♠❛♣♣✐♥❣ ❞❛r❦ ♠❛tt❡r ✐♥ t❤❡ ♠✐❧❦② ✇❛② Miguel Pato Wenner-Gren Fellow The Oskar Klein Centre for Cosmoparticle Physics, Stockholm University TeVPA 2015, Kashiwa, 30 Oct 2015
❞❛r❦ ♠❛tt❡r ✐♥ t❤❡ ✉♥✐✈❡rs❡ [PDG ’14] [ESO] [Clowe+ ’06] ✲ time ✛ redshift big bang cosmic microwave large scale dwarfs galaxies galaxy clusters nucleosynthesis background structure [PDG ’14] [Begeman+ ’91] [Springel+ ’06] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✶
❞❛r❦ ♠❛tt❡r ✐♥ ❣❛❧❛①✐❡s [PDG ’14] [ESO] [Clowe+ ’06] ✲ time ✛ redshift big bang cosmic microwave large scale dwarfs galaxies galaxy clusters nucleosynthesis background structure [PDG ’14] [Begeman+ ’91] [Springel+ ’06] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✶
❞❛r❦ ♠❛tt❡r ✐♥ t❤❡ ♠✐❧❦② ✇❛② [PDG ’14] [ESO] [Clowe+ ’06] ✲ time ✛ redshift big bang cosmic microwave large scale dwarfs galaxies galaxy clusters nucleosynthesis background structure [PDG ’14] [Begeman+ ’91] [Springel+ ’06] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✶
❞❛r❦ ♠❛tt❡r ✐♥ ❛♥❞r♦♠❡❞❛ [PDG ’14] [ESO] [Clowe+ ’06] ✲ time ✛ redshift big bang cosmic microwave large scale dwarfs galaxies galaxy clusters nucleosynthesis background structure [PDG ’14] [Begeman+ ’91] [Springel+ ’06] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✶
❤✐st♦r✐❝❛❧ ♣❛r❡♥t❤❡s✐s✿ ❛♥❞r♦♠❡❞❛ The kinematics of an object is a prime tool to learn about its mass. The kinematics of Andromeda has been studied since the [Yates & Garden ’89] 1930s through the Doppler shift of spectral lines in the gas. ∆ ✗ = � v ❧♦s c ✗ 0 [Babcock ’39, Rubin & Ford ’70, Freeman ’70, Rogstad & Shostak ’72, Bosma ’78, Rubin+ ’80, ’82, ’85] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✷
❤✐st♦r✐❝❛❧ ♣❛r❡♥t❤❡s✐s✿ ❛♥❞r♦♠❡❞❛ The kinematics of an object is a prime tool to learn about its mass. The kinematics of Andromeda has been studied since the [Yates & Garden ’89] 1930s through the Doppler shift of spectral lines in the gas. ∆ ✗ = � v ❧♦s c ✗ 0 [Babcock ’39, Rubin & Ford ’70, Freeman ’70, Rogstad & Shostak ’72, Bosma ’78, Rubin+ ’80, ’82, ’85] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✷
❤✐st♦r✐❝❛❧ ♣❛r❡♥t❤❡s✐s✿ ❛♥❞r♦♠❡❞❛ The kinematics of an object is a prime tool to learn about its mass. The kinematics of Andromeda has been studied since the [Yates & Garden ’89] 1930s through the Doppler shift of spectral lines in the gas. ∆ ✗ = � v ❧♦s c ✗ 0 [Babcock ’39, Rubin & Ford ’70, Freeman ’70, Rogstad & Shostak ’72, Bosma ’78, Rubin+ ’80, ’82, ’85] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✷
❤✐st♦r✐❝❛❧ ♣❛r❡♥t❤❡s✐s✿ ❛♥❞r♦♠❡❞❛ The kinematics of an object is a prime tool to learn about its mass. The kinematics of Andromeda has been studied since the [Yates & Garden ’89] 1930s through the Doppler shift of spectral lines in the gas. ∆ ✗ = � v ❧♦s c ✗ 0 [Babcock ’39, Rubin & Ford ’70, Freeman ’70, Rogstad & Shostak ’72, Bosma ’78, Rubin+ ’80, ’82, ’85] c = GM ( ❁ r ) Under Newtonian gravity, a spherical mass induces v 2 . r The rotation provided by the visible mass falls off as v c ✴ 1 ❂ ♣ r at large r . A flat rotation curve implies ✄ a dark matter halo with M ( ❁ r ) ✴ r . ✄ Modifications of gravity at galactic scales are also feasible. [Milgrom x3 ’83] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✷
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①② The Milky Way is a complex bound system of stars, gas and dark matter. [Brunier] Milky Way We can identify the following main components: edge−on ✎ supermassive black hole, with mass 4 ✂ 10 6 ▼ ☞ ; bulge/bar ✎ stellar bulge, with barred shape of scale length 2 � 3 kpc and mass 10 10 ▼ ☞ ; Sun gas disk stellar disk Galactic centre ✎ stellar disc, decomposed into thin and thick components of scale length 10 kpc and total mass 10 10 ▼ ☞ with a marked spiral structure; not to scale! ✎ gas, in molecular, atomic and ionised phases (mainly H) with a patchy distribution towards the centre and a disc-like structure otherwise; and ✎ dark matter halo, extending hundreds of kpc. The Sun is located slightly above the Galactic plane at R 0 ✬ 8 kpc from the Galactic centre, in between two major spiral arms, and travels together with the local standard of rest at about 220 km/s in a roughly circular orbit. [Binney & Tremaine ’87] ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✸
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①② The Milky Way is a complex bound system of stars, gas and dark matter. [Brunier] Milky Way We can identify the following main components: edge−on ✎ supermassive black hole, with mass 4 ✂ 10 6 ▼ ☞ ; dark halo bulge/bar ✎ stellar bulge, with barred shape of scale length 2 � 3 kpc and mass 10 10 ▼ ☞ ; Sun gas disk stellar disk Galactic centre ✎ stellar disc, decomposed into thin and thick components of scale length 10 kpc and total mass 10 10 ▼ ☞ with a marked spiral structure; not to scale! ✎ gas, in molecular, atomic and ionised phases (mainly H) with a patchy distribution towards the centre and a disc-like structure otherwise; and ✎ dark matter halo, extending hundreds of kpc. ✣ t♦t = ✣ ❜✉❧❣❡ + ✣ ❞✐s❝ + ✣ ❣❛s + ✣ ❞♠ The Sun is located slightly above the Galactic plane how can we constrain the parameters of a at R 0 ✬ 8 kpc from the Galactic centre, in between galactic mass model? two major spiral arms, and travels together with the local standard of rest at about 220 km/s in a roughly circular orbit. ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✸
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①② ✣ t♦t = ✣ ❜✉❧❣❡ + ✣ ❞✐s❝ + ✣ ❣❛s + ✣ ❞♠ ✏ ⑤④③⑥ ⑤ ④③ ⑥ ✏ ✏ � ✏ ✏ ✏ � ✮ ✏ � kinematics traces total potential � R ✘ 0 ✿ 1 � 30 kpc rotation curve tracers � � R ✘ 8 � 60 kpc star population tracers � R ✘ 100 � 300 kpc satellite kinematics � R ✘ 300+ kpc timing in Local Group � � � ✠ photometry traces individual baryonic components bulge star counts, luminosity, microlensing disc star counts, luminosity, stellar dynamics gas emission lines, dispersion measure ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✹
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①② ✣ t♦t = ✣ ❜✉❧❣❡ + ✣ ❞✐s❝ + ✣ ❣❛s + ✣ ❞♠ ✏ ⑤④③⑥ ⑤ ④③ ⑥ ✏ ✏ � ✏ ✏ ✏ � ✮ ✏ � kinematics traces total potential � R ✘ 0 ✿ 1 � 30 kpc rotation curve tracers � � R ✘ 8 � 60 kpc star population tracers � R ✘ 100 � 300 kpc satellite kinematics � R ✘ 300+ kpc timing in Local Group � � � ✠ photometry traces individual baryonic components bulge star counts, luminosity, microlensing disc star counts, luminosity, stellar dynamics gas emission lines, dispersion measure ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✹
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①②✿ st❡❧❧❛r ❜✉❧❣❡ ✚ ❧❣ ✚ ❜✉❧❣❡ = ✚ 0 f ( x ❀ y ❀ z ) ✚ ❧❣ morphology f ( x ❀ y ❀ z ) [Binney+ ’97] [Stanek+ ’97] e � r 1 � 1 2 24 ✍ Stanek+ ’97 (E2) 0.9:0.4:0.3 optical e � r 2 s ❂ 2 1 � 1 2 25 ✍ Stanek+ ’97 (G2) 1.2:0.6:0.4 optical e � r 2 s ❂ 2 + r � 1 ✿ 85 e � r a 20 ✍ Zhao ’96 1.5:0.6:0.4 infrared a e � r 2 s ❂ (1 + r ) 1 ✿ 8 1 � 1 2 20 ✍ Bissantz & Gerhard ’02 2.8:0.9:1.1 infrared Ferrer potential 1 � 1 2 43 ✍ Lopez-Corredoira+ ’07 7.8:1.2:0.2 infrared/optical e � r 2 s ❂ (1 + r ) 1 ✿ 8 1 � 1 2 15 ✍ Vanhollebecke+ ’09 2.6:1.8:0.8 infrared/optical s❡❝❤ 2 ( � r s ) + e � r s 1 � 1 2 13 ✍ Robin+ ’12 1.5:0.5:0.4 infrared ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✺
✶✳ t♦✉r ♦❢ t❤❡ ❣❛❧❛①②✿ st❡❧❧❛r ❞✐s❝ ✚ ❧❣ ✚ ❞✐s❝ = ✚ 0 f ( x ❀ y ❀ z ) ✚ ❧❣ morphology f ( x ❀ y ❀ z ) [de Jong+ ’10] [Juri´ c+ ’08] [Juri´ c+ ’08] e � R s❡❝❤ 2 ( z ) Han & Gould ’03 2.8:0.27 thin optical e � R �❥ z ❥ 2.8:0.44 thick e � R �❥ z ❥ Calchi-Novati & Mancini ’11 2.8:0.25 thin optical e � R �❥ z ❥ 4.1:0.75 thick e � R �❥ z ❥ de Jong+ ’10 2.8:0.25 thin optical e � R �❥ z ❥ 4.1:0.75 thick ( R 2 + z 2 ) � 2 ✿ 75 ❂ 2 1.0:0.88 halo e � R �❥ z ❥ Juri´ c+ ’08 2.2:0.25 thin optical e � R �❥ z ❥ 3.3:0.74 thick ( R 2 + z 2 ) � 2 ✿ 77 ❂ 2 1.0:0.64 halo e � R �❥ z ❥ Bovy & Rix ’13 2.2:0.40 single optical ♠✐❣✉❡❧ ♣❛t♦ ✭♦❦❝ st♦❝❦❤♦❧♠✮ ✻
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