominated by errorsand that the actual age (and therefore radius) spread in the ONCis probably quite small. Since there is no clear trend of Rwith Teffvisible in the data, we adopt the median radius of R ! 2:09 R"for all stars. This is a more robust value than the mean (2:3# 0:1)because of the outliers at large radius. We show below thatadopting a single value of R ! 2:09 R", as opposed to individualradii, has no effect on the calculated j distribution other than totighten it. Since rotation periods are very accurately determinedand have a large range, while radii are evidently poorly deter-mined but expected to have a very small range, we argue that thisis the most appropriate procedure if the intention is to obtain thebest estimate of the j distribution of a cluster population.

Fig. 6.—Rotation periods for stars in NGC 2264 withR$ I values appropriateto the log TeA range of 3.54–3.67. The periods come from Lamm et al. (2004) for142 stars andMakidon et al. (2004) for 31 additional stars that were not detected asperiodic by Lamm et al. (2004). Only quality 1 stars from Makidon et al. (2004)were used. This distribution differs from the one shown in Fig. 5 for Orion at the99.7% confidence limit according to a K-S test.

Fig. 5.—Rotation periods for stars in the ONC with spectral types (K4–M2)appropriate to the log TeA range of 3.54–3.67. Periods are based on the work ofStassun et al. (1999) and Herbst et al. (2002) as summarized in the latter paper.Effective temperatures are assessed by spectral type, as reported by Hillenbrand(1997), and employ the calibration of Cohen & Kuhi (1979). One star, with aperiod of 35 days, lies outside the boundaries of this figure.

HERBST & MUNDT974 Vol. 633

spin period [day]

num

ber o

f sta

rs

Herbst & Mundt (2005)

weak magnetic field strong magnetic field → coupling with disk

No Cavity Cavity

If the magnetic torque is strongerthan the viscous torque, the diskwould be truncated at thecorotation radius

Inner Cavity (Analogy with T-Tauri stars)

JovianSaturnian

The rotation period distribution for the 173 stars in NGC 2264that lie within the specified color range appropriate to a spectralclass range of K4–M2 is shown in Figure 6. The 142 stars withperiods detected by Lamm et al. (2005) and appropriate values ofcolor were supplemented by 31 stars of quality 1 from Makidonet al. (2004). Reasons for not using quality 2 stars fromMakidonet al. (2004) are given by Lamm et al. (2005). A double-sidedKolmogorov-Smirnov (K-S) test shows that there is no signifi-cant difference between the distribution shown in Figure 6 andthe period distribution for stars in the same color range chosenonly from the sample of Makidon et al. (2004). It is also quiteclear that the period distributions of the ONC and NGC 2264stars in this mass range are not drawn from the same parentpopulation. A K-S test indicates that they are different at the99.7% confidence limit. While this contradicts the statement inMakidon et al. (2004) that there is no significant difference be-tween ‘‘Orion’’ and NGC 2264, it should be kept in mind that by‘‘Orion’’ those authors are generally not referring to the ONC butto the greater Orion association. In fact, as Figure 7b of Makidonet al. (2004) shows, their period distribution in NGC 2264 doesdiffer from that in the ONC at the 99% confidence limit when aK-S test is applied. Other features of this distribution have beendiscussed by Lamm et al. (2005) and include its bimodality, withpeaks near 1 and 4 days and the extended tail of slowly rotatingstars.

Rotation periods for the three MS clusters are shown inFigure 7. Combined, there are 148 stars, enough to reasonablydefine the distribution in a statistical sense. However, it is notentirely valid to simply combine these three clusters becausethey do not have the same period distributions, as is evident fromthe figures and confirmed by a K-S test. Clearly, ! Per has ahigher proportion of rapid rotators than do the other two clusters.From a strictly empirical point of view, this could be caused byan age difference between the clusters and a general slowdown ofrotation with age expected from wind losses, by mass-dependentrotation properties and a difference in the mass distributionsbetween the clusters, or by some other selection effect. It is easierto explore these issues in the j plane than in the P plane, so wepostpone the task of combining the data until after a discussion ofradii. The combined period distribution shown in the bottom

right panel of Figure 7 is not strictly valid given the real differ-ences between the clusters. However, because these differencesare relatively small and a main feature of the combined plot,namely, its evident bimodal nature, is worth noting, we show thedistribution as a didactic exercise.To summarize, even without correcting for the effects of ra-

dius, a few things are clear about the rotation distributions ofPMS and recently arrived MS stars of solar-like mass. First, thereare indications in Figure 7 that the rotational bimodality observedfor the ONC and NGC 2264 continues into the early MS phase;this becomes more evident when the j distributions are discussedbelow. Second, the period distributions are significantly differentfrom one another at each age step. And third, the trend is for moststars to spin faster as they age, exactly as one would expect ifangular momentum conservation were involved, at least to somedegree. To assess things more physically and quantitatively, weneed to examine j rather thanP. This, in turn, requires that we takeaccount of the stellar radii, a task to which we now turn.

3.2. Stellar Radii

Figure 8 shows the distribution of radii as a function of log TeAfor ONC stars in our periodic sample. As expected, there is awide scatter but no clearly evident trend with temperature. Alldata were taken directly from Hillenbrand (1997). Taken at facevalue, the wide range of radii would indicate stellar ages thatrange from about 0.1 to 10Myr (Palla & Stahler 1999). As notedpreviously, our position is that this scatter is dominated by errorsand that the actual age (and therefore radius) spread in the ONCis probably quite small. Since there is no clear trend of Rwith Teffvisible in the data, we adopt the median radius of R ! 2:09 R"for all stars. This is a more robust value than the mean (2:3# 0:1)because of the outliers at large radius. We show below thatadopting a single value of R ! 2:09 R", as opposed to individualradii, has no effect on the calculated j distribution other than totighten it. Since rotation periods are very accurately determinedand have a large range, while radii are evidently poorly deter-mined but expected to have a very small range, we argue that thisis the most appropriate procedure if the intention is to obtain thebest estimate of the j distribution of a cluster population.

Fig. 6.—Rotation periods for stars in NGC 2264 withR$ I values appropriateto the log TeA range of 3.54–3.67. The periods come from Lamm et al. (2004) for142 stars andMakidon et al. (2004) for 31 additional stars that were not detected asperiodic by Lamm et al. (2004). Only quality 1 stars from Makidon et al. (2004)were used. This distribution differs from the one shown in Fig. 5 for Orion at the99.7% confidence limit according to a K-S test.

Fig. 5.—Rotation periods for stars in the ONC with spectral types (K4–M2)appropriate to the log TeA range of 3.54–3.67. Periods are based on the work ofStassun et al. (1999) and Herbst et al. (2002) as summarized in the latter paper.Effective temperatures are assessed by spectral type, as reported by Hillenbrand(1997), and employ the calibration of Cohen & Kuhi (1979). One star, with aperiod of 35 days, lies outside the boundaries of this figure.

HERBST & MUNDT974 Vol. 633

spin period [day]

num

ber o

f sta

rs

Herbst & Mundt (2005)

weak magnetic field strong magnetic field → coupling with disk

No Cavity Cavity

Estimates of Cavity Opening

Königl (1991) magnetic field for the magnetic coupling accretion rate 10-6MJ/yr → ～ a few hundred Gauss

Stevenson (1974) proto-Jovian magnetic field ～1000 Gauss

<

Cavity

Present Saturnian magnetic field < 1 Gauss ≒ late stage of Saturnian satellite formation

<

No Cavity

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”　

α = 10−3 − 10−2

τin = 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

(Ida, presentation)

Analogy with Saturnian System

(Ida, presentation)

Analogy with Jovian System

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, in prep.)

• 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

• Application to Solar/Super-Earths Systems