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Yale Galaxy Lunch
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Adrian Price-Whelan
February 26, 2014
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Yale Galaxy Lunch
Adrian Price-Whelan
February 26, 2014
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Transcript
Adrian Price-Whelan Kathryn Johnston David Hendel David Hogg adrn/streams POTENTIAL
MILKY WAY THE OF THE
Cosmic Microwave Background ! ! Galaxies-ish cosmology
HOW?
DARK MATTER Millenium simulation
VIRIALIZED SPHERES Simple halo models are Vc( r ) ⇡
Const . r d ( r ) dr / Const . (r) / ln(r) ⇢(r) / r 2
ρ r Navarro, Frenk, White 1996 ⇢(r) / 1 r(r
+ Rs)2
BUT…
Via Lactea simulation Simulations predict SUBSTRUCTURE
Simulated haloes are x y z y e.g., Jing &
Suto 2002 TRIAXIAL
Simulated haloes are e.g., Jing & Suto 2002 TRIAXIAL Properties
vary with radius
AXIS RATIOS 10 kpc 100 kpc Prolate Oblate Triaxial Vera-Ciro
et al. 2011
ORIENTATION 10 kpc 100 kpc Vera-Ciro et al. 2011 aligned
orthogonal
ORIENTATION 10 kpc 100 kpc Vera-Ciro et al. 2011 aligned
orthogonal
Ryden et al. 1999 Isophotal Twisting
TRIAXIALITY Aquarius Via Lactea
How do the BARYONS fit in ?
Pontzen & Governato 2012
Shape: spherical? prolate? triaxial? Inertia: aligned at all radii? !
Substructure: how much?
DARK MATTER
DARK MATTER :(
GRAVITATIONAL LENSING Luminous matter (isophotes) Total mass (lensing) SLACS; Barnabé
et al. 2011
3D We need a view
ORBITS trace MASS
( x1, v1) ( x2, v2) ( x1) ( x2)
= 1 2 (v2 2 v2 1 )
( x1, v1)
d(⌫v2 r ) dr + 2 r ⌫v2 r =
⌫ d dr Velocity dispersion Potential
BUT…
RANDOM?
Satellite
How do STREAMS form ?
TIDAL SHOCKING EVAPORATION
EVAPORATION rtide ⇠ f ✓ m Menc ◆1/3 R f
⇠ O(1) M m m << M
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)
rtide
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
(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
2.5 x 106 M☉ 2.5 x 107 M☉ 2.5 x
108 M☉ 2.5 x 109 M☉
−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]
tub = t(EJ > e↵ (rj))
2.5 ⇥ 106M Time [Myr] |v vs | t=tub |r
rs | t=tub [kpc] [km/s] mass loss
Time [Myr] |v vs | t=tub |r rs | t=tub
[kpc] [km/s] 2.5 ⇥ 107M
Time [Myr] |v vs | t=tub |r rs | t=tub
[kpc] [km/s] 2.5 ⇥ 108M
Time [Myr] |v vs | t=tub |r rs | t=tub
[kpc] [km/s] 2.5 ⇥ 109M
rtide
~75 kpc
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)
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
p(W | W p, ⌧, , K) = p(X |
Xp, ⌧, ) |J(⌧)| p(X | Xp, ⌧, ) = [N(r | rs + Krtide ˆ rs, rtide) ⇥ N(v | vs, v)]t=⌧
How many STARS do we need ?
8
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 )
Recovered potential parameters
~4% ERRORS
Time-dependent / non-integrable potentials Multiple streams Missing dimensions / realistic
uncertainties No progenitor
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!