Development of Multiple Tidal Arms
in a Satellite Galaxy (    ), Andreas Burkert (University of Munich) !#" %$'&()*,+-/.0,1324657,89:;=</!>?A@$6B,CEDFEG6>?HI$
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ikjTI"}9!5783_!>?@I$6BC3D>?HI$ JK +_- _!>?@,832Ala`cx_,Ml9!"`<'5H]796a5X}7_V_]-/N_83NA9 &y (I>% m?$ Hn_^N8 !JoDKQAD_x/AQav pI- S^2%9 ]%qtr,+]3-3>!?_H]!IN sE]ES v,Fx/GQa6-3>?83HNApQa- 2S ly Ü!-  SÍW)lÐËBM * T_a)A"}x` v9* qu A>Í1 ?Ð %] H,$ JAJA%] wAa^3+_"x V,Oax- 4 -/S ,8NI^E9E!9mEF N~5c%7 5D,j7 "9 u ju] u >y;=?z~B<Hx%{%] Qyw,6zA+_[ [ x-GG_;],8|< VIA{-9/y5M6z97_[ y%]G%y]E@zaV8 x%cW}QAD ~!D}QÇ4,~6Ç,-,A´_M ´`V_]_l-`EScRMDl 4I;=Í x<'9A Ð|lEITIUW-%VE&5(7A;=</=9:M:>?A@I$!BACEDE.AlEÜ_Vac'Í xDa`!Ð 9lE t -%9 &( ]%t 9 I^Et ]LAJAM'K]
Hx%"}Qa9%] 5w,-%7>+_?"- H6_%] &wA!(+_& ("- 8  y dI Í xQlEY ËÐûa] ¾pJ¿,K 8N x%p~Q_BM !" ~>| x%?QH_6D,%] l,9w,Ü+_- "- S >^?6H!N~N &c%J(=D,K 9%M x:QA,D,]L,4,JM'-K]ELAV_x%M'Q- ]E!S V>8Y - ? S]ba<RQa- !Ha`L![ _GTI]UWVIVEc%&D (u)>*?l H_J%] K w,x/+_Q"- I`!N!l`Üc/-,DMB4,,%- }<R~!QaÇ - ,S %´ )l ;=<'9'57 ju ;=j < {yz*57;=B< ! E#]!57 j u %%] yza"9 x/IQ_TR_49 ~ EM  !t ]_] `Jc'K Dx%4Q !}>~!?QÇ H,;,%´ %] =< )* 96=Í í M6ä ö% í ÉæÐ  X ú Dñ ]!,. 8A 9
+_-AL,MRNA;~- S j57N_6>?@_$6B,CEDE&()*,+_-,M 39:AE2AlFG,!>?HI$ JK +DE%% &r(_9/>)E?*,}HI+_~!QÇ$- JSAKL3%´ +_TI"- )U}8V* }3_5Q% 7!Dj´8_u7R% N;=JA A< {"8a~yÍ í zx/ä Qö[ í DGÉ Ð5]X ú 7ñV]!c%. D,]!+_E- V S >}?~!HÇ N,J´_K M x/Q~)*- IS >$,?S`Hy c¡£¢k¤ªªªªªª(e.g., Piatek & Pryor 1955)(e.g., Belokurov et al. 2006)
2SDSSJ1049+5103

¡¥

3t = 134

t = 192

0G.C.

first leading
first trailing-200

second leading
second trailing(Barnes & Hut 1986)-400-200kpc

km s200] >g?QHa ] ! _QPÇa-]_Ä Ca_6Ç£Hau´]]  P!Qx!Qa-  S [#`4 _E;#9!Q5<67>?j?vAH_Çx%Q$IJD ´ K _+I-,8[ M'pP9 M y]E~V|A,cWVDE8 > Xp_qFÇaÁI] ]_IC~E- Q->_S ?H~]
%Qa_- 6AÄ Ç)A£* ´_]_M gQ]A9W F S
V_9-A5M'7 9 jy u ,;8< )* [,8p]
M | A^EVA4 S400

^Q_  ¦u 2: (a) «¬ ­ ®
%¯% }~ EfC%J 5 ° %«¬ %Q
yQz
QG EsIE{yz G@ }~  EJ
E±^_  %u (b) « ­ E® ¯%   fCEJ 5 ° E}~ a²|{yz G@ % x %J(b)03000
first arms

trailing arm

trailing arm

E -40

Jz 2500
leading arm

-80

0100

200

2000

3000leading arm

first arms

0100200300

3000
second arms

trailing arm

trailing arm

E -40

Jz 2500
leading arm-800100200

2000

3000leading arm

second arms

0100200

300

3000
third arms

trailing arm

trailing arm

E -40

Jz 2500
leading arm

-80

0100

200

2000

300

leading arm

third arms

0100200time(a) Ms / Mg = 7.11x10 -6

0.10

first arms
0.08

0.10

second arms
third arms

0.06

f(Jz)

leading arms

f(E)

0.05

0.04

trailing arms
0.02
0.00
80-60-40
E-20

0.00
1800

02000

2200
Jz

2400

2600

(b) Ms / Mg = 1.78x10 -5(b) Ms / Mg = 1.78x10 -5

0.10

0.10

f(J z)

f(E)

kpc

0.00
1800-80-60-40-20

2000

2200

2400Jz

02600

2800

30002800

3000

E(c) Ms / Mg = 3.55x10 -5$ ³3Á~^ED5,7,AI¦ ,A~ a
?M'H,I9]%$a«J,)*,%Q~_~-x!M&3( Ed¶_}´]!~6[r,ÇGsAV]´'K,¾¾_43¿D!µÌ¾uÍ W¿> ÐµÌÍ <· Ð SRd !] JK x:Qa-%>?H9  t 9
p3Iq t ]J6¾K ¿Ix%Qa$^!-'D>?4,H_-AQL,MRµÌÍ NRÐAEM ;~µÌ-Í <S· ÐÎ83:

2

0.05

0.05

0.00-100300time(a) Ms / Mg = 7.11x10 -6)

km s0(a)softening length

1/20

third leading
third trailingt = 66(2)

Plummersatellite body200(1)(, Ç ô í ä~Ñ 2Aô  í ð äa] ÑAC-%57!&()*]TE-/>?H!C3D 2 JlS ^9%]!Z;=[</! 25lA7'FV3>G,,?!8A>@_9/2?$6HB$ JK +_-  9L3_T_UWVE>?z2{l!]TEA-'" FE_G,S+ 2y!S >ly ?EHEAV IJFE9!KG,5A!$'7,>A?_HI8$ 9x 9!>?HN JK x/Q~- ST ¦ ^_  ( ; V1: kpc,
  kpc, V U kpc)
!#%H
EJ%@
 |
§Q¨
©ª aO

400

Willman 1(c) Ms / Mg = 3.55x10 -5

30.10

first arms
0.08

second arms
0.10

third arms

0.06
f(E)

1

leading armsf(Jz)trailing arms

0.04

0.05

0.02
0.00
-120

1-100

-80

-60

-40

-20

00.00
1800

20

2000

2200

2400Jz

E2600

23411

Willman 1
53

Barnes, J., & Hut, P., 1986, Nature, 324, 446
Belokurov, V., et al., 2006, ApJ, 637, L29

Montuori, M., et al., 2006, submitted to ApJ (astro-ph/0611204)

2(a) Ms / Mg = 4.44x10 -5(a) Ms / Mg = 4.44x10 -5

0.10

first arms
0.08

Willman, B., et al., 2006, submitted to AJ (astro-ph/0603486)

third arms

0.10

f(E)

trailing armsf(J z)

0.04
0.05

trailing arms

leading arms

0.02

30.00
-20-1000.00
800

10E1000

1200

1400Jz(b) Ms / Mg = 1.48x10 -5(b) Ms / Mg = 1.48x10 -5

0.10
0.08
0.10

0.06
f(E)

f(Jz)

0.04
0.05

4:u( )

30.02
0.00-50-40-30-20-1000.00
1400

1600

1800

E

2000

2200

2400

2600

2800

3000

Jz

(c) Ms / Mg = 8.89x10 -6(c) Ms / Mg = 8.89x10 -6

0.08

0.10

0.06

f(E) 0.04

f(J z) 0.05

0.02

0.00
-80

-60

-40
E

-20

00.00
2000

2200

2400
Jz

712

Change in galaxy mass (Ms = 10 M )Change in satellite mass (Mg = 1.13x10 M )11(a)(b)(Ms /M g )1/3

(Ms /M g )1/3|<∆E>|/EC|<∆E >|/E C
leading arms

leading arms

trailing arms

trailing arms
first arms

first arms
second arms

second arms

third arms

third arms

10-1

1

1010-1

1

Ms /Mg712

Change in galaxy mass (Ms = 10 M )-1Change in satellite mass (Mg = 1.13x10 M )-13x10(c)(d)(Ms /M g )1/3|<∆J >|/JC
1010
Ms /Mg

3x10(Ms /M g )1/3|<∆J >|/JC

-1

10-1

leading arms

leading arms

trailing arms

trailing arms

first arms

first arms

Odenkirchen, M., et al., 2001, ApJ, 548, L165
Piatek, S., & Pryor, C., 1995, AJ, 109, 1071

second arms

third arms

leading arms

0.06

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!¾¿.µÌÍ <· Ð S3d !_] x/JQaK -/x/>Qa?-/H_>Q?µÌÍH_WÐ9 MµÌÍ  t · Ðå9 8,p qt ]J3K ¾A¿a$,^ED_4I-,L_M%N,;I- S

first arms

second arms

second arms

second arms

third arms

third arms
-2-2

3x10

110Ms /Mg

3x10

110Ms /Mg

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%u%«. " %D}~ Q J D % ¶%JE}~ Q
J  J%!# %e´ G %e }I%~  a ¸Q¹ a 8%e º»}~ EJ QJX2