Yale Galaxy Lunch

Transcript

1. Adrian Price-Whelan Kathryn Johnston David Hendel David Hogg adrn/streams POTENTIAL MILKY WAY THE OF THE
2. Cosmic Microwave Background ! ! Galaxies-ish cosmology
3. HOW?
4. DARK MATTER Millenium simulation
5. VIRIALIZED SPHERES Simple halo models are Vc( r ) ⇡ Const . r d ( r ) dr / Const . (r) / ln(r) ⇢(r) / r 2
6. ρ r Navarro, Frenk, White 1996 ⇢(r) / 1 r(r + Rs)2
7. BUT…
8. Via Lactea simulation Simulations predict SUBSTRUCTURE
9. Simulated haloes are x y z y e.g., Jing & Suto 2002 TRIAXIAL
10. Simulated haloes are e.g., Jing & Suto 2002 TRIAXIAL Properties vary with radius
11. AXIS RATIOS 10 kpc 100 kpc Prolate Oblate Triaxial Vera-Ciro et al. 2011
12. ORIENTATION 10 kpc 100 kpc Vera-Ciro et al. 2011 aligned orthogonal
13. ORIENTATION 10 kpc 100 kpc Vera-Ciro et al. 2011 aligned orthogonal
14. Ryden et al. 1999 Isophotal Twisting
15. TRIAXIALITY Aquarius Via Lactea
16. How do the BARYONS fit in ?
17. Pontzen & Governato 2012
18. Shape: spherical? prolate? triaxial? Inertia: aligned at all radii? ! Substructure: how much?
19. DARK MATTER
20. DARK MATTER :(
21. GRAVITATIONAL LENSING Luminous matter (isophotes) Total mass (lensing) SLACS; Barnabé et al. 2011
22. 3D We need a view
23. ORBITS trace MASS
24. ( x1, v1) ( x2, v2) ( x1) ( x2) = 1 2 (v2 2 v2 1 )
25. ( x1, v1)
26. d(⌫v2 r ) dr + 2 r ⌫v2 r = ⌫ d dr Velocity dispersion Potential
27. BUT…
28. RANDOM?
29. Satellite
30. How do STREAMS form ?
31. TIDAL SHOCKING EVAPORATION
32. EVAPORATION rtide ⇠ f ✓ m Menc ◆1/3 R f ⇠ O(1) M m m << M
33. TIDAL SHOCKING K ! K + K E ! E 2 K E ⇡ 4 3 G2m ✓ M V ◆2 hr2 tide i R4 v ⇠ " 8 3 G2 ✓ M V ◆2 hr2 tide i R4 #1/2 (at pericenter)
34. rtide
35. rtide R ⇠ ⇣ m M ⌘1/3 v ⇡ ✓ Gm rtide ◆1/2 V ⇡ ✓ GMenc R ◆1/2 v V ⇠ ⇣ m M ⌘1/3 v ⇠ ⇣ m M ⌘1/2 ⇣rtide R ⌘ 1/2 V and
36. (r) = GM r disk( R, z ) = GMdisk q R 2 + ( a + p z 2 + b 2)2 spher( r ) = GMspher r + c halo ( x, y, z ) = v 2 h ln( C1x 2 + C2y 2 + C3xy + ( z/qz )2 + r 2 h ) Law & Majewski 2010
37. 2.5 x 106 M☉ 2.5 x 107 M☉ 2.5 x 108 M☉ 2.5 x 109 M☉
38. −100 −50 0 50 Y [kpc] 2.5e6M¯ 2.5e7M¯ 2.5e8M¯ 2.5e9M¯ −100 −50 0 50 X [kpc] −100 −50 0 50 Z [kpc] −100 −50 0 50 X [kpc] −100 −50 0 50 X [kpc] −100 −50 0 50 X [kpc]
39. tub = t(EJ > e↵ (rj))
40. 2.5 ⇥ 106M Time [Myr] |v vs | t=tub |r rs | t=tub [kpc] [km/s] mass loss
41. Time [Myr] |v vs | t=tub |r rs | t=tub [kpc] [km/s] 2.5 ⇥ 107M
42. Time [Myr] |v vs | t=tub |r rs | t=tub [kpc] [km/s] 2.5 ⇥ 108M
43. Time [Myr] |v vs | t=tub |r rs | t=tub [kpc] [km/s] 2.5 ⇥ 109M
44. rtide
45. ~75 kpc
46. Each star: PARAMETERS Progenitor: ⌧ub K true 6D position unbinding time leading/trailing tail true 6D position M mass today Potential: anything! W = (l, b, d, µl, µb, vr) W p = (l, b, d, µl, µb, vr)
47. THE POSTERIOR Gaussian errors p( , W , W p, ⌧, K | D, Dp) = 1 Z p(D | W )p(Dp | W p)p(W | W p, ⌧, , K)p( )p(⌧)p(K) Priors Likelihood
48. p(W | W p, ⌧, , K) = p(X | Xp, ⌧, ) |J(⌧)| p(X | Xp, ⌧, ) = [N(r | rs + Krtide ˆ rs, rtide) ⇥ N(v | vs, v)]t=⌧
49. How many STARS do we need ?
51. disk( R, z ) = GMdisk q R 2 + ( a + p z 2 + b 2)2 spher( r ) = GMspher r + c halo ( x, y, z ) = v 2 h ln( C1x 2 + C2y 2 + C3xy + ( z/qz )2 + r 2 h )
52. Recovered potential parameters
53. ~4% ERRORS
54. Time-dependent / non-integrable potentials Multiple streams Missing dimensions / realistic uncertainties No progenitor
55. David Hogg (NYU) Kathryn Johnston (Columbia) David Hendel (NYU) Ana Bonaca (Yale) Dan Foreman-Mackey (NYU)` Marla Geha (Yale) Andreas Küpper (Columbia) David Law (Toronto) Sarah Pearson (Columbia) Barry Madore (Carnegie) Steve Majewski (UVA) Allyson Sheffield (Columbia) Thanks!