3-Dimensional dynamics of the galactic bulge
Soto Vicencio, M.H.
Citation
Soto Vicencio, M. H. (2010, March 24). 3-Dimensional dynamics of the galactic bulge.
Retrieved from https://hdl.handle.net/1887/15120
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CHAPTER 5
Stellar proper motions in three off-axis galactic bulge fields
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7I@5H=CBG K<=7< =BJC@J98 H<9 7CA6=B5H=CB C:+ * =A5;9G 5B8 5F7<=J5@ C6G9FJ5
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Table 5.1 +IAA5FM C:C6G9FJ5H=CBG
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"I@M × × + / =H<9F98
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Figure 5.2 (FCD9F ACH=CBG 69:CF9 5B8 5:H9F H<9 7CFF97H=CB =B / :CF =9@8 @IGH9F GH5FG <5J9 5@@ 5 G=B;@9 J9@C7=HM K<=7< H<9F9:CF9 6=5G H<9 F9@5H=J9 N9FCDC=BH K<9B 75@7I@5H=B;
H<9 DFCD9F ACH=CB C: 6I@;9 GH5FG ,<9 @5HH9F GH5FG AIGH H<IG 69 9L7@I898 :FCA H<9 F9:9F9B79 :F5A9 IG98 HC 75@7I@5H9 6I@;9 DFCD9F ACH=CBG Top row, DFCD9F ACH=CBG =Bpixels yr−1 69:CF9 H<9 7CFF97H=CB :CF / 7<=D =B =9@8 K<9F9 6@57? 8CHG 5F9 6I@;9 GH5FG 5B8 ;F9M 8CHG 5F9 H<CG9 7@5GG=98 5G 7@IGH9F GH5FG Second row, DFCD9F ACH=CBG =B D=L9@Gμx5B8μy 5G 5 :IB7H=CB C:
H<9x − y 7CCF8=B5H9G 69:CF9 H<9 7CFF97H=CB Third row, G5A9 5G G97CB8 FCK 6IH 5:H9F 5DD@M=B;
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J=898 IG =B 588=H=CB K=H< H<9 H<F99 @CK :CF9;FCIB8 9LH=B7H=CB 9@8G 7@CG9 HC H<9 ;5@57H=7 A=BCF 5L=G 5@F958M DF9G9BH98 =B #* 5B8 # ,KC 5GD97HG C:H<9 GH 9DC7< 85H5 5F9 BCH =895@ = H<9 9LDCGIF9G 5F9 5@@ @CB; GC H<5H K9 75BBCH A95GIF9 DCG=H=CBG :CF H<9 6F=;<H GH5FG == H<9 9LDCGIF9G 5F9 BCH 8=H<9F98 K<=7< @=A=HG CIF 56=@=HM HC 6I=@8 5 DC=BHGDF958 :IB7H=CB (+ AC89@ !B CF89F HC 5HH9BI5H9 H<9 9::97H C: H<9 IB89FG5A
D@=B; C:H<9 (+ K9 7<CG9 H<9 / @H9F K<=7< <5G H<9 K=89GH 5B8 H<9F9:CF9 @95GH IB89FG5AD@98 (+
G =H K5G 5@F958M A9BH=CB98 H<9 C6G9FJ5H=CBG :CF CIF H<F99 9@8G <5J9 7CA6=B98
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G97CB8 9DC7< C6G9FJ5H=CBG K9F9 8=H<9F98 =B CF89F HC A5L=A=N9 577IF57M 5B8 9BGIF9 H<5H 9FFCFG =B H<9 DFCD9F ACH=CB K9F9 BCH 8CA=B5H98 6M H<9 G97CB8 G9H C:9LDCGIF9G ,56@9 GIAA5F=N9G CIF C6G9FJ5H=CB =B 6CH< 9DC7<G :CF CIF H<F99 9@8G
!H <5G 699B DFCJ9B H<5H :CF 5 K=89 F5B;9 C: F95@=GH=7 (+ DFC@9G H<9 σ IB79FH5=BHM
=B H<9 79BHFC=8 C:5 GH9@@5F =A5;9G C::I@@ K=8H< 5H <5@:A5L=AIAF W HM 5B8 G=;B5@ HC BC=G9 F5H=CS/N =G ;=J9B 6M 0.7 × F W HM/(S/N) #* !B H<9 75G9 C:CIF DFCD9F ACH=CBG K<9F9 FGH 9DC7< C6G9FJ5H=CBG K9F9 D9F:CFA98 =B / ( F W HM 0.12”
=B / 5 GH5F 89H97H98 5H σ 75B 69 79BH9F98 K=H< 5 DF97=G=CB C: 4.2 mas ,<9F9:CF9
5 H=A9 65G9@=B9 C: MF =B CIF 9@8G K9 <5J9 MFG C:65G9@=B9 M=9@8G 5B 577IF57M C:0.6 mas yr−1 K<=7< 7CFF9GDCB8G HC23 km s−1 5H H<9 8=GH5B79 C:H<9 6I@;9 C:56CIH
?D7 'B H<9 CH<9F <5B8 CIF G97CB8 9DC7< C6G9FJ5H=CBG K<=7< <5J9 699B 8=H<9F98
5B8 <5J9 5 <=;<9F F9GC@IH=CB 5B8 9J9B H<CI;< H<9M DFCJ=89 5 <=;<9F 577IF57M H<5B H<CG9 C:H<9 FGH 9DC7< 75B BCH =ADFCJ9 CIF DFCD9F ACH=CB DF97=G=CB 69MCB8 H<9 @=A
=HG C:H<9 FGH 9DC7< C6G9FJ5H=CBG K<=7< =B 588=H=CB 5F9 IB8=H<9F98 ,<IG H<9 GD5H=5@
J5F=5H=CBG C:H<9 (+ K=H<=B H<9 + / =A5;9 B89FGCB #=B; <5J9 BCH 699B 7CBG=89F98 =B CIF 5B5@MG=G ,<9G9 (+ GD5H=5@ J5F=5H=CBG =B + =:=;BCF98 75B DFC8I79 10% C:9FFCF =B 7CF9 D<CHCA9HFM K<=7< =G F98I798 K<9B 5 @5F;9F 5D9FHIF9 =G H5?9B !B H<9 75G9 C:5GHFCA9HF=7 A95GIF9A9BHG H<9 9::97HG 5F9 5H H<9 D=L9@ @9J9@ 0.001”
:CF + K<=7< =G B9;@=;=6@9 7CBG=89F=B; H<9 9FFCF =BHFC8I798 6M H<9 FGH 9DC7< &9K A95GIF9A9BHG =B7@I8=B; CB@M + A95GIF9A9BHG K=@@ =B7@I89 H<=G 9::97H =B CIF 5GHFC
A9HF=7 A95GIF9A9BHG =B H<9 :IHIF9
( *'( * %',!'& % +-* % &,+
B89FGCB #=B; <5J9 89G7F=698 5 DFC798IF9 :CF 577IF5H9 5GHFCA9HF=7 A95GIF9
A9BHG IG=B; +, / ( 5B8 GI6G9EI9BH@M ID85H98 H<9G9 :CF + / B89FGCB
#=B; 'F=;=B5@@M H<9G9 H97<B=EI9G <5J9 699B 89G=;B98 HC KCF? K=H< 6CH< 9DC7<G 8=H<9F98 K<9F9 5 7CAACB (+ AC89@ =G IG98 :CF 5@@ H<9 8=H<9F98 9LDCGIF9G ,<=G (+
AIGH 69 7CBG=GH9BH K=H< 5@@ H<9 9LDCGIF9G 5B8 =G IG98 HC C6H5=B H<9 79BHFC=8G C:957<
GH5F ,<IG :CF CIF IB8=H<9F98 FGH 9DC7< C6G9FJ5H=CBG K9 <5J9 D9F:CFA98 GCA9 J5F=
5H=CBG HC H<9 CF=;=B5@ B89FGCB #=B; F97=D9 !B CF89F HC =ADFCJ9 H<9 79BHFC=8 89H9FA=B5H=CB CIF A9H<C8 89H9FA=B9G 5 (+ 6M 957< 9LDCGIF9 GH5FH=B; :FCA 5B 5B5@MH
=75@ AC89@ ,<=G AC89@ 7CBG=GHG C:5 5IGG=5B (+ AI@H=D@=98 6M 5 DC@MBCA=5@ K<9F9 H<9 BIA69F C: H<9 7CADCB9BHG :CF H<9 DC@MBCA=5@ 577CIBHG :CF H<9 K=B;G C: H<9 (+
5B8 CH<9F G97CB85FM :95HIF9G !B 957< 9LDCGIF9 H<9 (+ AC89@ GH5FHG :FCA H<=G AC89@
69=B; HH98 HC H<9 6F=;<H9GH IBG5HIF5H98 GH5FG =B H<9 =A5;9 H<9 DFC79GG H<9B =H9F
5H9G IG=B; 5 <=;<9F CF89F DC@MBCA=5@ K=H< 5B FC6IGH CIH@=9F 7F=H9F=CB K<=7< F9B9G H<9 G9@97H=CB IBH=@ =H 7CBJ9F;9G 9H5=@G C:H<9 H97<B=EI9 75B 69 :CIB8 =B #* 5B8 K=@@ BCH 69 F9D95H98 <9F9
'B79 H<9 (+ <5G 699B 75@7I@5H98 :CF 957< 9LDCGIF9 K9 75B 89H9FA=B9 H<9 DFCD9F ACH=CBG ,<9G9 5F9 C6H5=B98 GH5FH=B; :FCA 5 A5GH9F =A5;9 K<=7< <5G 699B ;9B9F5H98 6M
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.3 Top row, DFCD9F ACH=CB 8=GHF=6IH=CB :CF / ( =B =9@8 Second and third row, DFCD9F ACH=CB 8=GHF=6IH=CB CB =B8=J=8I5@ :F5A9G C: / (
7CA6=B=B; 5@@ H<9 FGH 9DC7< 9LDCGIF9G =B / @H9F ,<9B H<9 A5GH9F =A5;9 =G IG98
=B ' !& HC 89H97H GH5FG K=H< IL9G CJ9F15σ K<=7< DFC8I79 5 A5GH9F @=GH C:GH5FG ,<9 A5GH9F @=GH =G IG98 HC 89H97H H<9 G5A9 GH5FG =B 5@@ H<9 9LDCGIF9G :CF 957< 9LDCGIF9 H<9 A5GH9F 7CCF8=B5H9G 5F9 IG98 5G =B=H=5@ ;I9GG HC H<9 GH5F DCG=H=CB !B H<9 75G9 C:DFCD9F ACH=CB K=H< / ( =B 5@@ H<9 9DC7<G 5 G=AD@9 @=B95F HF5BG:CFA5H=CB =G GI:7=9BH HC HF5BG:CFA H<9 A5GH9F 7CCF8=B5H9G HC 957< 9LDCGIF9 9 ; #* CF CIF G97CB8 9DC7<
+ / =A5;9G K9 <5J9 IG98 5 H<=F8 CF89F DC@MBCA=5@ HF5BG:CFA5H=CB HC 577CIBH
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
Figure 5.4 +5A9 5G =; 6IH :CF H<9 =9@8
:CF H<9 ;9CA9HF=7 8=GHCFH=CBG :CIB8 =B + CF 957< GH5F 5 (+ H =G H<9B 7CADIH98 HC
;=J9 5 69GH HH=B; DCG=H=CB =B 957< 9LDCGIF9
/=H< H<9 DCG=H=CBG 75@7I@5H98 :CF 957< 9LDCGIF9 K9 75B H<9B 9LHF57H H<9 DFCD9F AC
H=CBG ,<9 DFCD9F ACH=CBG AIGH 69 G9D5F5H98 :FCA H<9 F9GH C: H<9 9::97HG =B7@I898 K=H<=B H<9G9 DCG=H=CBG ,<9G9 =B7@I89 5 ;9B9F5@ HF5BG:CFA5H=CB H<5H A5DG H<9 DCG=
H=CBG C:957< 9LDCGIF9 HC H<CG9 C:H<9 F9:9F9B79 :F5A9 H<9 DFCD9F ACH=CBG H<9 5J9F5;9 DCG=H=CB F9G=8I5@ 5G 5 :IB7H=CB C: D=L9@ D<5G9 :CF 957< =A5;9 K<=7< =G GI6HF57H98 :FCA 957< A95GIF9A9BH 5B8 5J9F5;9 F9G=8I5@ DCG=H=CB 5G 5 :IB7H=CB C: H<9 RH< FCKS 9::97H
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.5 +5A9 5G =; 6IH :CF H<9 =9@8
B89FGCB #=B; ,<=G DFC79GG =G =H9F5H=J9 =H DFC8I79G 5 DFCD9F ACH=CB GC@IH=CB
=B 957< @CCD :CF 957< GH5F ,<9 GC@IH=CB =G C6H5=B98 :FCA 5 K9=;<H98 @=B95F @95GHGEI5F9
H K=H< F9>97H=CB C:CIH@=9FG K<9F9 H<9 K9=;<HG 5F9 9GH=A5H98 :FCA H<9 IL 89H97H98 /9 AIGH GHF9GG H<5H H<9G9 5F9 relative DFCD9F ACH=CBG H<9M 5GGIA9 H<5H H<9 5J9F5;9 ACJ9A9BH C:5@@ H<9 GH5FG =B H<9 9@8 =G N9FC 6GC@IH9 DFCD9F ACH=CBG KCI@8 F9EI=F9 5 G9@97H=CB C:9LHF5;5@57H=7 GCIF79G 5G 5 F9:9F9B79 =B H<9 G5A9 9@8 ,<9 N9FCA95B 5GGIADH=CB KCF?G K9@@ :CF 6I@;9 9@8G 6IH 6F95?G 8CKB K<9B A5BM GH5FG <5J9 H<9 G5A9 D97I@=5F J9@C7=HM +I7< =G H<9 75G9 C:H<9 =9@8 K<9F9 A5BM C:H<9 6F=;<H GH5FG
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
Table 5.2 (FCD9F %CH=CB =GD9FG=CBG
=9@8 <=D & σl σb σlb rlb
mas yr−1 mas yr−1 mas2 yr−2
=9@8 ( ± ± ± ± / ± ± ± ± / ± ± ± ± / ± ± ± ±
@@ ± ± ± ±
=9@8 ( ± ± ± ± / ± ± ± ± / ± ± ± ± / ± ± ± ±
@@ ± ± ± ±
=9@8 ( ± ± ± ± / ± ± ± ± / ± ± ± ± / ± ± ± ±
@@ ± ± ± ±
&CH9rlb=G H<9 (95FGCB 7CFF9@5H=CB 7C9:7=9BH
=B H<9 A5GH9F @=GH 7CFF9GDCB8 HC H<9 ;@C6I@5F 7@IGH9F & % ,C A5?9 A5HH9FG KCFG9 H<9 A95B DFCD9F ACH=CB =G 8=::9F9BH :CF H<9 :CIF 7<=DG C: / ( G=B79 H<9 7@IGH9F GH5F :F57H=CB 89D9B8G CB DCG=H=CB !B CF89F HC F9ACJ9 H<=G 9::97H K9 <5J9 8=G75F898 H<9 7@IGH9F GH5FG =B 957< =A5;9 :FCA H<9 A5GH9F @=GH /9 <5J9 8CB9 H<=G G9@97H=CB 6M A95BG C:H<9 DFCD9F ACH=CBG 75@7I@5H98 =B7@I8=B; 5@@ H<9 GH5FG =B H<9 9@8 H<9 7@IGH9F GH5FG 75B H<IG 69 95G=@M =89BH=98 5B8 F9ACJ98 H5?=B; 58J5BH5;9 C:=HG GA5@@ 8=GD9FG=CB 'B79
=89BH=98 H<9 DFCD9F ACH=CBG <5J9 699B F975@7I@5H98 =B7@I8=B; CB@M BCB7@IGH9F GH5FG
=B K<=7< =G F95GCB56@9 IG9 H<9 5GGIADH=CB C:5J9F5;9 ACJ9A9BH N9FC ,<=G DFC798IF9
=G =@@IGHF5H98 =B ;IF9 :CF CB9 C: H<9 7<=DG / !B 5 G=A=@5F K5M K9 F9D95H98 H<9
@5HH9F DFC798IF9 :CF 7@IGH9F GH5FG =B CF89F HC 9L7@I89 6I@;9 7CBH5A=B5H=CB 5G =H =G G<CKB
=B§
&$1+!+
'IF DFCD9F ACH=CB F9GI@HG 75B 69 C6G9FJ98 =B ;IF9G 5B8 DFCD9F ACH=CB 8=GD9FG=CBG 5B8 BIA69FG D9F 9@8 5F9 G<CKB =B H56@9 C@CFA5;B=HI89 8=5;F5AG :CF H<9 H<F99 9@8G K<=7< =B7@I89 H<9 DFCD9F ACH=CB =B:CFA5H=CB 5@GC 5DD95F =B ;IF9G
5B8 ,<9 FGH =B8=75H=CB C:H<9 7CFF97H D9F:CFA5B79 C:CIF A9H<C8 5DD95FG
=B ,56@9 K<=7< 8C9G BCH G<CK 5BM 9J=89B79 C:5 G=;B=75BH J5F=5H=CB CF =B7CBG=G
H9B7M C:H<9 ?=B9A5H=7G 69HK99B H<9 / 5B8 ( 7<=DG 5G =H KCI@8 69 9LD97H98 =B 5 F9@=56@9 DFCD9F ACH=CB 89H9FA=B5H=CB +=A=@5F@M K9 B8 H<5H H<9 8=GHF=6IH=CBG C:H<9
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.6 =BB98 % G C: =9@8 9@8(l, b) = (3.58◦, −7.17◦) K=H< Bfit > 5 ,<9 D5F5A9H9F Bfit7CFF9GDCB8G HC H<9 A=B=AIA BIA69F C:9LDCGIF9G HH98 6M H<9 DFCD9F ACH=CB GC@IH=CB C:
957< GH5F +CA9 D@CHG <5J9 699B 7C@CF7C898 IG=B; H<9 DFCD9F ACH=CBG 5B8 89F=J98 8=GD9FG=CBG Top row, left to right +H9@@5F 89BG=HM A95B @CB;=HI8=B5@ DFCD9F ACH=CB A95B @5H=HI8=B5@ DFCD9F ACH=CBG Bottom, left to right -B6=BB98 % @CB;=HI8=B5@ 8=GD9FG=CB =B DFCD9F ACH=CBG @5H=
HI8=B5@ 8=GD9FG=CB =B DFCD9F ACH=CBG
DFCD9F ACH=CB 8C BCH 8=::9F 8F5A5H=75@@M :FCA CB9 9@8 HC H<9 CH<9F H<=G 5;F99A9BH =B H<9 DFCD9FACH=CB 8=GHF=6IH=CB G99AG HC 9LH9B8 9J9B HC H<9 9@8G DF9G9BH98 =B #*
5B8 #I=>?9B <9B79:CFH< # 7@CG9 HC H<9 ;5@57H=7 A=BCF 5L=G 'IF H<F99 9@8G 5H DCG=H=J9 @CB;=HI89G G99A HC <5J9 5 GD<9F=75@ 8=GHF=6IH=CB K=H< BC G=;B=75BH 7CFF9
@5H=CB 69HK99Bl 5B8 b DFCD9FACH=CBG 5H H<9 G5A9 H=A9 σl 5B8 σb 5F9 G@=;<H@M 6=;;9F H<5B H<9 8=GD9FG=CBG :CIB8 =B A=BCF 5L=G 9@8G =B #* 5B8 # H FGH =BGD97H=CB K9 75B =B:9F HKC F95GCBG HC H<=G =B7F95G9 =B H<9 8=GD9FG=CBG 8I9 HC 5B =BHF=BG=7 =B7F95G9 577CF8=B;@M HC H<9 @C75H=CB C:H<9 9@8G 5B8 5@GC 8I9 HC H<9 <=;<9F 7CBH5A=B5H=CB 6M :CF9;FCIB8 8=G? DCDI@5H=CBG 5B8 H<9F9:CF9 5 897F95G9 C: H<9 HCH5@ BIA69F C: 6I@;9 GH5FG 89H97H98 /9 K=@@ HFM HC 8=G79FB 69@CK K<=7< C:H<9G9 9::97HG DF9J5=@ IG=B; H<9 5GG=GH5B79 C:H<9 % =B:CFA5H=CB
,<9 6=BB98 % G :CF H<9 H<F99 9@8G G<CK GCA9 8=GH=B7H=J9 :95HIF9G @@ H<9 9@8G 5F9 5::97H98 6M G5HIF5H=CB C: H<9 6F=;<H GH5FG =B H<9 FGH 9DC7< 85H5 K<=7< <5G @=A=H98 CIF DFCD9F ACH=CBG HC A5=B G9EI9B79 %+ GH5FG 69@CK H<9 HIFBC:: =9@8G =B #* CB H<9 CH<9F <5B8 7CIBH98 K=H< A5BM G<CFH9F 9LDCGIF9G K<=7< 5@@CK98 H<9A HC F957<
H<9 HIFBC:: 5B8 F98;=5BH 6F5B7< * G97CB8 7@95F :95HIF9 DF9G9BH =B H<9 H<F99
9@8G 5B8 =B GD=H9 H<9 8=::9F9B79 =B BIA69FG =G 5 ;F58=9BH D9FD9B8=7I@5F HC H<9 A5=B
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
Figure 5.7 =BB98 % G C: =9@8 9@8(l, b) = (2.91◦, −7.96◦) K=H< Bfit > 6
G9EI9B79 =B H<9 A95Bμl ,<=G ;F58=9BH K<=7< :CF 5 ;=J9B 7C@CF G<CKG 5 8F=:H HCK5F8 B9;5H=J9μl <5G 699B 5@F958M C6G9FJ98 =B H<9 79BHF5@ 9@8G =B #* =B CIF 9@8G <CK
9J9F <5G 5 BC=G=9F 5DD95F5B79 K<=7< K9 69@=9J9 =G 8I9 HC H<9 F98I798 GH5H=GH=7G ,<9
;F58=9BH 75B 69 9LD@5=B98 5G 5 G=;B5HIF9 C:H<9 FCH5H=CB H<FCI;< H<9 ;5@5LM 5G ;IF9
G<CKG :CF CB9 C: H<9 9@8G K<9F9 <=;< DCG=H=J9 μl G<CI@8 7CFF9GDCB8 A5=B@M HC :CF9;FCIB8 DCDI@5H=CB FCH5H=B; =B :FCBH C: H<9 6I@;9 !BH9F9GH=B;@M 5 G=A=@5F 6IH BC=G
=9F :95HIF9 5DD95FG =B H<9 A95BμbD5B9@G H<=G A=;<H 69 75IG98 F5H<9F 6M 5 7CA6=B5H=CB C:DFC>97H=CB 9::97H C:H<9 6I@;9 CF6=HG 5B8 7CBH5A=B5H=CB 6M H<9 8=G? K<=7< K9 KCI@8 69 56@9 HC 8=G79FB CB@M K<9B K9 5DD@M CIF +7<K5FNG7<=@8 AC89@ HC H<9G9 9@8G G =H
<5G 699B A9BH=CB98 =B DF9J=CIG GHI8=9G BCFA5@@M H<9 FCH5H=CB C:H<9 ;5@57H=7 6I@;9 =G 8=:7I@H HC C6G9FJ9 6975IG9 C: H<9 GHFCB; 7CBH5A=B5H=CB 6M 8=G? 5B8 <5@C 5B8 H<9 F5D=8 897F95G9 =B BIA69FG C:H<9 6I@;9 DCDI@5H=CB 5G CB9 ACJ9G C::5L=G
(FCD9F ACH=CB 8=GD9FG=CBG 89@=J9F 5 8=::9F9BH D=979 C: =B:CFA5H=CB =9@8 G<CKG 5 F5H<9F BC=GM 8=GHF=6IH=CB C:8=GD9FG=CB CJ9F H<9 A5=B G9EI9B79 =9@8 5B8 =9@8 8=GD9FG=CBG CB H<9 CH<9F <5B8 G<CK H<5H H<9 :5=BH9F A5=B G9EI9B79 GH5FG <5J9 7CAD5F5H=J9@M 5 GA5@@9F 8=GD9FG=CB H<5B 6F=;<H A5=B G9EI9B79 GH5FG ,<=G 75B 69 =BH9F
DF9H98 5G H<9 8=GH5B79 9::97H H<5H K9 KCI@8 9LD97H :CF :5=BH9F GH5FG @M=B; :5FH<9F 5K5M 5B8 H<5H H<9F9:CF9 G<CK GA5@@9F DFCD9F ACH=CB =H =G 5@GC 5 B=79 89ACBGHF5H=CB H<5H BC=G9 8C9G BCH 8CA=B5H9 CIF F9GI@HG
CBG=GH9BH@M K=H< H<9 5B5@MG=G C:#* 5B8 # K9 :C@@CK98 5 G=A=@5F DFC798IF9 HC 8=GG97H H<9 GH9@@5F DCDI@5H=CBG =B CIF 9@8G /9 <5J9 7<CG9B 5 7FI89 8=GH5B79 AC8I@IG 5G 5 =B8=75HCF C:H<9 8=GH5B79G HCK5F8 H<9 ;5@57H=7 6I@;9 H<9 EI5BH=HM % K<=7< 75B 69
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.8 =BB98 % G C: =9@8 9@8(l, b) = (9.86◦, −7.61◦) K=H< Bfit > 5
89B98 5G
M∗ = m814W − 3 × (m814W − m606W)
<5G 699B IG98 HC F9ACJ9 H<9 G@CD9 C:H<9 A5=B G9EI9B79 GH5FG =B H<9 % :CF CIF DFCD9F ACH=CB G5AD@9 ,<9 :57HCF AI@H=D@M=B; H<9 7C@CF =G =B #* 8I9 HC H<9 8=::9F9B79 =B @H9FG K=H< H<9 A=BCF 5L=G 9@8G +5;=HH5F=IG! 5B8 5589TG /=B8CK 6CH<
IG98 / 5B8 / @H9FG
=;IF9 =@@IGHF5H9G CIF 8=GH5B79 AC8I@IG % 5B8 =HG F9GD97H=J9 D<CHCA9HF=7 8=G
H5B79 5G 5 :IB7H=CB C: H<9 7C@CF :CF =9@8 !B CF89F HC C6H5=B 7CAD@9H9B9GG :FCA H<9 =B=H=5@ A5=B G9EI9B79 GI6G5AD@9 K<=7< =G 65G98 CB H<9 G9@97H=CB D9F:CFA98 =B # :CF 9@8 B95F & K9 <5J9 F9G9@97H98 5 B5FFCK9F 65B8 =B H<9 D<CHCA9HF=7 8=G
H5B79 B 5B5@MG=G HC H<9 5B;@9φlb H<9 9EI=J5@9BH HC H<9 J9FH9L 5B;@9 6IH =B H<9 lb J9@C7=HM D@5B9 =B 8=GH5B79 6=BG G<CKG 5 A=@8 =B7F95G9 C:H<=G 5B;@9 5G 5 :IB7H=CB C:
8=GH5B79 ,<9 5B;@9 φlb <5G 699B 75@7I@5H98 IG=B; 5B =H9F5H=J9 7@=DD=B; 5@;CF=H<A K<=7< F9>97HG GH5FG 69MCB8 3σ C:H<9 8=GHF=6IH=CB =B CF89F HC 5JC=8 7CBH5A=B5H=CB !B 588=H=CB K9 75@7I@5H98 H<9 +D95FA5B 7CFF9@5H=CB 7C9:7=9BH rS =B 957< 75G9 HC <5J9 5BCH<9F =B89D9B89BH A95GIF9A9BH C:H<9 7CFF9@5H=CB 69HK99Bμl5B8 μb FFCFG =Bφlb
7CA9 :FCA CCHGHF5D %CBH975F@C F95@=N5H=CBG K<9F9 ;IF9 G<CKG H<9 F9GD97H=J9 J9@C7=HM 9@@=DGC=8G :CF =9@8 FFCF 65FG =Bφlb 5B8 G=;B=75B79 C:rS 8C BCH =B8=75H9 5 F9@=56@9 G=;B=75BH 7CFF9@5H=CB 69HK99Bl 5B8 b :CF H<9G9 6=BG 5 F9GI@H H<5H <5G 699B F9D95H98 :CF =9@8 5B8 =9@8 +=A=@5F@M @5F?GCB 9H 5@ 5@GC @CC?98 :CF
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
Figure 5.9 %95B DFCD9F ACH=CBG 5B8 8=GD9FG=CBG 5G 5 :IB7H=CB C: H<9 D<CHCA9HF=7 D5F5@@5LM∗
:CF H<9 GI6G5AD@9 C: A5=B G9EI9B79 GH5FG =B =9@8 57< DC=BH 7CFF9GDCB8G HC GH5FG G=;B=75BH 7<5B;9G =B H<9 CF=9BH5H=CB C:H<9 J9@C7=HM 9@@=DGC=8 ;9B9F5H98 6M DFCD9F AC
H=CBG H<9=F =ADFCJ98 G5AD@9 C:+ DFCD9F ACH=CBG =B +5;=HH5F=IG! G<CK98 BC GI7<
HF5BG=H=CB
Figure 5.10 Left, (<CHCA9HF=7 D5F5@@5L % 5G 5 :IB7H=CB C: H<9 7C@CF =B =9@8 Middle, =G
H5B79 =B ?D7 5G 5 :IB7H=CB C: H<9 7C@CF Right, B;@9φlb 5G 5 :IB7H=CB C: 6=BB98 9EI5@
BIA69FG C:GH5FG <5J9 699B G9@97H98 D9F 6=B =B 588=H=CB H<9 +D95FA5B 7CFF9@5H=CB 7C9:7=9BH rS <5G 699B 75@7I@5H98 =B 957< 6=B HC <5J9 5 =B89D9B89BH 7CFF9@5H=CB A95GIF9A9BH 69HK99Bl 5B8b
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.11 .9@C7=HM 9@@=DGC=8G IG98 HC 75@7I@5H9 H<9 5B;@9φlb=B =9@8 B =H9F5H=J9 7@=DD=B;
5@;CF=H<A <5G 699B IG98 HC 9L7@I89 GH5FG 69MCB83σ *9>97H98 GH5FG 8IF=B; H<9 DFC79GG 5F9 9B7@CG98 6M GEI5F9G
5.4.1 NGC 6656 results
/9 <5J9 5@F958M A9BH=CB98 <CK CIF 9@8 K=H< H<9 <=;<9GH @5H=HI89 =9@8 <5G 699B G9D5F5H98 =B 5 7@IGH9F 5B8 6I@;9 7CADCB9BH 8IF=B; H<9 DFCD9F ACH=CB DFC798IF9 IG=B;
5 DIF9 ?=B9A5H=7 G9@97H=CB ,56@9 5B8 ;IF9 G<CK H<9 BIA69FG 5B8 8=GD9FG=CBG :CF H<9 7@IGH9F GH5FG @M=B; =B H<9 9@8 !B 5 ;@C6I@5F 7@IGH9F GI7< 5G & H<9 J9@C7=HM 8=GD9FG=CB C6G9FJ98 AIGH 69 J9FM GA5@@ =B CF89F HC A5=BH5=B 5 8MB5A=75@@M GH56@9 GHFI7HIF9 ,<=G ?=B8 C:69<5J=CIF 75B 69 7@95F@M C6G9FJ98 =B H<9 ;IF9
K<9F9 BC D5FH=7I@5F ;F58=9BH CF J5F=5H=CB =G F9J95@98 =B H<9 F9GD97H=J9 6=BB98 %
,<9 F58=5@ J9@C7=HM 8=GD9FG=CB :CF 7@IGH9F GH5FG =B H<=G 9@8 =B 7<5DH9F =G∼ 17 km s−1 K<=7< =G J9FM 7@CG9 HC H<9 =BHF=BG=7 9FFCF C:H<9 F58=5@ J9@C7=HM A95GIF9A9BHG +=A=@5F@M
K9 KCI@8 9LD97H H<5H ACGH C:H<9 DFCD9F ACH=CB 8=GD9FG=CB C6G9FJ98 =B H<=G GMGH9A =G 8I9 HC GMGH9A5H=7G 9FFCFG =B H<9 DFC798IF9 CBG9EI9BH@M K9 75B H9GH H<9 577IF57M C:
CIF DFCD9F ACH=CBG 6M A95GIF=B; H<=G C6G9FJ98 7@IGH9F 8=GD9FG=CB
,56@9 =B8=75H9G 5 8=GD9FG=CB =Bl 5B8 b C: ∼ 1.1 mas 5H H<9 / 7<=DG K<=7< 5H H<9 8=GH5B79 C:3.2 kpc +5AIG 9H 5@ :FCA H<9 +IB 7CFF9GDCB8G HC ∼ 17 km/sec &CH GIFDF=G=B;@M H<9 ( 8=GD9FG=CBG 5F9 56CIH HK=79 5G GA5@@ K<=7< K9 F9@5H9 K=H< 5 8=F97H 5 9::97H C:D=L9@ G=N9 =B H<9 A95GIF9A9BHG ,<9G9 8=GD9FG=CBG 5F9 5 7CBFA5H=CB C:H<9 EI5@=HM C:CIF A95GIF9A9BHG 5B8 D9F:97H@M G5H=G9G H<9 DF97=G=CB 57<=9J98 6M CIF F5
8=5@ J9@C7=H=9G =B H<9 G5A9 9@8 G99 7<5DH9F :CF 89H5=@G C:30 km/sec IFH<9FACF9
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
Figure 5.12 (FCD9F ACH=CB 8=GHF=6IH=CB :CF GH5FG 69@CB;=B; HC H<9 ;@C6I@5F 7@IGH9F &
C6G9FJ98 =B =9@8 ,<9G9 GH5FG <5J9 699B ?=B9A5H=75@@M G9D5F5H98 C:H<9 6I@;9 DCDI@5H=CB 8IF=B; H<9 DFCD9F ACH=CB DFC798IF9
K<9B D9F:CFA=B; 5 HKC8=A9BG=CB5@ 5IGG=5B H CJ9F H<9 DFCD9F ACH=CB 85H5 H<9 8=G
D9FG=CB 8FCDG =B H<9l 5B8 b 8=F97H=CBG HC ∼ 0.9 mas K<=7< 7CFF9GDCB8G HC ∼ 14 km/sec
@@ H<=G 7CBFAG H<9 F9@=56=@=HM C:CIF DFCD9F ACH=CB H97<B=EI9
5.4.2 A bulge sample kinematically selected
LHF57H=B; 5 DIF9 6I@;9 DCDI@5H=CB :FCA H<9 HCH5@ G5AD@9 =B7@I8=B; 8=G? GH5FG =G 8=:
7I@H ,<9 IB79FH5=B 6=B5FM :F57H=CB =B H<9 6I@;9 5B8 CJ9F@5DD=B; C: DCDI@5H=CBG =B H<9 % 5F9 GCA9 C:H<9 F95GCBG #* !B CF89F HC CJ9F7CA9 GI7< 8=:7I@H=9G 5B8 5@GC 7CBG=89F=B; H<9 GHFCB; 9J=89B79 C:5 FCH5H=CB ;F58=9BH H<FCI;< H<9 6I@;9 K<=7<
F9G9A6@9G H<9 ?=B9A5H=7G C:A=BCF5L=G 9@8G K9 HIFB HC H<9 ?=B9A5H=7G 5G CIF G9@97
H=CB 7F=H9F=CB #* 5B8 ACF9 F979BH@M @5F?GCB 9H 5@ <5J9 GI779GG:I@@M IG98 G=AD@9 7IHC::G =Bμl 5B8μb HC G9@97H 6I@;9 GH5F :CF A=BCF5L=G 9@8G 5 DIF9 6I@;9 DCD
I@5H=CB 75B 69 C6H5=B98 6M G9@97H=B; GH5FG K=H< B9;5H=J9 μl 5B8 AC89F5H9 |μb| ,<=G
Table 5.3 (FCD9F ACH=CB 8=GD9FG=CBG =B &
&
=9@8 & σl σb σlb rlb
(mas yr−1) (mas yr−1) (mas2 yr−2)
( ± ± ± ± / ± ± ± ± / ± ± ± ± / ± ± ± ±
@@ ± ± ± ±
+H9@@5F DFCD9F ACH=CBG =B H<F99 C::5L=G ;5@57H=7 6I@;9 9@8G
Figure 5.13 =BB98 % G :CF & GH5FG =B =9@8 (l, b) = (2.91◦, −7.96◦) ,<9 GH5FG
<5J9 699B G9@97H98 ?=B9A5H=75@@M IG=B; H<9 GA5@@ ?=B9A5H=7 8=GD9FG=CB C:H<9 7@IGH9F DFCD9F ACH=CBG
7IH DFC656@M 9L7@I89G GCA9 6I@;9 GH5FG CB H<9 B95F G=89 6=5G=B; H<9 GI6G5AD@9 HC :5F
G=89 C6>97HG 'B H<9 CH<9F <5B8 5 7CBG=89F56@9 8=G? 7CBH5A=B5H=CB :FCA H<9 :5F G=89 =G IB@=?9@M 8I9 HC H<9 @=B9 C:G=;<H C:CIF 9@8G
=;IF9 G<CKG H<9 F9GI@H C:H<9 G9@97H=CB =B CIF 9@8G K<9F9 H<9 56G9B79 C::95
HIF9G =B H<9 % 5G H<9 * 5B8 H<9 8=A=B=G<98 GH5H=GH=7G :CF CIF H<F99 C::5L=G 9@8G
<5J9 A589 8=:7I@H HC 7CBG=89F H<9A IB=JC75@@M 5G 5B C@8 DCDI@5H=CB 5G =H <5DD9BG =B H<9 A=BCF 5L=G 9@8G /9 5F9 BCH 56@9 HC 7<97? =:H<9 7IHG 5F9 9::97H=J9 =B F9ACJ=B; H<9
Figure 5.14 % G :CF GI6G5AD@9 C: ?=B9A5H=75@@M G9@97H98 GH5FG =B 957< 9@8 =B CIF GIFJ9M
F9M :5898 DC=BHG 7CFF9GDCB8 HC BCBG9@97H98 GH5FG
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
A5=B G9EI9B79 5B8 @5H9 HMD9 :CF9;FCIB8 DCDI@5H=CBG K=H<CIH H<9 5=8 C: 588=H=CB5@
=B:CFA5H=CB 5G DFCD9F ACH=CBG CK9J9F 7CBG=89F=B; H<9 F9G9A6@5B79 C: H<9 DFCD9F ACH=CB F9GI@HG =B H<9 C::5L=G 9@8G K=H< H<CG9 C: H<9 9@8G 5@CB; H<9 ;5@57H=7 A=BCF 5L=G K9 69@=9J9 H<9 G5A9 G9@97H=CB 7F=H9F=CB :CF 5 DIF9 6I@;9 DCDI@5H=CB G<CI@8 69 9:
:97H=J9 =B H<9 C::5L=G 9@8G K<9F9 H<9 56G9B79 C: CH<9F DCDI@5H=CBG =B H<9 % G =G A5=B@M 5 H97<B=75@ 8=:7I@HM F5H<9F H<5B 5B =BHF=BG=7 @57? C: :95HIF9G ,<=G A=;<H 69 GC@J98 =B H<9 :IHIF9 K=H< G<5@@CK9F 588=H=CB5@ C6G9FJ5H=CBG F957<=B; H<9 HIFBC:: 5B8
* F9;=CBG H H<9 G5A9 H=A9 6@I9 GHF5;;@9FG 75B BCH 69 89H97H98 8I9 HC H<9 G5A9 G5HIF5H=CB DFC6@9A
9B79 K9 8=GH=B;I=G< H<9 HKC DCDI@5H=CBG H<5H 7C9L=GH =B 957< % !BH9F9GH=B;@M
H<9 :57H H<5H H<=G ?=B9A5H=7 G9D5F5H=CB 69HK99B H<9 HKC DCDI@5H=CBG 6I@;9 5B8 8=G?
GH=@@ C77IFG 5H H<9 @CB;=HI89 C:CIF 9@8G ;=J9G IG 5 7@I9 56CIH H<9 F95@ 9LH9BH C:H<9 65F
!B H<9 :IHIF9 AC89@G 5G H<9 CB9 H<5H K9 89J9@CD98 IG=B; H<9 +7<K5NG7<=@8 H97<B=EI9
G99 7<5DH9F K=@@ =B7@I89 H<9 ?=B9A5H=7 =B:CFA5H=CB <9F9 9LDCG98 HC 8=G9BH5B;@9 H<9 57HI5@ 6I@;9 GHFI7HIF9 5B8 DFC8I79 5B =ADFCJ9A9BH =B H<9 65F6I@;9 D5F5A9H9FG ;9B
9F5H98 6M CIF AC89@ CB@M K=H< H<9 =B=H=5@ H<F99 A=BCF 5L=G9@8G
'&$-+!'&+
/9 <5J9 DF9G9BH98 =B H<=G 7<5DH9F ∼ 11000 B9K DFCD9F ACH=CBG :CF C::5L=G 9@8G C:H<9 ;5@57H=7 6I@;9 ,<9 F9GI@HG :CF H<9G9 H<F99 9@8G G<CK 5 F9A5F?56@9 5;F99A9BH K=H< H<9 F9GI@HG =B #* 5B8 # 5B8 H<IG GD95? C:5 6I@;9 K<9F9 H<9 ?=B9A5H=7G C6G9FJ98 =B H<9 79BH9F 5@CB; H<9 ;5@57H=7 A=BCF 5L=G 9@8G =G F9D95H98 HC GCA9 9LH9BH HC <=;<9F @CB;=HI89G /9 <5J9 7<97?98 H<5H H<9 FCH5H=CB C:H<9 6I@;9 =B GD=H9 C:H<9 F98I798 BIA69F C:DFCD9F ACH=CBG 6M 7CAD5F=GCB K=H< A=BCF 5L=G 9@8G =G GH=@@ J=G=6@9
=B CIF H<F99 9@8G K<=7< F957< l ∼ 10◦ H H<9 G5A9 H=A9 K9 <5J9 9LD@CF98 H<9 DCGG=6@9 7<5B;9G C:H<9 J9@C7=HM DFCD9F ACH=CB 9@@=DGC=8 =B H<9 9@8G 5G 5 :IB7H=CB C:H<9 8=GH5B79 G=A=@5F@M HC H<9 F9GI@HG C:@5F?GCB 9H 5@ K9 <5J9 BCH :CIB8 5 G=;B=75BH 7<5B;9 =B H<9 H=@H C:H<9 J9@C7=HM 9@@=DGC=8
@@ H<=G GI;;9GHG H<5H H<9 8MB5A=7G C:H<9 GH5FG 9J9B 5H H<9 @C75H=CB C:CIF 9@8G =G 8CA=B5H98 6M 6I@;9 CF6=HG ,<9 @5HH9F 5F;IA9BH =B HIFB GI;;9GHG =:K9 7CBG=89F H<9 5B=GCHFCD=9G DFC8I798 6M H<9 65F =B H<9 A=BCF 5L=G 9@8G G99 7<5DH9F H<5H K<5H K9 C6G9FJ9 G<CI@8 69 D5FH C:H<9 ;5@57H=7 65F ,<9 =ADCFH5B79 C:H<9 9LH9BH C:H<9 65F 75B 69 F9@5H98 K=H< H<9 9JC@IH=CB5FM GH5;9 C:H<9 6I@;9 9 ; CA69G H<5B5GGCI@5 5B8 H<IG H<9 DCH9BH=5@ C: H<=G =B:CFA5H=CB :CF ;5@57H=7 AC89@G =G =BJ5@I56@9 'IF +7<K5FNG7<=@8 AC89@ K=@@ =B7@I89 5@@ H<9 B9K 85H5 K9 <5J9 DF9G9BH98 =B H<9 B95F :I
HIF9 ,<=G K=@@ DFCJ=89 CIF AC89@ C:B9K =BG=;<HG =B H<9 57HI5@ 6I@;9 GHFI7HIF9 IBH=@
BCK DCCF@M 7CBGHF5=B98
=B5@@M K9 <5J9 DFCJ9B H<9 H97<B=75@ :95G=6=@=HM C: DFCD9F ACH=CBG A95GIF9A9BHG K=H< 5 A=LHIF9 C: 75A9F5G K=H< 8=::9F9BH ;9CA9HFM :CF FGH 5B8 G97CB8 9DC7< =9@8
K=H< =HG 7@IGH9F & <5G DFCJ=898 IG K=H< 5 8=F97H 5GG9GGA9BH C:H<9 577IF57M C:CIF DFCD9F ACH=CB DFC798IF9 K<=7< K=H< 5 8=GD9FG=CB C:0.9 mas CF ∼ 14 km/sec 7CFF9GDCB8G HC 5B 9L79@@9BH DFCC:C:H<9 DF97=G=CB 57<=9J98 6M CIF DFC798IF9
*9:9F9B79G
* * & +
B89FGCB " #=B; ! * (+(
B89FGCB " #=B; ! * (+(
B89FGCB " #=B; ! * +( #
B89FGCB " #=B; ! * "
B89FGCB " #=B; ! * + !BGHFIA9BH +7=9B79 *9DCFH 5H=ACF9 +,+7!
H<5B5GGCI@5 %&*+
5@@9FC + # %5HH9I77= 'F=;@=5 $ *=7< * %
9B>5A=B * 9H 5@ D" $
=BB9M " 9F<5F8 ' +H5F? 5@@M " -7<=85 # ! %&*+
CA69G !-+
@5F?GCB / 9H 5@ D"
I8KCFH< # % "
K9? 9H 5@ D"
B;@A5=9F ( 5B8 9F<5F8 ' %&*+
9@HN=B; + =@ACF9
I@@6F=;<H " ( %7/=@@=5A *=7< * % D"
C@HNA5B " /5HGCB % 5IA / =@@A5=F " FCH< " $=;<H * % $MB8G * 'T&9=@@ " "F "
#CNCKG?= + /C ONB=5? ( * %5C + +A=H< % +IA= , .9GHF5B8 / , 5B8 /MFNM?CKG?=
%&*+
#I=>?9B # %9FF=9@8 % * D" $
#I=>?9B # *=7< * % "
#I=>?9B # +( #
%=BB=H= !-+ %
%=BB=H= D"
*5HH9B6IFM & " %5C + 965HH=GH5 . ( +IA= , 9F<5F8 ' 89 $CF9BN= %&*+
*5HH9B6IFM & " %5C + +IA= , +A=H< % %&*+
*=7< * % "
*=7< * % D"
*=7< * % *9=HN9@ CK5F8 2<5C D" $
%7/=@@=5A *=7< * % D"+
+5AIG & #F5JHGCJ . (5J@CJ % @75=BC 5B8 $=@@9F / ++
+58@9F % *=7< * % ,9FB8FID % " +IA= , 9H 5@ %&*+
=A9BG=CB5@ MB5A=7G C:H<9 5@57H=7 I@;9
+D59B<5I9F "CB9G /=H<:CF8 "
+7<K5FNG7<=@8 % D"
+7<K5FNG7<=@8 % D"
+CHC % *=7< * % #I=>?9B # D" $
,9FB8FID % *=7< * % +58@9F % "
,CBFM " 5J=G % "
.=9=F5 # 9H 5@ "
2965@@CG +CHC % #I=>?9B # *=7< * % =B DF9D5F5H=CB
2<5C + +D9F;9@ & *=7< * % "
2<5C + *=7< * % +D9F;9@ & %&*+
2<5C + %&*+
2C775@= % 9H 5@ $
