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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
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