=56>?@AB
Constraints on gas giant satellite formationfrom the interior states

1. Canup & Ward, 2006, Nature–of partially differentiated satellites“Gas-starved” disk model, CD#EFG

2. Barr & Canup, 2008, Icarus–“Gas-starved” model HIJKLMEFNOP•

Amy C. Barr, Robin M. Canup

3. Barr & Canup, 2010, Nat. Geosic.

Icarus 198 (2008) 163-177–

LHB impact model•!"#$%& '()*+,-M2.

PIA01802 (NASA/JPL)QR#STUVWTXWYZ[O, CD#EFG

2010/10/21 /0-12%318456789:;<

QR#STUVWYZ[O, CD#LHB

4. Barr et al., 2010, Icarus–2\3>NOP]^_^`Hab•

CD#EF cdLHBef• g\hijklmKnopq]rsgLM– tuCvwxyz{|}~•pq]€•• EF‚ƒ + „…†‡ˆ‰Šƒ < LMj}~‹Œ•Ž|}~•gLM• STUV 'ÏÐ#2410 km, -®¯°>YT±²LM.
– |}~•no• Ñ•Ò¡¢ & ÓÔÕ¿À (Anderson et al., 2001)– }~mÖ•Œ¯°• gLM>tuCGH••]‘’Œ“\j”•!
» –—[<^#EFC˜ !acc , ™š•Ž Td» ›œ•_`–ž^<]Ÿ '¡¢£¤>¥EF‚ƒ.
» ¦§¨„…†©ª(26Al)>¥«¬– STUV (-®¯°>YT±²LMWo}³H}~)» EFC˜ > 0.6 Myr , CAItuvw 4 Myr ´µHEF¶·– TX%'¸M>¹ºLMWo}³H}~.
» CAItuvw 2 Myr ´µHEF¶·• ™š>»¼C˜ ½dM¾™š>¿ÀÁÂ\ÃÄ³• ~ 300 km >gÒ× (Anderson et al., 2001)• noÌj•y (Zimmer et al., 2000)

Callisto (PIA01478, NASA/JPL)– ÒØ 50 ~ 200 km H
ÙÚ ~ ÙÛ km>Üœ{•y (ÝÞ, 2008)ÅÆÇ ]ÈÉH‹ŒKÊ
=56{ËnoÌ]ÍÎ

• TX 'ÏÐ#765 km, ¸Mß{2àáH)â•LM.
– |}~•no\}~mK¯°• ÓÔÕãäå œæKgÒ×>Üœ
46 ± 24 km ~ 158 ± 23 km(Anderson & Schubert, 2007)(Iess et al., 2007)

Rhea(PIA12648, NASA/JPL/Space Science Institute)|}~H•ŒKÊ>çè

|}~H•ŒKÊ>çè

• EF‚ƒ + „…†‡ˆ‰Šƒ < g>éê• EF‚ƒ + „…†‡ˆ‰Šƒ < g>éê– EFHãŒë• "Tacc ËEFC˜ !acc Hì•"Tacc!acc, critical– ‰Šƒ Qrad Ëïðß>ñGòó)â•½d!acc >Øíî]••”•

Qrad ( t ) = Qrad (0) exp(" # t )QradNo!

éêLMjõHtuœæŒòó
öFœæŒ Qrad Ë›œ•OKOK
tend, shorttstarttend, criticaltend, long

CAI>tuôDtime0|}~H•ŒKÊ>çè
(A)ùútu‹ŒÕl

(B)õHEFmKÕlHöFœæŒƒø

time“æz{>-1• EF‚ƒ + „…†‡ˆ‰Šƒ < g>éê"Tacc÷HEFmKÕlH
öFœæŒƒø• EFƒ]üÖ€•mKw… (ÓÔÁlýþPÿ< E vs g>!ƒ L = 3 x 10 J /kg)
gw

5– STUVË"#}~‹Œ : Eg, Callisto = 2 x 106 J/kg > Lw– TXË}~m••jW‰Šƒ]‚$‹Œ\}~m%Œ

"TaccõHtu‹ŒÕlEg, Rhea ~ 105 J/kg
2660
• Al & Fe&B{‚ƒmKw… (McKinnon, 2006)
tstartQrad+tend

tstartQrad+– STUVËCAItuvw 2.6 - 3 Myr´µHEF¶·

tend• -›ˆø™šNOPHIJKEFNOP (Squyres et al., 1988)
t0t0=="Tacc + Qrad

No"Tacc + Qrad

LM>tuôD]••”•
ûtstart >Øíî]••)OK– TXË ~ 103 yr {EFmÖ®}~m••– ÅÆê• Impactor'(>•Ž]ÍÎ
• „…‰Šƒ]«¬)#• -›ˆø™šNOP>*"† : ¦•!acc ½dSTUVË"#}~• EFƒ\‰Šƒ]+,«¬mKEFNOPË••=56>á³• EFNOP]b•ÖWgLM>ƒ-vw
LM>tuCG\EFC˜H••]‘’Œ.

LMEFC>?0~ Subnebula model >Š@ ~• 'AB.-›ˆø™šNOP (Lunine & Stevenson, 1982)– C•™šDŽWC•W¦•EFC˜ (103 - 104 yr)• ÅÆê#STUVW^_^`Ë"#}~ ½d¿À\EF• LMËxy\GH?@{tu– ./•ê• 01çèH Gas-starved disk model ]2b• EF‚ƒ\„…†‡ˆ‰Šƒ>+,]«¬• 34‹5âê

UV]«¬‹Œ\®J\›œú•ŒË#– )â• Impactor» Iº³J_KW300 - 500 km (Mosqueira & Estrada, 2003)• 'xy.Gas-starved disk model (Canup & Ward, 2006#´µCWNOP)– Solar nebulavw>LJúä\mKinflow– M•™šDŽWM•WN•EFC˜ (105 - 106 yr)– Impactor Ë›œ•\Ÿ
• /0HãŒ‚ƒËÒ¡¢£¤>¥• LMË¯°{EF ½dn°OPQ• LMß>ˆø}R]SúTx– EF6õ>CGz{mv75{â••– ›œ• Impactor» 1 m for Rhea

• Q8W9:HãŒƒ;<ËÍÎ• ¦§¨„…†=>>¥«¬=56'õW.

» ~ O(1) km or less for Callisto

LMEFC>?0EF‚ƒ>XF®ä~ ™š•Ž Td >XF®ä ~• Ò¡¢{>ë• = /0‚ƒ - „…YZ
[ LM>–—[<^ ][ ™š>–—[<^ ]" #[\DŽ" SB #Stefan-Boltzmann Ù2ui2 = v esc+ v"2 #/0_Ž

C p #]ƒ

!
!
!
!
!

T = T ( t ) #Ò¡¢•Žr = r( t ) #ÏÐMM=" acc #EF^
*CWNOP{ewæKî]f%!
!

2GM ( t )2v esc=#`a_Žr(t )v esc#Ííb,{>cQñ_Ž
2Td #™š•Ž'Impactor•Ž.
v" =" acc #EFC˜ (dT<–—[<^)!

!

™š¹n¢•Ž (K)ÝMß¸Mß

-›ˆø™š
(Lunine & Stevenson, 1982)

Gas-starved disk(CWNOP)• –—[<^< Td >gä%Œhi
– jí#-›ˆøNOPWØí#CWNOP + YUkMHãŒ gap tu• STUV : 70 K ~ 165 K (lmî : 100 K)• TX # 70 K ~ 250 K (lmî : 95 K)

EF‚ƒ>XF®ä ~ ozæŒ¤p ~„…†‡ˆ‰Šƒ>XF®ä
q26 ( t ) #É?ˆø"Kä>…ƒø

• ¾i>™šËqr³HÜ• (Semenov et al., 2003)• sQt¤p• u >EF^ # )â•LMHãŒÓÔvQ w xyz{HãŒvQ
• Impactor Ë›œ• ½dÒ¡¢£¤>¥‚ƒœæŒ
õòó75• |»\Q8HãŒƒ;<ËÍÎ%(% + acc ("'* , 30 km$62 $1 *'7& 2.6 #10 m s )&10 yr )– |»j}ú~˜U•<P ~– Q8>€•C˜ >mr#hi>‰l"26 #‰Š Ù!

t f ( r) #ÏÐ r >Šj

tuœæKôD!
!
• ÏÐ r >Òê{>ë•#C˜ t ËCAItuC]‚ \‹Œ• 26Al>¥]«¬:¦§¨=>>¹{Ëƒ„³H…ƒøj†•!
– 60Fe >100‡´j• EFmKõ®éB••vˆ ½d-)…ƒø®«¬3 x 106 yr for Rhea!~ 108 yr for Callisto(Zaranek & Parmentier, 2004)„…†‡ˆ‰Šƒ>XF®ä
q26 ( t ) #É?ˆø"Kä>…ƒø

Qrad

mr#hi>‰l"26 #‰Š Ù!

t f ( r) #ÏÐ r >Šj

tuœæKôD!
!
• ÏÐ r >Òê{>ë•#C˜ t ËCAItuC]"T ‚ \‹Œg>éê
• H2O*NH3>‹Œ•Ž (Leliwa-Kopystynski et al., 2002)#NH3>o•^• LMno>ƒÔ%'\ˆ•DŽ]Ÿ

.

final

• 26Al>¥]«¬:¦§¨=>>¹{Ëƒ„³H…ƒøj†•– 60Fe >100‡´j!
tstart tend• EFmKõ®éB••vˆ ½d-)…ƒø®«¬time(Hobbs, 1974)

ÁÂ#EF¹>STUV>•Ž}R>u•
EF¹EF¹ÁÂ#EF¹>STUV>•Ž}R>u•
EF¹• Td = 100 K• !acc = 0.4 Myr• tstart = 2.5 Myr• X=0‹Œ•Ž

EF¹‹Œ•Ž• Td = 100 K• !acc = 0.4 Myr• tstart = 2.5 Myr• X=0•“>“”•{ËSTUVË}~‹Œ•}~m••KÊ>–—[<^hi]•ÊŒ
•Td, !acc, tstart, X ]–Œ
– No NH3•Td ½dSTUV : 70 K ~ 165 K (lmî EF¹>•Ž}R: 100 K)– No NH3
EF¹>•Ž}R

TX # 70 K ~ 250 K (lmî : 95 K)
EF¹•!acc ½d10 yr (-›ˆøNOP) ~ 107EF¶·yr (solar nebula>life time)•tstart éBK½d0 yr (CAItu6õ) ~ ( subnebula >life time) - !acc
26Al jüÖ‘‰mKC>•X ½d0 ~ 0.3 (NH3>-)o•^, Schubert et al.,•Ž}R'C•’í.
1986)
EF¹3EF¶·éBK

26Al jüÖ‘‰mKC>•Ž}R'C•’í.

— ˜™HËNH3Ëšzä†ú••\«’wæÖ•Œ•›M¹'¿À. ~ 0.007 (Bockelee-Morvan et al., 2004)
EF6õ>•Ž}R•ý`9—œU*•P<ž¹'¿À. ~ 0.01 (Waite et al., 2009)

EF6õ>•Ž}R•STUVgÒ×¹'å

STUV>ƒ- ~ EFC˜WEF€•C˜%ì•† ~H2O>‹Œ•Ž

tstart = 2 Myr
tstart = 3 Myr
tstart = 4 Myr•. ~ 0.05 (Spohn & Schubert, 2003)

STUVj}~m••–—[<^hi“”Ç #•NH3•m•¥>!ƒËÍÎ•éêH¦mKCê{}~mK\§26Al>-)…ƒø

]oÊKEFõ>•Ž}RTd = 100 K
tstart = 5 Myr(1) !acc < 0.6 Myr {ËEFƒ&B{}~‹Œ(2)¤•ú\®CAItuvw
3.9 Myr ´µHSTUVËEF]¶·mK!acc < 106 yr {Ë}~‹ŒÕlj†•

0.6 x 106

3.9!acc > 3 x 106 yr {ËNH3j¨Œ\…

EFƒãä‰ŠƒjŸ½noòóC•>Õl®
½Q8]¡â¢‹”•†( Q8>€•C˜ ~ 108 yr )• tend,c : STUVj}~‹Œ£ä£ä>EF¶·C˜– “æãäù•\}~‹Œ•ãäN•EFC˜•ãä©•tuCG]"e\‹ŒTd = 100 K : STUV±²{>™š•ŽTG : YZ[O±²{>™š•Ž

YZ[O\STUV>ªä}B

TX>ƒ- ~ EFC˜WEF€•C˜%ì•† ~•26Al>-)…ƒø

]oÊKEFõ>•Ž}ROK

tstart = 4 Myr

OKOKTd = 95 K

tstart = 5 Myr!acc < 105 yr {Ë• «•¬- : YZ[OË}~mÖWSTUVË|}~•¬-

tstart = 2 Myr– TG jjjŒòó¬-Ë®jŒtstart = 3 Myr• YZ[O\STUV]ªä}BŒ–—[<^hij•y“”Ç #•¥>!ƒËÍÎ
³CŽ : tend,c (Myr)Zice : gÒ×>Üœ
¤•ú\®CAItuvw
1.9 Myr ´µHTXËEF]¶·mKNH3j¨Œ\…
•ãäN•EFC˜•ãä©•tuCG•ãäM•™š•Ž]"e\‹Œ½¯oòóC•!acc > 106 yr {Ë‰ŠƒjŸ– }~Ž>¯•Ë•°³{šŒ”•†jšŒTXj}~m••–—[<^hiEFƒjŸ½noòóC•75#/0HãŒ‚ƒ– ´4>“”{Ë”›œ•” impactor \¤p~ 1 m for Rhea, 4 km - 800 m for Callisto , 30 - 6 m for Ganymede– “”µ¶» ¯vw>·¸^ ~ z{\LM>/0HãJÖ¹ºæŒ^» z{G»>/0^ ~ z{\LM>/0^– z{Ë"#l(‹Œ\Ÿ ½dimpactor size >-)î]‘’Œ– ©•/0_Ž
ui < 0.5 km/s for Rhea , ui < 2.0 km/s for Callisto• M_Ž ½d/0HãŒ)¼tuË¢â•• (Pierazzo et al., 1997)• shock heating j}ú½œ !heat vs |»j}ú½œ !cool– TX\YZ[O{Ë !heat < !cool– STUV{Ë !heat > !cool(Gault & Heitowit, 1963; O’Keefe & Ahrens, 1982)• /0HãŒ‚ƒjnoz{}ú”•†jšŒz\Ê• CW model HIJKLMEFNOP– EF‚ƒ \ ¦§¨„…†©ª>‰Šƒ ]«¬– ›œ• impactor ¤p• STUV>EFC˜Ë 0.6 Myr ´j{šŒ• STUVËCAItuvw ~ 4 Myr ´µHEF]¶·mK– [\³•M¾™š> life time ~ 3 Myr– Solar nebula >¾¹Ë%CAItuvw 4 Myr ´µ{šJK”•†]¿À– EFõ>STUV>ƒ-Hs•ÖËÁÂ•êjÃŒ• N§¨„…†©ª ½dQ8j¢“ŒË#» Q8HãJÖƒ]Äj)•BæÅWSTUVË}~mÖmz%» ƒD>}Â ½dQ8]Æ•– Solid-state convection ?