3-Dimensional dynamics of the galactic bulge Soto Vicencio, M.H.

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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 1

Introduction

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From Galileo to Sapley’s model of the galaxy

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HF5H98 +<5D@9M F95@=N98 H<5H H<=G 8=GHF=6IH=CB K5G 7<5F57H9F=GH=7 C: ;@C6I@5F 7@IGH9FG

5B8 H<IG <9 F95GCB98 H<5H =: ;@C6I@5F 7@IGH9F 8I9 HC H<9=F G=N9 K9F9 5 =ADCFH5BH GHFI7

HIF5@ 9@9A9BHG =B H<9 ;5@5LM H<9M G<CI@8 69 F9DF9G9BH5H=J9 A5F?9FG C: H<9 GHFI7HIF9 C: H<9 %=@?M /5M 9B79 H<9 5DD5F9BH 8=GHF=6IH=CB C: ;@C6I@5F 7@IGH9FG AIGH 69 5 7@95F =B8=75H=CB C: H<9 @C75H=CB C: H<9 +IB K<=7< 7CI@8 BCH H<9B 69 7@CG9 HC H<9 79BH9F C: H<9 ;5@5LM 5G H<9 #5DH9MB -B=J9FG9 7@5=A98 6IH F5H<9F EI=H9 :5F :FCA =H ,<9 8=G

H5B79G IG98 6M +<5D@9M K9F9 C6H5=B98 :FCA H<9 5DD5F9BH 6F=;<HB9GG C: J5F=56@9 GH5FG 5G

9D<9=8G :CF K<=7< =BHF=BG=7 6F=;<HB9GG K5G ?BCKB !B=H=5@@M 577CF8=B;@M HC H<9 G=N9 C: H<9 #5DH9MB AC89@ H<9 8=GH5B79G :CIB8 :CF H<9 7@IGH9FG D@5798 H<9A K9@@ 69MCB8 H<9

@=A=HG C: H<9 ;5@5LM +<5D@9M 5H FGH F9GC@J98 H<=G D5F58CL 6M H<9 7CA6=B5H=CB C: HKC GMGH9AG K<9F9 H<9 ;@C6I@5F 7@IGH9F K9F9 A9A69FG C: 5 G97CB8 @5F;9F 8=GHF=6IH=CB H<5B H<9 ;5@5LM 9 @5H9F 7<5B;98 H<=G DCG=H=CB 5B8 6C@8@M 7@5=A98 H<5H H<9G9 ;@C6I@5F 7@IG

H9FG AIGH 69 7CID@98 HC H<9 %=@?M /5MTG GHFI7HIF9 5B8 H<9F9:CF9 H<9 ;5@5LM G<CI@8 69 H=A9G 6=;;9F H<5B H<9 G=N9 DF98=7H98 6M #5DH9MB ,<=G 7@5=A 75IG98 A5BM 7CBHFCJ9F

G=9G G=B79 H<9 #5DH9MB -B=J9FG9 K5G 5@F958M ;9B9F5@@M 5779DH98 ,<IG 6CH< AC89@G K9F9 8=GDIH98 :CF G9J9F5@ M95FG 6M H<9 5GHFCBCA9FG +<5D@9MTG 9GH=A5H98 G=N9 :CF H<9

%=@?M /5M K5G GCA9K<5H HCC @5F;9 A5=B@M 6975IG9 C: <=G 5GGIADH=CB C: B9;@=;=6@9

=BH9FGH9@@5F 56GCFDH=CB

%CGH C: H<9 CDDCG=H=CB HC +<5D@9MTG AC89@ K5G FCCH98 =B H<9 69@=9: H<5H GD=F5@ B96I

@59 K9F9 ;5@5L=9G G=A=@5F HC H<9 %=@?M /5M 969F IFH=G :FCA H<9 $=7? C6G9FJ5HCFM K5G CB9 C: H<CG9 5BH5;CB=GH HC +<5D@9MTG =895G <9 5F;I98 H<5H =: H<9 GD=F5@ B96I@59 K9F9

;5@5L=9G C: H<9 G=N9 DFCDCG98 6M +<5D@9M H<9M KCI@8 B979GG5F=@M <5J9 699B =B7CB79=J

56@M 8=GH5BH +=B79 H<9F9 K5G BC 9J=89B79 H<5H H<9M K9F9 GC 8=GH5BH +<5D@9MTG 7CB79D

H=CB <58 HC 69 KFCB; ,<9 8=G7CJ9FM C: BCJ59 =B GD=F5@ B96I@59 6M 9CF;9 *=H7<9M =B ;5J9 :CF FGH H=A9 H<9 DCGG=6=@=HM HC C6H5=B F9@=56@9 9GH=A5H=CBG C: H<9 8=GH5B79G HC H<9 GD=F5@G /<9F9 H<9G9 8=GH5B79G 7@95F@M D@5798 H<9 GD=F5@G CIHG=89 H<9 @=A=HG C: H<9

%=@?M /5M IFH=G 75@7I@5H98 5 HMD=75@ 8=GH5B79 C: %D7 :CF GD=F5@ B96I@59 IH K<=@9 BCJ59 K9F9 IG98 6M IFH=G HC GIDDCFH H<9 =G@5B8 IB=J9FG9 7CB79DH 5B8 H<9 #5DH9MB AC89@ 8=A9BG=CBG :CF H<9 %=@?M /5M B9K DFCD9F ACH=CB F9GI@HG =B BCJ59 K9F9 IG98 5;5=BGH H<9 @5HH9F 975IG9 8F=55B J5B %55B9B =B 75@7I@5H98 H<9 DFCD9F ACH=CBG :CF G9J9F5@ GD=F5@ B96I@59 5B8 :CIB8 H<5H =: H<9 H<9G9 GD=F5@ K9F9 5G 8=GH5BH 5G DFCDCG98 6M IFH=G H<9=F J9@C7=H=9G K9F9 9LHF9A9@M @5F;9 ,<IG HKC 7@95F@M CDDCG=H9 DCG=H=CBG

=B 5GHFCBCAM 7C9L=GH98 5H H<9 H=A9 ,<CG9 :5JCIF=B; +<5D@9MG AC89@ C: H<9 %=@?M

(7)

=A9BG=CB5@ MB5A=7G C: H<9 5@57H=7 I@;9

/5M K<=7< <9@8 H<5H H<9 8=A9BG=CBG C: H<9 %=@?M /5M K9F9 8=F97H@M F9@5H98 HC H<9 8=GHF=6IH=CB C: ;@C6I@5F 7@IGH9FG 5B8 H<CG9 :5JCIF=B; IFH=GT J=9K K<=7< GIDDCFH98 H<9 #5DH9MB -B=J9FG9 8=A9BG=CBG 5B8 7CBG=89F98 H<9 GD=F5@ B96I@59 5G 9LHF5;5@57H=7 GHFI7HIF9G

!B H<=G G79B5F=C 6CH< 5BH5;CB=GH DCG=H=CBG 7F5G<98 =B H<9 “great debate” =B H<9 &5

H=CB5@ 7589AM :CF +7=9B79G =B !B =H +<5D@9M 5B8 IFH=G 8965H98 <=G F9GD97

H=J9 DCG=H=CBG 56CIH H<9 G=N9 C: H<9 %=@?M /5M 5B8 H<9 B5HIF9 C: GD=F5@ B96I@59 J9B H<CI;< H<9 8965H9 8=8 BCH G9HH@9 5BM C: H<9 EI9GH=CBG 588F9GG98 =H <9@D98 HC 6F=B; HC H<9 5HH9BH=CB C: H<9 G7=9BH=7 7CAAIB=HM H<9 A5=B DFC6@9AG C: 957< H<9CFM CK9J9F

=B H<9 56G9B79 C: 7FI7=5@ 9J=89B79 H<9 CDDCG=B; G=89G K9F9 BCH F97CB7=@98

:9K M95FG 5:H9F H<9 8965H9 B5@@M H<9 B5HIF9 C: GD=F5@ B96I@59 K5G G9HH@98 9

75IG9 8K5F8 I66@9 =B 7CI@8 F9GC@J9 K=H< H<9 B9K =B7< H9@9G7CD9 5H %CIBH /=@GCB H<9 CIH9F F9;=CBG C: % 5B8 % B8 H<9G9 F9;=CBG DFCJ98 HC 69 J9FM G=A=@5F HC H<CG9 C: ;FCID C: GH5FG DF9J=CIG@M F9GC@J98 ,<9B K<9B <9D9=8G GH5FG K9F9 =89B

H=98 =B 6CH< % 5B8 % 5 F9@=56@9 8=GH5B79 9GH=A5H=CB K5G DCGG=6@9 6M A95BG C:

H<9 <9D9=8 6F=;<HB9GGD9F=C8 F9@5H=CB ,<IG 5 J5@I9 C: ?D7 K5G 75@7I@5H98 :CF H<9 8=GH5B79 HC % 5B8 %

After Shapley’s model: Oort and Lindblad

H H<9 G5A9 H=A9 "5B 'CFH K<C 898=75H98 G9J9F5@ M95FG HC H<9 GHI8M C: <=;< J9@C7=HM GH5FG :CIB8 G9J9F5@ :57HG K<=7< K9F9 8=:7I@H HC F97CB7=@9 K=H< #5DH9MBTG -B=J9FG9 ,<9 8=GHF=6IH=CB C: <=;< J9@C7=HM GH5FG G99A98 HC <5J9 5 7@95F 5GMAA9HFM 56CJ9

?AG97 K<9F9 69@CK H<5H J5@I9 F5B8CA 8=F97H=CBG 8CA=B5H98 -B89F H<9 #5DH9MB -B=J9FG9 H<9G9 <=;< J9@C7=HM GH5FG 7CI@8 >IGH 69@CB; HC 5 8=::9F9BH GHFI7HIF9 8MB5A=

75@@M 897CID@98 :FCA H<9 ;5@5LM 'B H<9 CH<9F <5B8 H<9 @=A=H C: ?AG97 =AD@=98 5B 5J9F5;9 F58=5@ J9@C7=HM C: ?AG97 5B8 5 5J9F5;9 A5GG C: % BCH<9F 8=:7I@H :57H HC F97CB7=@9 K=H< #5DH9MBTG H<9CFM K5G H<5H ;@C6I@5F 7@IGH9FG K<=7< HMD=75@@M <5J9

<=;< J9@C7=H=9G 7CI@8 BCH 69 ;F5J=H5H=CB5@@M 6CIB8 HC 5 ;5@5LM 5G GA5@@ 5G H<9 CB9 DFC

DCG98 6M #5DH9MB CBG9EI9BH@M G=B79 ;@C6I@5F 7@IGH9FG K9F9 J9FM A5GG=J9 =H G99A98 EI=H9 IB@=?9@M H<5H H<9M KCI@8 69 7F95H98 5H 5 F5H9 9BCI;< HC F9D@9B=G< H<CG9 9G75D98 8I9 HC H<9 <=;< J9@C7=H=9G 5B8 H<9 GA5@@ 9G75D9 J9@C7=HM C: H<9 ;5@5LM =B #5DH9MBTG AC89@ @@ H<=G @98 HC 'CFH HC =B:9F H<5H H<9 GMGH9A5H=7 <=;< J9@C7=H=9G =B GH5FG 5B 5@GC

=B 7@IGH9FG K9F9 5GGC7=5H98 K=H< 5B =BHF=BG=7 FCH5H=CB 5FCIB8 H<9 ;5@57H=7 79BH9F

!H K5G 9FH=@ $=B86@5B8 5 +K98=G< H<9CF=GH K<C 7CBB97H98 5@@ H<9 :57HG =B 5 7C<9F

9BH D=7HIF9 $=B86@5B8 =B DFCDCG98 5 AC89@ :CF H<9 ;5@5LM CDDCG98 HC #5DH9MB

=B K<=7< H<9 ;5@5LM 7CI@8 69 8=J=898 =B G9J9F5@ GI6GMGH9AG 957< CB9 C: H<9A K=H<

5 D5FH=7I@5F FCH5H=CB J9@C7=HM GMAA9HF=7 K=H< F9GD97H H<9 G5A9 ;5@57H=7 79BH9F ,<=G 8=::9F9BH=5@ FCH5H=CB K5G F9GDCBG=6@9 :CF H<9 J9@C7=H=9G C6G9FJ98 =B <=;< J9@C7=HM GH5FG

;@C6I@5F 7@IGH9F 5B8 ** $MF59 J5F=56@9G ,<IG H<9 GIB 69@CB;98 HC 5 GI6GMGH9A K<=7<

FCH5H98 =B 5@ACGH 7=F7I@5F CF6=HG 5FCIB8 H<9 ;5@57H=7 79BH9F K=H< J9@C7=H=9G 5FCIB8

?AG97 B8 H<9F9:CF9 5@@ H<CG9 GC75@@98 @CKJ9@C7=HM GH5FG K9F9 57HI5@@M GH5FG =B H<9 G5A9 GI6GMGH9A 5B8 DFC656@M =B H<9 GC@5F B9=;<6CF<CC8

+CCB 5:H9F $=B86@5B8TG AC89@ K5G DI6@=G<98 'CFH :CIB8 56IB85BH C6G9FJ5H=CB5@

85H5 K<=7< GIDDCFH98 H<9 DF98=7H=CBG =B =H 'CFH +=A=@5F@ HC H<9 9LD@5B5

(8)

!BHFC8I7H=CB

H=CB C: H<9 @CKJ9@C7=HM GH5FG <9 7CBG=89F98 H<9 <=;<J9@C7=HM GH5FG 5G A9A69FG C: 5 GI6GMGH9A K<=7< 9GG9BH=5@@M FCH5H98 5H @CK J9@C7=HM K=H< F9GD97H HC H<9 ;5@57H=7 79BH9F

5B8 5H H<9 G5A9 H=A9 <5J9 5 @5F;9 J9@C7=HM 8=::9F9B79 K=H< F9GD97H HC H<9 +IB !B 58

8=H=CB 'CFH 75@7I@5H98 H<9 7CBG9EI9B79G C: ;5@57H=7 FCH5H=CB =B H<9 GC@5F B9=;<6CF<CC8 6M A95BG C: GCA9 7CBGH5BHG K<=7< F997H98 H<9 C6G9FJ98 F58=5@ J9@C7=H=9G 5B8 DFCD9F ACH=CBG =B H<9 ;5@5LM 'H<9F 5GHFCBCA9FG 5@GC :CIB8 G=A=@5F 9J=89B79 =B CH<9F G5AD@9G

" + (@5G?9HH 5B8 " (95F79 DFCJ98 H<5H ACJ9A9BHG =B ' 5B8 HMD9 GH5FG K9F9 7CB

G=GH9BH K=H< H<9 FCH5H=CB C: H<9 $=B86@5B8'CFH AC89@ +I6G9EI9BH@M +<5D@9MTG AC89@

C: H<9 5@5LM 5B8 H<9F9:CF9 H<9 AC89@ C: $=B86@58 5B8 'CFH K5G ;9B9F5@@M 5779DH98 CK9J9F =B GD=H9 C: H<9 9J=89B79 HKC =ADCFH5BH 8=G7F9D5B7=9G =B +<5D@9MTG AC89@ F9

A5=B98 H<9 DFCD9F ACH=CBG C: GD=F5@ B96I@59 5B8 H<9 G75@9G 5B8 8=GH5B79G =B +<5D9MTG AC89@ ,<9 ?9M HC H<9 @5HH9F K5G H<9 @CB; GCI;<H 56GCFDH=CB

I66@9 GC@J98 H<9 =B7CBG=GH9B7M C: DFCD9F ACH=CBG =B GD=F5@G =B 6M F9A95GIF=B;

H<9 CF=;=B5@ J5B %55B9B 85H5 5B8 588=B; B9K D@5H9G HC <=G 5B5@MG=G ,<9 A95GIF9

A9BHG 75FF=98 CIH 6M <=AG9@: 5589 5B8 &=7<C@GCB K9F9 =B 8=F97H 8=G5;F99A9BH K=H<

J5B %55B9B F9GI@HG ,<9 7CB7@IG=CB K5G H<5H J5B %55B9B F9GI@HG K9F9 5B 5FH=:57H C: H<9 DFCD9F ACH=CB A95GIF9A9BH K<=7< K5G 9LHF9A9@M 7CAD@=75H98 K=H< H<9 H97<BC@C;M C: H<9 9DC7< 9B79 CB9 C: H<9 DF=B7=D5@ 5F;IA9BHG 5;5=BGH H<9 9LHF5;5@57H=7 B5HIF9 C:

H<9 GD=F5@ B96I@59 K5G CJ9F

,<9F9 K5G H<9 ;9B9F5@ GIGD=7=CB H<5H GCA9 A97<5B=GA C: 56GCFDH=CB A=;<H 69 DF9G9BH

=B C6G9FJ5H=CBG H<9 5DD5F9BH GHFI7HIF9 C: H<9 %=@?M /5M G<CK98 JC=8G CF C6G7IF9 F9;=CBG =B K<=7< 5@ACGH BC GH5FG K9F9 89H97H56@9 ,<9G9 5F95G 89JC=8 C: GH5FG K9F9 8MB5A=75@@M 8=:7I@H HC 9LD@5=B G=B79 H<9M =AD@=98 H<9 9L=GH9B79 C: BIA9FCIG HIBB9@

G<5D98 CD9B=B;G =B H<9 5@5LM 5FB5F8 577IAI@5H98 BIA9FCIG D@5H9G G<CK=B;

GI7< 85F? D5H7<9G 5B8 @5B9G =B H<9 %=@?M /5M 5H H<9 69;=BB=B; C: H<9 HK9BH=9H< 79BHIFM

A5>CF=HM C: 5GHFCBCA9FG 6M 5779DH98 H<9 DF9G9B79 C: @5F;9 7@CI8G C: C6G7IF=B;

A5HH9F =B H<9 ;5@5LM H<9 A5HH9F C: 8=G7IGG=CB H<9B K5G H<9 8=GHF=6IH=CB C: GI7< A5HH9F

!B8=F97H 9J=89B79 C: 56GCFDH=CB 5DD95F98 K<9B "C<5BB9G 5FHA5BB =B BCH98 H<5H

=B 5 F5D=8@M F9JC@J=B; 6=B5FM GH5F δ 'F=CB=G H<9 =CB=N98 75@7=IA @=B9G 5 !! 8=8 BCH D5F

H=7=D5H9 =B H<9 ;9B9F5@=N98 CDD@9F G<=:H C: H<9 F9GH C: H<9 GD97HFIA .9GHC % +@=D<9F :CIB8 G=A=@5F RGH5H=CB5FM @=B9GS =B G9J9F5@ CH<9F GH5FG 5B8 H<IG 7CB7@I898 H<5H H<9G9

@=B9G GH5H=CB5F=9G K<9B A95GIF98 K=H< F9GD97H H<9 @C75@ GMGH9A C: GH5FG AIGH <5J9 5B

=BH9FGH9@@5F CF=;=B CIHG=89 H<9 +C@5F +MGH9A

CK9J9F 8=F97H 9J=89B79 C: ;9B9F5@ 56GCFDH=CB K5G BCH DI6@=G<98 IBH=@ 6M

* " ,FIAD@9F ,FIAD@9F K5G 5B 9LD9FH =B ;@C6I@5F 7@IGH9FG 5B8 8IF=B; <=G F9G95F7<

<58 IG98 HKC A9H<C8G HC 89H9FA=B9 8=GH5B79G HC H<9 7@IGH9FG ,<9 FGH A9H<C8 7CB

79FB98 H<9 A95GIF9A9BH C: 6F=;<HB9GG 5B8 7C@CIF :CF H<9 GH5FG =B H<9 7@IGH9F 6M A95BG C: H<9=F GD97HF5@ HMD9G ,<9B 6M D@CHH=B; 5DD5F9BH 6F=;<HB9GG J9FGIG GD97HF5@ HMD9 5B8 7CAD5F=B; H<=G D@CH K=H< K9@@ ?BCKB F9@5H=CBG C: =BHF=BG=7 6F=;<HB9GG J9FGIG GD97HF5@

HMD9 9FHNGDFIB;*IGG9@ 8=5;F5A :CF GH5FG =B H<9 GC@5F B9=;<6CF<CC8 <9 K5G 56@9 HC A5?9 9GH=A5H=CBG C: H<9 8=GH5B79 HC H<9 7@IGH9F ,<9 G97CB8 A9H<C8 7CBG=GH98 C: H<9

=BJ9FG9 F9@5H=CB 69HK99B 8=GH5B79 5B8 5DD5F9BH G=N9 C: H<9 7@IGH9F K<9F9 <9 5GGIA98 H<5H 5@@ H<9 7@IGH9FG 5B5@MN98 <58 5@ACGH 9EI5@ @=B95F 8=5A9H9F 5B8 H<9F9:CF9 H<9=F 5B

;I@5F G=N9 K5G G=AD@M 5 8=GH5B79 9::97H ,<9 DFC6@9A H<5H :5798 ,IAD@9F K5G H<5H 6CH<

(9)

=A9BG=CB5@ MB5A=7G C: H<9 5@57H=7 I@;9

A95GIF9G C: 8=GH5B79 K9F9 =B7CBG=GH9BH @IGH9FG K=H< @5F;9 8=GH5B79G <58 5B;I@5F 8=

5A9H9FG @5F;9F H<5B 9LD97H98 ,IAD@9F 8=G75F898 H<9 DCGG=6=@=HM H<5H 7@IGH9FG =B7F95G98 H<9=F G=N9 K=H< H<9 8=GH5B79 5B8 5GGIA98 H<5H GCA9 ?=B8 C: =BH9FGH9@@5F 56GCFDH=CB C:

@=;<H <58 HC 9L=GH =B5@@M <9 75@7I@5H98 H<5H =: H<9 @5HH9F 5@H9FB5H=J9 K5G 7CFF97H 5B 56

GCFDH=CB C: A5;?D7 K5G 9LD97H98 !B 588=H=CB <9 DFCJ98 H<9 7CBG=GH9B7M C: <=G 5F;IA9BH K=H< H<9 C6G9FJ98 =B7F95G9 =B F9889B=B; C: GH5FG 5H 5BM ;=J9B 7C@CF K=H< H<9

=B7F95G9 C: 8=GH5B79

BCH<9F =ADCFH5BH 8=G7CJ9FM =B H<9 D=7HIF9 C: GD=F5@G K<=7< K9F9 5H H<=G DC=BH 57

79DH98 5G D99FG C: H<9 %=@?M /5M K5G H<9 G9D5F5H=CB =B GH9@@5F DCDI@5H=CBG ,<9 BCH=CB C: GH9@@5F DCDI@5H=CBG K5G =BHFC8I798 6M /5@H9F 5589 =B 5589 GHI8=98 H<9 BI

7@9IG C: H<9 GD=F5@ % =HG 7CAD5B=CBG % 5B8 & 5B8 HKC ACF9 9@@=DH=75@G 9 F95@=N98 H<5H H<9 6F=;<H9GH GH5FG =B H<9 GD<9FC=85@ 79BHF5@ F9;=CB C: % K9F9 F98

;=5BHG =B 7CBHF5GH HC H<9 8CA=B5H=B; 6@I9 GID9F;=5BHG :CIB8 =B 5FAG 9B79 5589 89B98 HKC 8=GH=B7H GH9@@5F DCDI@5H=CBG “population I” K<=7< 7CBG=GH98 C: MCIB; C6

>97HG 5GGC7=5H98 K=H< GD=F5@ GHFI7HIF9G 5B8 H<9F9:CF9 DF9:9F9BH=5@@M @C75H98 =B 5FAG 5B8 population II K<=7< 7CBG=GH98 C: C6>97HG 5GGC7=5H98 K=H< H<9 GD<9FC=85@ 7CADCB9BH C:

H<9 ;5@5L=9G CF ;@C6I@5F 7@IGH9FG L5AD@9G C: DCDI@5H=CB ! 5F9 C6>97HG C: 5 K=89 F5B;9 C: 5;9G GI7< 5G MCIB; <CH GH5FG =B ' 5GGC7=5H=CBG 9D<9=8G 8IGH @5B9G 5B8 =CB=N98 M8FC;9B F9;=CBG (CDI@5H=CB !! CB H<9 CH<9F <5B8 5F9 A5=B@M 5GGC7=5H98 K=H< H<9 C@8 GH5FG :CIB8 =B ;@C6I@5F 7@IGH9FG <5@C9G 5B8 6I@;9G

=B5@@M H<9 8=G7CJ9FM =B C: H<9 7A F58=C 9A=GG=CB @=B9 C: B9IHF5@ M8FC;9B

CF=;=B5H=B; =B H<9 =BH9FGH9@@5F A98=IA <5G 699B IG98 HC A5D H<9 FCH5H=CB 5B8 GHFI7HIF9 C: H<9 M8FC;9B =B H<9 ;5@5LM ,<9 GHFI7HIF9 C: B9IHF5@ 5HCA=7 M8FC;9B <5G 699B IG98 5G 5 HF579F C: ;5@57H=7 GHFI7HIF9 9 ; =BB9M 9H 5@ 5B8 H<IG =G C: ?9M =ADCFH5B79 HC IB89FGH5B8=B; H<9 8MB5A=7G C: H<9 ;5@57H=7 79BH9F

,<9 D=7HIF9 C: H<9 %=@?M /5M F957<98 :FCA H<9 8=G7CJ9F=9G 5B8 H97<B=75@ 58J5B79

A9BHG 89G7F=698 =B H<=G G97H=CB =G CB9 C: 5 GD=F5@ ;5@5LM 5G A5BM CH<9FG C6G9FJ98 ,<=G G=AD@9 GH5H9A9BH <5G @9GG H<5B M95FG C: ;9B9F5@ 7CBG9BGIG 5G K9 <5J9 G99B 5@69=H =H 8C9G F9DF9G9BH >IGH H<9 ;9B9F5@ 7<5F57H9F=GH=7G C: H<9 %=@?M /5M ,<=G =B7CAD@9H9 D=7

HIF9 =G GH=@@ IB89F 89J9@CDA9BH 5B8 5G K9 K=@@ G99 =B H<9 B9LH G97H=CB A5BM G97CB85FM :95HIF9G <5J9 699B IBJ9=@98 =B H<9 @5GH M95FG

% '*&'&(,!'&' , % ^!$#1 / ¹

1.2.1 The Milky Way as a barred galaxy

9 .5I7CI@9IFG K5G H<9 FGH HC GI;;9GH H<5H H<9 %=@?M /5M =G 57HI5@@M 5 65FF98

;5@5LM 9 .5I7CI@9IFG K5G @98 HC H<=G 7CB7@IG=CB 5:H9F 5 89H5=@98 7CAD5F=GCB K=H<

CH<9FG GD=F5@ ;5@5L=9G IG=B; 7A 9A=GG=CB @=B9 85H5 ,<9 GD=F5@ AI@H=D@=7=HM C: H<9

%=@?M /5M F9G9A6@98 ACF9 7@CG9@M H<5H C: 65FF98 ;5@5L=9G CK9J9F H<9 <=;<9GH 89

J=5H=CB :FCA 5B 5L=GMAA9HF=7 DCH9BH=5@ =G C6G9FJ98 =B H<9 79BH9F C: H<9 ;5@5LM 5B8 H<9F9:CF9 =H =G =B H<9 ;5@57H=7 79BH9F K<9F9 ACGH C: H<9 65F :95HIF9G G<CI@8 69 GCI;<H (9H9FG GI;;9GH98 5 AC89@ :CF H<9 =BB9F F9;=CBG C: H<9 ;5@5LM K<=7< 7CI@8 F9DFC

8I79 H<93 kpc 5FA 5B8 H<9 9L79GG C: J9@C7=HM C6G9FJ98 =B 9A=GG=CB C: ! =B H<9 GC75@@98

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!BHFC8I7H=CB

:CF6=889B F9;=CBG ,<=G 9L79GG C: J9@C7=HM C:∼ 135 km sec⁻¹ 7CI@8 <5F8@M 69 9LD97H98

=B 5B 5L=GMAA9HF=7 DCH9BH=5@ ,<IG H<9 AC89@ GI;;9GH98 6M (9H9FG =BJC@J98 ;5G CK

=B; 5@CB; 7CB79BHF=7 9@@=DH=75@ GHF95A@=B9G GI7< 5G A=;<H 69 75IG98 6M 5 65F GHFI7HIF9

&9J9FH<9@9GG =B GD=H9 C: H<9 9B7CIF5;=B; F9GI@HG >IGH 89G7F=698 H<9 IG9 C: H<9 7A 9A=GG=CB @=B9 =AD@=9G GCA9 8=G58J5BH5;9G GI7< 5G @CK GD5H=5@ F9GC@IH=CB 5B8 8=::IG9 7A 7CBH=BIIA 9A=GG=CB ,<=G 75B 69 D5FH=5@@M GC@J98 6M IG=B; 9A=GG=CB @=B9G :FCA H<9 @9GG 56IB85BH 56IB85BH AC@97I@9G GI7< 5G ' + CF ' =BB9M 9H 5@

;9B9F5H98 5 AC89@ IG=B; H<9 7A ' 5B8 + @=B9 =B:CFA5H=CB !B H<9=F AC89@ H<9

;5G CK F9GI@HG G<CK98 5 A5F?98 65F GHFI7HIF9 =B H<9 ;5@57H=7 79BH9F K=H< 5 7CFCH5H=CB F58=IG C: r = 2.4 ± 0.5 kpc 5 65F D5HH9FB GD998 C: 63 km sec⁻¹kpc⁻¹ 5B8 5 65F =B7@=B5

H=CB C: φbar = 16 ± 0.2^◦ K=H< H<9 7@CG9F 9B8 =B H<9 FGH ;5@57H=7 EI58F5BH 77CF8=B; HC H<9 AC89@ H<9 ' 9A=GG=CB 5F=G9G =B H<9 D@579G K<9F9 ;5G =G C6@=;98 HC A=;F5H9 :FCA H<9 x1 :5A=@M C: CF6=HG HC x2 K<=7< DFC8I79 G<C7?G H<5H 75B 69 F97C;B=N98 =B H<9 (l, v) 8=5;F5A ,<9 x1 :5A=@M C: CF6=HG 5F9 DFC;F589 5@CB; H<9 65F K<=@9 x2 5F9 D9FD9B8=7I@5F HC H<9 65F GHFI7HIF9 +=A=@5F@M H<9 F=B; C: AC@97I@5F ;5G 89H97H98 K5G 5GGC7=5H98 HC H<9 65FTG CIH9F $=B86@5B8 F9GCB5B79 5B8 H<9 F9;=CBG C: @CK ;5G 89BG=HM =BG=893.5 kpc K=H<

7CFCH5H=CB !B 588=H=CB H<9 58J5B79A9BH =B H<9 D=7HIF9 C: H<9 ;5@57H=7 6I@;9 9LH9B8G HC CH<9F :95HIF9G ,<9 79BHF9 =HG9@: K<=7< =G 5GGC7=5H98 K=H< +;F 5 F58=C GCIF79 ?BCKB :CF 5 @CB; H=A9 <5G 699B =B H<9 @5GH 897589 DFCJ9B HC <5F6CIF 5 GID9FA5GG=J9 6@57?

<C@9 C:(3.6 ± 0.3) × 10⁶%=G9B<5I9F 9H 5@ ,<9 GIGD=7=CB 56CIH H<9 DF9G9B79 C: 5 6@57? <C@9 =B H<9 ;5@57H=7 79BH9F <58 F9A5=B98 :CF M95FG DFCD9F ACH=CB A95GIF9

A9BHG =B H<9 ;5@57H=7 79BH9F 9J9B HC F58=IG 5G GA5@@ 5G D7 G<CK98 5 9L79GG C:

A5GG 89BG=HM C:∼ 10¹² %D7⁻³ <9N 9H 5@ +=B79 5 GH9@@5F 7@IGH9F 7CI@8 BCH 69 F9GDCBG=6@9 :CF GI7< <=;< A5GG H<9F9:CF9 5 6@57? <C@9 5FCG9 5G H<9 @C;=75@ 5@H9FB5H=J9

=G9B<5I9F 9H 5@ H<FCI;< 89H5=@98 B95F!* =A5;=B; GD97HFCG7CDM K9F9 56@9 HC C6H5=B J9FM 577IF5H9 F58=5@ J9@C7=H=9G 5B8 DFCD9F ACH=CBG :CF GH5FG =B H<9 79BHF5@ S

H<9 CF6=HG C: H<9G9 GH5FG K9F9 7CBG=GH9BH K=H< H<9 9::97H C: 5 GID9FA5GG=J9 6@57? <C@9

&95F =B:F5F98 C6G9FJ5H=CBG 5F9 ;9B9F5@@M H<9 B5HIF5@ 7<C=79 :CF GHI8=9G C: H<9 ;5@57

H=7 6I@;9 H<=G =G 8I9 HC H<9 8=A=B=G<98 9::97H C: 9LH=B7H=CB 5H H<CG9 K5J9@9B;H<G 7CA

D5F98 K=H< 6@I9F @H9FG +9J9F5@ DFC>97H <5J9 H5?9B 58J5BH5;9 C: H<=G 7<5F57H9F=GH=7 HC C6H5=B F9@=56@9 85H5 C: H<9 ;5@57H=7 6I@;9 ,<9 !B:F5F98 GHFCBCA=75@ +5H9@@=H9 !*+

@5IB7<98 =B M=9@898 H<9 FGH GIFJ9M C: H<9 ;5@57H=7 6I@;9 5H H<9G9 K5J9@9B;H<G :9K M95FG @5H9F H<9 !B:F5F98 ,9@9G7CD9 !*, CKB 56C5F8 H<9 +D579 +<IHH@9 =B 5G D5FH C: H<9 +D579@56 A=GG=CB G75BB98 5 @5F;9 :F57H=CB C: H<9 G?M =B G9J9F5@ =B:F5F98 K5J9@9B;H<G K=H< 5 F9GC@IH=CB C:∼ 1^◦ !HG F9GI@HG K9F9 IG98 6M #9BH 5A9 5N=C

HC C6H5=B H<9 H<F99 8=A9BG=CB5@ @IA=BCG=HM 8=GHF=6IH=CB C: H<9 %=@?M /5M :FCA 5 2.4μm A5D C: H<9 BCFH<9FB 5@57H=7 D@5B9 ,<9=F F9GI@HG <CK9J9F K9F9 >IGH HH98 K=H<

5L=GMAA9HF=7 8=GHF=6IH=CBG 'B H<9 7CBHF5FM @=HN +D9F;9@ :CIB8 56IB85BH 9J

=89B79 :CF 5 ;5@57H=7 65F =B H<9 %5HGIACHC 9H 5@ !* 85H5 ,<9 65F AC89@98 K5G

=B H<9 FGH ;5@57H=7 EI58F5BH H<9 H=D C: H<9 @CB; 9B8 5B8 K5G 7CBG=GH9BH K=H< DF9J=CIG DF98=7H=CBG 6M +=B<5 5B8 $=GNH IFHCB K<C FGH DCGHI@5H98 5 H=@H98 65F HC 9LD@5=B H<9 C6G9FJ98 ?=B9A5H=7G C: ! 5B8 ' @=HN +D9F;9@ <CK9J9F K9F9 BCH 56@9 HC 7CBGHF5=B H<9 H=@H C: H<9 65F K=H< H<9=F 85H5 ,<9 ACGH GD97H57I@5F F9GI@HG F9

;5F8=B; H<9 ;5@57H=7 65F GC :5F 7CA9 :FCA H<9 CGA=7 57?;FCIB8 LD@CF9F '

(11)

=A9BG=CB5@ MB5A=7G C: H<9 5@57H=7 I@;9

G5H9@@=H9 ,<9 ' G5H9@@=H9 DFC8I798 @CK 5B;I@5F F9GC@IH=CB A5DG C: H<9 5@57H=7 6I@;9 5H 5B8 μm C6H5=B98 :FCA H<9 =::IG9 !B:F5F98 57?;FCIB8 L

D9F=A9BH !* =BGHFIA9BH /9=@5B8 9H 5@ !B GI7< A5DG 5:H9F 7CFF97H=CB :CF 9LH=B7H=CB 5B8 GI6HF57H=CB C: 5B 9AD=F=75@ AC89@ :CF H<9 ;5@57H=7 8=G? 7@95F 5GMAA9

HF=9G 5FCG9 K<=7< K9F9 7CBG=GH9BH K=H< 5 HF=5L=5@ 6I@;9 +=A=@5F@M K9? 9H 5@

5@GC IG=B; ' !* =A5;9G 7<5F57H9F=N98 H<9 ACFD<C@C;M 5B8 89H9FA=B98 H<9

=B:F5F98 @IA=BCG=HM 5B8 A5GG :CF H<9 ;5@57H=7 6I@;9 ,<9M 58CDH98 G9J9F5@ HF=5L=5@ 5B5

@MH=75@ :IB7H=CBG HC F9DF9G9BH H<9 JC@IA9 9A=GG=J=HM C: H<9 GCIF79 B8=B; H<5H 5 65F@=?9 GHFI7HIF9 DFCJ=898 H<9 69GH H HC H<9 85H5 7CAD5F98 HC 5L=GMAA9HF=7 6I@;9 AC89@G ,<=G 5IGG=5BHMD9 65F K=H< 5 R6CLMS ;9CA9HFM K5G 5@=;B98 K=H< H<9 ;5@57H=7 D@5B9

6IH FCH5H98 K=H< =HG B95F9B8 =B H<9 FGH ;5@57H=7 EI58F5BH 5H 5B 5B;@9 C:20^◦± 10^◦K=H<

F9GD97H HC 5@57H=7 79BH9F +IB @=B9 5B8 5L=G F5H=C C: 1 : 0.33 ± 0.11 : 0.23 ± 0.08 !B 588=H=CB 7CA6=B98 K=H< +, =B:CFA5H=CB H<=G 65F AC89@ DFC8I798 5 D<CHCA9HF=7 89

H9FA=B5H=CB :CF H<9 A5GG C: H<9 6I@;9 C: 1.3 × 10¹⁰% +I6G9EI9BH F9G95F7< :C7IG98 CB H<9 '!* =A5;9G DFC8I798 89DFC>97H=CBG C: H<9 8=A9BG=CB5@ 8=GHF=6IH=CB C: H<9 6I@;9 IG=B; G9J9F5@ 8=::9F9BH H97<B=EI9G =BB9M 9F<5F8 +D9F;9@ IG98 5 BCBD5F5A9HF=7 89DFC>97H=CB 5@;CF=H<A $I7MTG A9H<C8 :CF H<=G DIFDCG9 GGIA

=B; :C@8 GMAA9HFM H<9=F AC89@ DFC8I798 5 65F K=H< 5L=G F5H=C 5B8 5 @9B;H< C:

∼ 1.8 kpc K<=7< =B HIFB =AD@=9G 5 7CFCH5H=CB F58=IG C: ∼ 3 kpc %CF9 F979BH@M =GG5BHN

9F<5F8 ;9B9F5H98 5 B9K @IA=BCG=HM 8=GHF=6IH=CB :CF H<9 =BB9F %=@?M /5M IG=B; 5 BCBD5F5A9HF=7 D9B5@=N98 A5L=AIA@=?9@=<CC8 5@;CF=H<A C: 89DFC>97

H=CB ,<9 5@;CF=H<A 5@GC IG98 5G 7CBGHF5=BHG H<9 5DD5F9BH A5;B=HI89 @=B9C:G=;<H

8=GHF=6IH=CBG C: 7@IAD ;=5BHG 5B8 =B7@I898 5FAG ,<=G AC89@ H<IG @98 HC 5 @CB;9F 65F H<5B DF9J=CIG 89DFC>97H=CBG ∼ 3.5 kpc K=H< 5L=G F5H=C C: 5B8 5 65F

=B7@=B5H=CB C:20^◦ ≤ φ_bar ≤ 25^◦

+H5F 7CIBHG <5J9 5@GC 699B IG98 =B H<9 @5GH M95FG HC 8=G9BH5B;@9 GCA9 =ADCFH5BH 65F D5F5A9H9FG 9B>5A=B 9H 5@ IG98 5 75H5@C; C:∼ 30 A=@@=CB A=8=B:F5F98 GCIF79G

H5?9B 6M H<9 GD579 H9@9G7CD9 Spitzer HC 89H9FA=B9 H<9 8=GHF=6IH=CB C: GH5FG =B 5@57H=7

@CB;=HI89 @5H=HI89 5B8 5DD5F9BH A5;B=HI89 !H K5G :CIB8 H<5H H<9 G=AD@9GH GHFI7HIF9 K<=7< >IGH=98 H<9 85H5 K5G 5 @=B95F 65F C: <5@:@9B;H< ∼ 4.4 kpc 5B8 65F =B7@=B5H=CB φbar = 44^◦ ± 10^◦ ,<9 5DD5F9BH 7CBHF58=7H=CB 69HK99B H<9 ;5@57H=7 65F 5H φbar 20^◦ CF φbar 40^◦ K<=7< F9GI@HG :FCA H<9 8=::9F9BH H97<B=EI9G G99AG HC 69 G9HH@98 6M H<9 KCF?G C: $CD9N CFF98C=F5 9H 5@ 5B8 56F9F5$5J9FG ,<9M <5J9 5@GC 5B5@MN98

=B:F5F98 GH5FG 7CIBHG =B H<9 ;5@57H=7 79BH9F 5B8 9GH56@=G<98 H<5H HKC GHFI7HIF9G G99A HC 7C9L=GH =B H<9 6I@;9 5 HF=5L=5@ 6I@;9 FCI;<@M 9LH9B8=B; IBH=@ |l| ≤ 10 5B8 5 H<=B

9@CB;5H98 65F C: 8=A9BG=CBG7.8 × 1.2 × 0.2 ?D7 9B79 H<9 ;5@57H=7 6I@;9 GH=@@ G99AG HC

?99D A5BM C: =HG G97F9HG

%=7FC@9BG=B; @7C7? 9H 5@ <5G 5@GC 699B 5 GCIF79 C: =B:CFA5H=CB C: H<9 A5GG 5B8 J9@C7=HM 8=GHF=6IH=CB C: H<9 ;5@57H=7 6I@;9 %=7FC@9BG=B; C77IFG K<9B 5 A5GG H<9

@9BG DF9GIA56@M 5 GH9@@5F A5GG 7FCGG9G H<9 @=B9 C: G=;<H C: 5BCH<9F C6G9FJ98 GH5F H<9 GCIF79 'B ;5@57H=7 G75@9G AI@H=D@9 @9BG98 =A5;9G 5F9 G9D5F5H98 6M 5 :9K A=@=5F7G97

CB8G 5B8 H<9F9:CF9 5F9 F5F9@M F9GC@J56@9 CK9J9F H<9 IL 5AD@=75H=CB 9::97H =B H<9 C6G9FJ98 GH5F =G 95G=@M C6G9FJ56@9 5B8 5@@CKG H<9 89H9FA=B5H=CB C: H<9 A5GG9G =BJC@J98

=B GCA9 75G9G J9B H<CI;< H<9G9 9J9BHG 5F9 F5F9 H<9 F9;I@5F C6G9FJ5H=CB C: A=@@=CBG

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!BHFC8I7H=CB

C: GH5FG 5@@CKG H<9 89H97H=CB C: <IB8F98G C: H<9A 9J9FM M95F ,<9 A=7FC@9BG=B; CDH=

75@ 89DH< =G H<9 DFC656=@=HM H<5H 5 GCIF79 GH5F 5H 5 79FH5=B 8=GH5B79 :FCA IG =G @9BG98

89D9B8=B; CB@M CB H<9 A5GG 89BG=HM 5@CB; H<9 @=B9 C: G=;<H HC H<=G GH5F ,<IG CDH=75@

89DH< 75B 69 IG98 5G 5 8=5;BCGH=7 C: H<9 6I@;9 GHFI7HIF9 (57NM OBG?= G<CK98 H<5H H<9 J5@I9 :CIB8 =B H<9 ;5@57H=7 6I@;9 :CF H<9 CDH=75@ 89DH< τ = (3.3 ± 1.2) × 10⁻⁶ =G H<F99 H=A9G <=;<9F H<5B H<9 J5@I9 9LD97H98 :CF 5B 5L=GMAA9HF=7 6I@;9 ,<9F9:CF9 <9 9LD@5=B98 H<9 CDH=75@ 89DH< K=H< 5 65F 56CIH15^◦ :FCA H<9 @=B9 C: G=;<H =G7F9D5B7=9G 69HK99B B9K9F A95GIF9A9BHG C: H<9 CDH=75@ 89DH< 5B8 H<9 J5@I9G DF98=7H98 :CF %=@?M /5MTG AC89@G 5F9 GH=@@ :CIB8

1.2.2 Bar evolution

7CBG=89F56@9 :F57H=CB C: H<9 HCH5@ C: 8=G? ;5@5L=9G =G 65FF98 ∼ 50% 5FG 5F9 H<9B 5B =ADCFH5BH :95HIF9 K<=7< C:H9B 5DD95F 8IF=B; H<9 9JC@IH=CB C: GCA9 ;5@5L=9G &CF

A5@@M =B 9LH9FB5@ ;5@5L=9G H<9 65F 7CADCB9BH =G 95G=@M =89BH=56@9 K<9B H<9 ;5@5LM =G :579CB CF 7@CG9 HC =H J9B =B 5 98;9CB CF 9B8CB @=B9 C: G=;<H H<9 9B8 C: H<9 65F =B H<9 @=B9 C: G=;<H 5 65F K=@@ DFC8I79 :95HIF9G =B H<9 6I@;9 K<=7< 75B 69 89H97H98 ,<IG

H<9 56IB85BH =B:CFA5H=CB 7C@@97H98 =B H<9G9 65F ;5@5L=9G 75B ;=J9G IG =ADCFH5BH 7@I9G 56CIH H<9 9JC@IH=CB C: CIF CKB ;5@5LM

=GH=B7H=J9 7CADCB9BHG 75B 69 G9D5F5H98 :FCA H<9 @=;<H 8=GHF=6IH=CB C: GD=F5@ ;5@5L

=9G K<9F9 7IGHCA5FM HCC@G =B H<9 7@5GG=75H=CB C: H<9 6I@;9G 5F9 H<9 +9FG=7 =B89L 5H

H9B=B; 5B8 7C@CF ,<9 7CADCB9BHG H<IG F97C;B=N98 5F9 BCFA5@@M 5 8=G? 5 6I@;9 5B8CF 5 65F 89D9B8=B; CB H<9 7@5GG=75H=CB =BH9F9GH=B; 9L5AD@9 C: 89H97H=CB C: 65FG 6M 8=::9F9BH C6G9FJ5H=CB5@ H97<B=EI9G =G H<9 KCF? C: #I=>?9B %9FF=9@8 K<9F9 8=F97H ?=B9A5H=75@ 9J=89B79 C: H<9 65F =G C6H5=B98 :FCA H<9 @=B9 C: G=;<H J9@C7=HM 8=5

;F5A $'+. !B H<CG9 8=5;F5AG 6I@;9G 7CBH5=B=B; 5 65F G<CK 5 8=GH=B7H=J9 R9=;<H

G<5D9S K<=7< =G 89F=J98 :FCA H<9 HF5BG=H=CB 69HK99B 65F CF6=HG 5G CF6=HG 75B BCH

=BH9FG97H H<9AG9@J9G 5B8 5G 5 F9GI@H H<9F9 K=@@ 69 ;5DG =B H<9 $'+. K<9B 5 65F =G DF9G9BH &CK585MG H<F99 8=::9F9BH ?=B8 C: 6I@;9G 75B 69 8=GH=B;I=G< =B H<9 @=H9F5HIF9

H<9 8=GH=B7H=CB =B H<9G9 6I@;9 HMD9G =G BCH CB@M F9@5H98 HC H<9=F 9LH9FB5@ G<5D9 6IH 5@GC HC H<9 IB89F@M=B; :CFA5H=CB <=GHCFM H<5H <5G @98 HC H<9 DF9G9BH GH5H9 9B79 H<9 H<F99 HMD9G C: 6I@;9G 5F9 7@5GG=75@ 6CLMD95BIH 5B8 8=G?M H<5B5GGCI@5 @5GG=75@

6I@;9G 5F9 69@=9J98 HC 69 :CFA98 :FCA ;F5J=H5H=CB5@ 7C@@5DG9 CF <=9F5F7<=75@ A9F;9FG C:

@9GG9F C6>97HG K<=7< C77IFG ;9B9F5@@M 95F@M 5B8 69:CF9 H<9 :CFA5H=CB C: H<9 8=G? ,<9G9 6I@;9G 7@CG9@M F9G9A6@9 9@@=DH=75@ ;5@5L=9G =B H<9=F ?=B9A5H=7G F58=5@ DFC@9G 5B8 GH9@

@5F DCDI@5H=CBG ,<IG C@8 GH9@@5F DCDI@5H=CBG 5B8 9@@=DH=75@ G<5D9G 8CA=B5H9 =B H<9G9 6I@;9G CLMD95BIH 6I@;9G CB H<9 CH<9F <5B8 5F9 H<9 B5HIF5@ 7CBG9EI9B79 C: 65F 9JC

@IH=CB 65F =G :CFA98 =B H<9 8=G? DF9GIA56@M :FCA 5 =B=H=5@ D9FHIF65H=CB =B H<9 8=G?

,<9 9JC@IH=CB C: H<9 CF6=H :5A=@=9G =B H<9 65F DFC8I79G @5H9F H<9 65F 6I7?@=B; =B K<=7<

GCA9 CF6=HG F957< GCA9H=A9G <=;< @5H=HI89G H<9 DFC>97H=CB C: H<9G9 <=;<@5H=HI89 GH9@@5F :5A=@=9G ;=J9 H<9 7<5F57H9F=GH=7 6CLMD95BIH G<5D9 77CF8=B; HC &6C8M G=AI@5H=CBG

9 ; CA69G 9H 5@ H<5B5GGCI@5 5B8 F9:9F9B79G H<9F9=B H<9 9JC@IH=CB C:

H<9 65F 5B8 =HG 9L7<5B;9 C: A5HH9F K=H< H<9 =BB9F 8=G? 75IG9G H<9 GH9@@5F DCDI@5H=CBG HC 69 A=L98 ID =B H<9 6I@;965F GHFI7HIF9 5B8 H<9 =BB9F 8=G? K<9B H<9 F58=IG =G G=A=

(13)

=A9BG=CB5@ MB5A=7G C: H<9 5@57H=7 I@;9

@5F &9J9FH<9@9GG H<9 A5>CF=HM C: H<9 6I@;965F DCDI@5H=CB 5;9 G<CI@8 69 <=;<9F H<5B H<CG9 =B H<9 8=G? 9J9B H<CI;< H<9 65F =BGH56=@=HM 75B HF=;;9F GCA9 @C75@ GH5F :CFA5H=CB

=B5@@M 8=G?@=?9 6I@;9G CF DG9I8C6I@;9G 7CA6=B9 GCA9 :95HIF9G C: 65FG 5B8 8=G?G ,<9M G99A HC 69 :CFA98 =B 5 G=A=@5F K5M 5G H<9 6CLMD95BIH 6I@;9G :FCA 5 =BGH56=@=HM

=B H<9 DF99L=GH=B; 8=G? CK9J9F =B H<=G 75G9 =H =G H<9 65F HCFEI9 K<=7< 8F=J9G ;5G HC H<9 =BB9F 8=G? ,<IG 5B =BB9F 8=G? =G :CFA98 K<=7< 9LH9B8G IBH=@ H<9 =BB9F $=B86@5B8 F9GCB5B79 K<9F9 5 F=B; 75B 5@GC 69 :CFA98 ,<9 B9K 8=G? K=@@ 577IAI@5H9 A5GG 5B8 K=@@ HF=;;9F GCA9 GH5F :CFA5H=CB =B H<9 79BHF5@ D5FH C: H<9 8=G? !B H<9 9B8 5 G=N956@9 8=G? =G :CFA98 ,<9 DFCD9FH=9G C: H<9G9 6I@;9G 75B GCA9H=A9G 69 H<9 CB9G 9LD97H98 =B 8=G? GMGH9AG ,<9M 75B 7CBH5=B 5 G=;B=75BH DCDI@5H=CB C: MCIB; GH5FG 5B8 7CBG=89F

56@9 5ACIBHG C: ;5G ,<9G9 HKC 7<5F57H9F=GH=7G 5F9 ACF9 DFCBCIB798 H<5B =B H<9 HKC CH<9F HMD9G C: 6I@;9G

@@ H<=G @958G HC 5 7CAD@=75H98 D=7HIF9 C: 65F 9JC@IH=CB K<=7< 75B BCH 95G=@M 69 G=AD@=98 %CF9CJ9F H<9 G79B5F=C C: 65F 89GHFI7H=CB 8I9 HC H<9 9L7<5B;9 C: 5B;I@5F ACA9BHIA K=H< H<9 =BB9F 8=G? K<=7< =B &6C8M G=AI@5H=CBG A5?9G H<9 65F ACF9 A5GG=J9 5B8 G@CK IBH=@ =H 89GHFCMG =HG9@: 5G 699B DFCDCG98 5G 5 7M7@=75@ DFC79GG 9 ;

CA69G !B H<=G DFC79GG C: 89GHFI7H=CB 5B8 F9:CFA5H=CB C: 65FG =B H<9 79BH9F C:

;5@5L=9G ;5G G99AG HC D@5M 5 7FI7=5@ FC@9

1.2.3 Modeling the dynamics of the Milky Way

G9@:7CBG=GH9BH AC89@ K<=7< 5;F99G K=H< H<9 8MB5A=75@ 5B8 D<CHCA9HF=7 85H5 =B H<9

;5@57H=7 6I@;9 <5G 699B 5 8=:7I@H ;C5@ HC 57<=9J9 ,<9 G75F7=HM C: GI=H56@9 85H5 5B8 H<9 H97<B=75@ DFC6@9AG =BJC@J98 <5J9 G9F=CIG@M F9GHF=7H98 H<9 BIA69F C: AC89@G 5DD@=98 HC H<9 ;5@57H=7 6I@;9

'B9 C: H<9 :9K =G #9BHTG AC89@ #9BH K<=7< 5GGIA9G 5 7CBGH5BH A5GGHC@=;<H F5H=C =B CF89F HC HIFB H<9 @IA=BCG=HM AC89@ 89G7F=698 =B #9BH 5A9 5N=C

=BHC 5 A5GG AC89@ 5B8 DCH9BH=5@ ,<9 %=@?M /5M =G 5GGIA98 HC 69 5B C6@5H9 =GCHFCD=7 GHFI7HIF9 K=H< 5 6@57? <C@9 =B =HG 79BH9F ,<9 F9GI@HG C: H<=G AC89@ GI779GG:I@@M F9DFC

8I798 5 J5F=9HM C: GH9@@5F J9@C7=HM 8=GD9FG=CBG <CK9J9F =H K5G IB56@9 HC F9DFC8I79 H<9 C6G9FJ98 ! 5B8 ' FCH5H=CB 7IFJ9 5H GA5@@ F58=IG

+7<K5FNG7<=@8 :CFAI@5H98 5 H97<B=EI9 K<=7< <5G 699B GD97=5@@M IG9:I@

=B H<9 AC89@=B; C: H<9 %=@?M /5M ,<9 +7<K5FNG7<=8 H97<B=EI9 7CBG=GHG C: H<9 75@7I

@5H=CB C: 5 GI=H56@9 CF6=H @=6F5FM 89F=J98 :FCA 5 DCH9BH=5@ K<=7< =B HIFB =G 7CBG=GH9BH K=H< H<9 89BG=HM 8=GHF=6IH=CB C: H<9 ;5@5LM GHI8=98 FA98 K=H< H<9 CF6=HG =BH9;F5H98 =B H<9 DCH9BH=5@ H<9 D<5G9GD579 8=GHF=6IH=CB :IB7H=CB =G HH98 6M 5 &CB&9;5H=J9$95GH

+EI5F9 5@;CF=H<A &&$+ HC 5 G9H C: C6G9FJ56@9G 'B9 C: H<9 A5=B 8=:7I@H=9G 5G K9 K=@@ G99 =B <5DH9F C: H<9 +7<K5FN7<=@8 H97<B=EI9 =B 65FF98 ;5@5L=9G =G HC 89B9 5

@=6F5FM F9DF9G9BH5H=J9 C: H<9 D<5G9GD579 ,<=G =G 8I9 HC H<9 =B56=@=HM HC 89H9FA=B9 H<9 H<F99 =BH9;F5@G C: ACH=CB C: H<9 65FF98 DCH9BH=5@ H<9G9 5F9 EI5BH=H=9G 7CBG9FJ98 8IF

=B; H<9 CF6=H HF5>97HCFM K<=7< 5F9 9LHF9A9@M IG9:I@ HC 7CBGHF5=B H<9 @=6F5FM HC F95@=GH=7 CF6=HG

2<5C GI779GG:I@@M 5DD@=98 H<9 +7<K5FNG7<=@8 H97<B=EI9 =B 5 G9@:7CBG=GH9BH AC89@ :CF H<9 %=@?M /5MTG 6I@;9 2<5CTG =BDIH =B:CFA5H=CB :CF H<9 AC89@ =B7@I898

(14)

!BHFC8I7H=CB

H<9 '!* 89DFC>97H=CB 6M K9? 9H 5@ 5B8 5 G9H C: 8=::9F9BH C6G9FJ5H=CBG K<=7< 7CBG=GH98 C: F58=5@ J9@C7=H=9G 5B8 DFCD9F ACH=CBG =B 5589TG /=B8CK +58@9F 9H 5@ 5B8 +D59B<5I9F 9H 5@ F9GD97H=J9@M F58=5@ J9@C7=HM 5B8 8=GD9FG=CBG 5H H<9

8^◦7^◦ 9@8 %=BB=H= 9H 5@ 5B8 −1^◦2^◦ 9@8 @IA 9H 5@ H<9 CJ9F5@@

GC@=86C8M FCH5H=CB 7IFJ9 :FCA 6I@;9 GH9@@5F HF579G 5G %=F5G +=' A5G9FG ' !* GH5FG

5B8 D@5B9H5FM B96I@59 9>CB;<9 56=B; 2<5CTG AC89@ M=9@898 5 69GH H K=H< 5 8=::9F9B79 K=H< H<9 =BDIH 89BG=HM 8=GHF=6IH=CB 5B8 F9DFC8I798 F95GCB56@M K9@@ CH<9F C6G9FJ56@9G GI7< 5G H<9 J9@C7=HM 8=GD9FG=CB 7CBG=89F56@9 :F57H=CB C: H<9 CF6=HG :CIB8 =B H<9 69GH H C: H<9 AC89@ K9F9 :CIB8 HC 69 7<5CH=7 <CK9J9F F9;I@5F CF6=HG 7CBHF=6IH98 ACGH C: H<9 A5GG HC H<9 65F6I@;9

M 7CBHF5GH HC 2<5CTG AC89@ 5 7CAD@9H9@M 8=::9F9BH H97<B=EI9 K5G 5DD@=98 =B B

;@A5=9F 9F<5F8 ,<9 @5HH9F IG98 5 GCD<=GH=75H98 <M8FC8MB5A=75@ 7C89 HC AC89@ H<9 ;5G CK =BG=89 ∼ 10 ?D7 F58=IG ,<9 DCH9BH=5@ 7CBG=GH98 C: 5 AI@H=DC

@5F 9LD5BG=CB C: H<9 89DFC>97H=CB 89G7F=698 =B =BB9M 9F<5F8 +D9F;9@ 5B8 H<9F9:CF9 :FCA H<9 '!* =A5;9 ,<9 AC89@ K5G 56@9 HC F9DFC8I79 A5BM ;5G 8MB5A=75@ :95HIF9G K=H< =HG :CIF5FA98 GD=F5@ GHFI7HIF9 !B 588=H=CB 5B =BH9F9GH=B; 65F F58=IG C: Rbar ∼ 3.5 kpc 5B8 65F =B7@=B5H=CB C: φbar ∼ 20^◦− 25^◦K9F9 :CIB8

P5:B9FTG 8MB5A=75@ AC89@ 75A9 657? HC +7<K5FNG7<=@8TG ;5@5LM 6I=@8=B;

H97<B=EI9 G=A=@5F 5DDFC57< HC 2<5CTG AC89@ K5G 5DD@=98 HC H<9 7CBGHFI7H=CB 7CA

6=B=B; 5 8=GHF=6IH=CB :IB7H=CB 89D9B8=B; CB 7@5GG=75@ =BH9;F5@G F9;I@5F CF6=HG 5B8 BCB7@5GG=75@ =BH9;F5@G =FF9;I@5F CF6=HG ,<IG H<9 +7<K5FNG7<=@8 H97<B=EI9 K5G IG98 HC 8=GH=B;I=G< 69HK99B H<9 F95@ 8=GHF=6IH=CB :IB7H=CB 5B8 CB9 ;9B9F5H98 CB@M 6M H<9 7@5GG=75@ 7CADCB9BH +=A=@5F@M HC H<9 HKC DF9J=CIG AC89@G P5:B9FTG AC89@ HH98 H<9

8=A9BG=CB5@ A5GG 89BG=HM C: =BB9M 9F<5F8 +D9F;9@ C6H5=B98 :FCA H<9 89DFC>97H=CB C: H<9 '!* GIF:579 D<CHCA9HFM !B 588=H=CB <9 =B7@I898 H<9

?=B9A5H=75@ 85H5 :FCA H<9 9@8G 5589TG /=B8CK H<9 8^◦7^◦ 9@8 %=BB=H= 9H 5@

H<9 @5GH HKC IG98 =B 2<5CTG AC89@ 5@GC 5B8 5@GC H<9 12^◦3^◦ 9@8 ,<=G AC89@ IG98 5 @=6F5FM 7CBH5=B=B; F9;I@5F CF6=HG 5B8 GI7799898 =B HH=B; H<9 5J5=@56@9 85H5

=BG=89 ?D7 K=H< F95GCB56@9 577IF57M %CGH C: H<9 89J=5H=CB :FCA H<9 =BDIH 89BG=HM C77IFF98 CIHG=89 7CFCH5H=CB H H<9 G5A9 H=A9 5 A5D C: A=7FC@9BG=B; CDH=75@ 89DH< C:

H<9 ;5@57H=7 79BH9F K5G ;9B9F5H98

, !+ , +!+

,<=G H<9G=G 5G =HG H=H@9 5BBCIB79G =G 56CIH H<9 8=A9BG=CB5@ ACJ9A9BHG C: GH5FG =B H<9

;5@57H=7 6I@;9 5B8 H<9 D<MG=75@ 5B8 GHFI7HIF5@ =AD@=75H=CBG 89F=J98 :FCA H<9 GH9@@5F

?=B9A5H=7G C6G9FJ98 'IF 5DDFC57< HC GC@J9 H<9 9B8@9GG DFC6@9A C: H<9 IB79FH5=BH=9G

=B H<9 57HI5@ GHFI7HIF9 C: H<9 ;5@57H=7 6I@;9 =G 65G98 CB H<9 7CBGHF5=BHG CB H<9 D<5G9

GD579 8=GHF=6IH=CB :IB7H=CB 89B=B; H<9 =BB9F ?=@CD5FG97G C: H<9 ;5@5LM ,<IG =B CF89F HC C6H5=B GI=H56@9 6I@;9 7CBGHF5=BHG K9 <5J9 IG98 H<9 HKC H97<B=EI9G H<5H 75B 89@=J9F GI7< =B:CFA5H=CB F58=5@ J9@C7=H=9G 5B8 DFCD9F ACH=CBG

J9FM 7<5DH9F C: H<=G H<9G=G 7CFF9GDCB8 HC 8=::9F9BH GH5;9G =B 5 DFC>97H K<=7< 5H

H9ADHG HC IBJ9=@ H<9 GHFI7HIF5@ DFCD9FH=9G C: H<9 ;5@57H=7 6I@;9 H<FCI;< H<9 GHI8M C:

F9;=CBG K=H< @CK :CF9;FCIB8 9LH=B7H=CB ,<9G9 F9;=CBG 7CAACB@M B5A98 RK=B8CKGS

(15)

=A9BG=CB5@ MB5A=7G C: H<9 5@57H=7 I@;9

<5J9 <=GHCF=75@@M 699B H<9 B5HIF5@ GC@IH=CB HC H<9 9F79 9LH=B7H=CB 8I9 HC H<9 8=G? 8IGH

@5M9F K<=7< C6G7IF9G H<9 79BHF5@ F9;=CBG C: H<9 ;5@5LM ,<9 7CAD@9H9 DFC>97H =B7@I89G H<9 C6G9FJ5H=CB C: 9@8G 57FCGG H<9 ;5@57H=7 6I@;9 9@8G 5H H<9 79BH9F 7@CG9 HC H<9

;5@57H=7 A=BCF 5L=G H<F99 ACF9 5H DCG=H=J9 @CB;=HI89G CB H<9 B95F 9B8 C: H<9 65F 5B8

ACF9 =B H<9 :5F9B8 C: H<9 65F 5H B9;5H=J9 @CB;=HI89G ,<9 DFC>97H K5G CF=;=B5@@M

=BH9B898 HC 69 9BH=F9@M =B H<9 F95@A C: H<9 ?=B9A5H=7G 5B8 8MB5A=7G 5B8 H<9F9:CF9

<5G @=HH@9 7CBGHF5=BHG F9@5H98 K=H< 56IB85B79G CK9J9F K9 <5J9 BCH @9:H H<=G 9BH=F9@M IB5HH9B898 5G K9 9LD@5=B 69@CK ,<=G DFC>97H =G GH=@@ CB;C=B; ,<9 F9GI@HG C: H<=G H<9G=G K=@@ 69 7CAD@9A9BH98 =B H<9 B95F :IHIF9 K=H< B9K =B:CFA5H=CB 89F=J98 :FCA H<9 9@8G CB H<9 :5F9B8 C: H<9 65F ,<9 KCF? DF9G9BH98 <9F9 895@G K=H< H<9 9@8G 7@CG9 HC H<9

;5@57H=7 A=BCF 5L=G 5B8 5H DCG=H=J9 @CB;=HI89G

!B Chapter 2 K9 F9DCFH CB∼ 3200 B9K F58=5@ J9@C7=H=9G K<=7< <5J9 699B C6H5=B98

=B @CK :CF9;FCIB8 9LH=B7H=CB K=B8CKG C: H<9 ;5@57H=7 6I@;9 'IF F58=5@ J9@C7=H=9G K9F9 C6H5=B98 IG=B; H<9 .!%'+!- 75A9F5 K<=7< 5@@CK98 IG HC 7CBGHFI7H F58=5@ J9

@C7=HM 7I69G =B 957< 75G9 ,<9 =ADCFH5B79 C: H<CG9 7I69G =G F9@5H98 K=H< H<9 DF99L=GH=B;

+, =A5;9G =B H<CG9 9@8G 9 ; #I=>?9B *=7? #I=>?9B C6H5=B98 :FCA H<9 +, 5F7<=J9G ,<9 !- 7I69G 7CA6=B98 K=H< H<9 F9B98 GD5H=5@ =B:CFA5H=CB :FCA H<9 +, /( =A5;9G K9F9 IG98 HC 8=G9BH5B;@9 H<9 GD97HF5@ =B:CFA5H=CB C: 957< GH5F IG=B; 5 B9K 897CBJC@IH=CB 5@;CF=H<A ,<9 F9GI@HG C: H<=G DFC79GG 5F9 H<9 GH9@@5F GD97HF5

=B H<9 DCG=H=CBG =B8=75H98 6M H<9 +, =A5;9G ,<9 GD97HF5 H<IG C6H5=B98 6M H<9 B9K H97<B=EI9 F957< 577IF57=9G HMD=75@@M C: ∼ 30 km/sec K<=7< =G G9J9F5@ H=A9G GA5@@9F H<5B H<9 C6G9FJ98 J9@C7=HM 8=GD9FG=CB C: H<9 ;5@57H=7 6I@;9∼ 110 km/sec *=7<

+58@9F 5B8 H<9F9:CF9 GI=H56@9 :CF H<9 GHI8M C: 8MB5A=7G 5G K9 K=@@ G99 =B 7<5DH9F

,<9 6I@;9 89BG=HM F5D=8@M 8FCDG CB79 K9 ACJ9 C::5L=G CBG9EI9BH@M :CF H<9 H<F99 A=BCF 5L=G 9@8G K9 7C@@97H98∼ 2000 F58=5@ J9@C7=HM A95GIF9A9BHG K<=@9 ∼ 1200 GI7<

A95GIF9A9BHG K9F9 C6H5=B98 :CF H<9 H<F99 C::5L=G 9@8G !B H<9 75G9 C: H<9 H<F99 A=BCF

5L=G 9@8G Sagittarius I, Baade’s Window 5B8 near NGC 6558 =H <5G 699B DCGG=6@9 HC ;C CB9 GH9D :IFH<9F 5B8 7CA6=B9 H<9 B9K F58=5@ J9@C7=H=9G K=H< H<9 DFCD9F ACH=CBG C: #I=

>?9B *=7< 9B79 K9 <5J9 7CBGHFI7H98 5 GA5@@ GI6G5AD@9 C: GH5FG D9F 9@8 K=H< K9@@ 89H9FA=B98 =A9BG=CB5@ ?=B9A5H=7 =B:CFA5H=CB ,<9 F9GI@HG C: H<=G GI6

G5AD@9 <=;<@=;<H J9FM 7@95F@M 5 8=GH=B7H=CB 69HK99B H<9 8=::9F9BH DCDI@5H=CBG DF9G9BH

=B H<9 7C@CFA5;B=HI89 8=5;F5A % C: 957< 9@8 %5=B G9EI9B79 HIFBC:: 5B8 *98

=5BH F5B7< * GH5FG G<CK 5 7@95F J9FH9L 89J=5H=CB K<=7< 75B 69 8=F97H@M F9@5H98 K=H< 5 G=;B5HIF9 C: HF=5L=@=HM C: H<9 ;5@57H=7 6I@;9 'B H<9 CH<9F <5B8 6F=;<H 6@I9 A5=B G9EI9B79 GH5FG 69MCB8 H<9 HIFBC:: G<CK J9@C7=HM 9@@=DGC=8G =B7CBG=GH9BH K=H< H<9 89

H9FA=B98 6I@;9 DCDI@5H=CBG ,<IG H<9 6F=;<H 6@I9 A5=B G9EI9B79 GH5FG =B H<9G9 9@8G G99A HC 69 GHFCB;@M 8CA=B5H98 6M 5 8=G? DCDI@5H=CB H H<9 G5A9 H=A9 =H <5G 699B C6G9FJ98 H<5H H<9 G=;B5HIF9 C: HF=5L=@=HM 897F95G9G K<9B ACJ=B; C:: H<9 D@5B9 69=B;

K95?9F :CF 9@8 near NGC 6558 K<=7< <5G H<9 @CK9GH @5H=HI89 b ∼ −6^◦ ,<9 @5HH9F

;=J9G IG 5B =ADCFH5BH 7@I9 56CIH H<9 9LH9BH C: H<9 ;5@57H=7 65F 5B8 H<9 =BI9B79 C: =HG DCH9BH=5@ CB H<9 =BB9F ?D7 C: H<9 ;5@5LM

+D59B<5I9F 9H 5@ K5G CB9 C: H<9 FGH HC C6H5=B 5 F9@=56@9 DFCD9F ACH=CB 75H5@C; :CF GH5FG C: H<9 ;5@57H=7 6I@;9 ,<9=F KCF? A589 IG9 C: D@5H9G H5?9B G9J9F5@

897589G 5D5FH HC C6H5=B DFCD9F ACH=CBG :CF 5 G5AD@9 C: GH5FG =B 5589TG /=B8CK

(16)

!BHFC8I7H=CB

,<=G G5AD@9 K5G H<9 GH5FH=B; DC=BH :CF GI6G9EI9BH GHI8=9G K<=7< 89H9FA=B98 @CK F9G

C@IH=CB 56IB85B79G =B A5BM C: H<9 GH5FG CF=;=B5@@M A95GIF98 ,9FB8FID 9H 5@

+58@9F 9H 5@ !B Chapter 3 K9 <5J9 9LD@CF98 H<=G G5AD@9 K<=7< =B 588=H=CB HC

=A9BG=CB5@ ?=B9A5H=7G 7CIBH K=H< 75@=6F5H98 56IB85B79G ,<9 CF=;=B5@ @CK F9G

C@IH=CB 56IB85B79G K9F9 F975@=6F5H98 IG=B; H<9 <=;< F9GC@IH=CB 56IB85B79 G75@9 6M

I@6F=;<H 9H 5@ ,<IG 5FA98 K=H< 5 G5AD@9 K=H< 8=A9BG=CB5@ ?=B9A5H=7G 5B8 GI=H56@9 56IB85B79G K9 <5J9 GHI8=98 H<9 J9@C7=HM 9@@=DGC=8G 89F=J98 :FCA G9J9F5@ G9

@97H=CB 7F=H9F=5 /9 :CIB8 5 G=;B=75BH J9FH9L 89J=5H=CB =B H<9 A9H5@ F=7< DCDI@5H=CB

[F e/H] > −0.5 K<=7< 8=8 BCH 5DD95F =B H<9 A9H5@ DCCF GI6G9H /<9B 5B5@MN=B; H<9 G5AD@9 ACF9 7@CG9@M 5G 5 :IB7H=CB C: A9H5@@=7=HM 5 GI889B HF5BG=H=CB =B H<9 ?=B9A5H=7G

=G :CIB8 5FCIB8[F e/H] = −0.5 dex :FCA 5B 5DD5F9BH@M =GCHFCD=7 C6@5H9 8=G? HC 5 65F +=A=@5F@M 5 G<5@@CK9F HF9B8 HCK5F8 @CK9F J9FH=75@ J9@C7=HM 8=GD9FG=CB σ_b 5H <=;<9F 56IB85B79G K5G :CIB8

Chapter 4DF9G9BHG H<9 89J9@CDA9BH C: 5 B9K +7<K5FNG7<=@8 AC89@ :CF H<9 %=@?M /5MTG 6I@;9 ,<9 AC89@ <5G 699B 7CBGHFI7H98 HC F9DFC8I79 H<9 8=GHF=6IH=CB C: DFCD9F ACH=CBG 5B8 D<CHCA9HF=7 D5F5@@5L9G :CF H<9 H<F99 A=BCF 5L=G 9@8G =B H<9 DFC>97H CF 957< 9@8 K9 G9@97H98 5 GI6G5AD@9 C: HIFBC:: 5B8 A5=B G9EI9B79 GH5FG =B CF89F HC 6I=@8 H<9 H5F;9H G9H C: 7CBGHF5=BHG K<=7< =G ;C=B; HC 69 HH98 !B 588=H=CB HC H<9 DFCD9F AC

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(17)

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(18)

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(19)

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(20)

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(21)

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3-Dimensional dynamics of the galactic bulge Soto Vicencio, M.H.