Caltech 03/2015

Tea talk at Caltech

Transcript

1. TIDAL STREAMS in Triaxial Systems Columbia University adrian price-whelan
2. Modeling streams in arbitrary potentials Chaos and tidal streams 2) 1)
3. What we [think we] know about dark matter halos
4. Via Lactea 2 simulation simulated halos are triaxial
5. 0.2 0.4 0.6 0.8 1.0 0.0 Jing & Suto (2002) (c/a) 0.6 0.8 1.0 0.4 (b/a) 0.5<(c/a)<0.6 minor/major intermediate/major
6. pdf 6 ⇥ 1011 < M/M < 2 ⇥ 1012 0.2 0.4 0.6 0.8 1.0 0.0 Schneider et al. (2012) (c/a) (b/a)
7. (c/a) ~ 0.6 (b/a) ~ 0.8 NFW ✓ For Milky Way mass halos…
8. what about REAL LIFE
9. Weak lensing Constraint on mean projected halo ellipticity van Uitert et al. (2012) eh ⇡ 0.4 ± 0.25 (c/a) proj = 0.6 ± 0.25
10. Diego et al. (2014) (c/a) ~ 0.55 Strong lensing
12. Sag. Orphan Pal 5
13. Tidal streams are sensitive to internal progenitor dynamics and the potential in which they form
14. Results from the Sagittarius stream: Newberg et al. 2007 Law & Majewski 2010 Ibata et al. 2013 Deg & Widrow 2013 Ibata et al. 2001 spherical Johnston et al. 2005 Vera-Ciro & Helmi 2013 oblate spherical triaxial maybe still spherical oblate → triaxial triaxial
15. How do streams form?
16. rtide ⇠ f ✓ m Menc ◆1/3 R f ⇠ O(1) m2 << m1 R
17. potential center L1 L2
19. Tidal disruption is simple
20. How should we fit stream data? With a generative model
21. progenitor Lagrange points progenitor orbit potential center Streakline Küpper et al. (2012)
22. t = 0 Streakline Küpper et al. (2012)
23. t = 1 Streakline Küpper et al. (2012)
24. t = 2 Streakline Küpper et al. (2012)
25. t = 3 Streakline Küpper et al. (2012)
26. model stream observed stars Streakline
27. Streakline
28. Rewinder
29. t = 0 Price-Whelan et al. (2014) Rewinder
30. Rewinder Price-Whelan et al. (2014) t = -1 evaluate likelihood
31. Rewinder Price-Whelan et al. (2014) t = -2 evaluate likelihood
32. Rewinder Price-Whelan et al. (2014) t = -3
33. ith star orbit progenitor orbit potential unbinding time velocity dispersion ~tidal radius leading/ trailing Price-Whelan et al. (2014) p(wi | wp, ✓p, ⌧i, ) progenitor internals {N(ri | rp ± rtide ˆ rp, r)|⌧i N(vi | vp, v)|⌧i
34. ⌧ub K unbinding time leading/trailing tail M mass today any parametrization per star progenitor potential marginalize out Rewinder model parameters
37. ⌧ub K unbinding time leading/trailing tail M mass today any parametrization per star progenitor potential (l, b, d, µl, µb, vr) (l, b, d, µl, µb, vr) marginalize out WE’RE HOSED Rewinder Price-Whelan et al. (2014)
38. Nparams / 6Nstars
39. 50 −100 −50 0 50 X [kpc] −100 −50 0 50 X [kpc] x z y Potential: Miyamoto-Nagai disk + Hernquist spheroid + Triaxial, log. halo (q1, qz, , vh, rh) Price-Whelan et al. (2014)
40. −100 −50 0 50 X [kpc] −100 −50 0 X [kpc] x “Data”: Price-Whelan et al. (2014) 8 “RR Lyrae” stars Gaia velocity errors 2% distance errors + Progenitor, same errors
41. 8 RR Lyrae stars Gaia velocity errors 2% distance error Price-Whelan et al. (2014)
42. Price-Whelan et al. (2014) 8 RR Lyrae stars 2% distance errors No proper motions
43. Price-Whelan et al. (2014) Recover unobserved proper motion for stars
44. Next Marginalize true phase-space positions of the stars Marginal likelihood has fixed dimensionality set by potential params., progenitor params Price-Whelan et al. (in prep.)
45. Nparams / 6Nstars Good: Bad: - test particle orbits (no N-body) - arbitrary potentials - observational uncertainties / missing data - less sensitive to observational biases
46. Tidal streams are sensitive to the Milky Way potential at large scales When modeling streams, must use a probabilistic model, e.g. Rewinder SMHASH will measure precise distances to stars in Sgr & Orphan streams
47. Chaos and tidal streams 2)
48. Mean density of streams evolves faster relative to spherical/oblate Chaos may become important, mixing can reduce density in streams In triaxial potentials:
49. For regular orbits: ˙ J = @H @✓ = 0 ˙ ✓ = @H @J = ⌦ ( x , v ) ! ( ✓ , J )
50. Angle-action coords.
51. Triaxial / 3 dof = 6D phase space = 3D torus embedded in Regular orbit:
52. x y px py
53. θ1 θ2 J1 J2
54. ⌦2/⌦1 θ1 θ2 J1 J2
55. x = X k ak e i!kt !k = nk ⌦1 + mk ⌦2 + lk ⌦3 ⌦i = Fi(J1, J2, J3)
56. NAFF FFT orbit Convolve with Hanning filter Find and subtract strongest component [repeat] Laskar (1990) Valluri & Merritt (1998) (Numerical Approximation of Fundamental Frequencies)
57. 1 2 ⌦1 ⌦2 Frequency Diffusion Chaotic orbit Regular orbit
58. Regular Chaotic Frequency Diffusion Price-Whelan et al. (2015)
59. Regular Chaotic
60. Frequency diffusion rate measures the magnitude of chaos for a given orbit
61. How chaotic are triaxial potentials?
62. Choose a potential: - Triaxial NFW - (c/a) = 0.6 - (b/a) = 0.8
63. ~30,000 orbits E = E0 vx = vz = y = 0 x z
64. x z Price-Whelan et al. (2015) short axis tubes Intermediate axis long axis tubes box
65. How does chaos effect ensembles of orbits?
66. Triaxial / 3 dof = 6D phase space = 3D torus Regular orbit: Triaxial / 3 dof = 6D phase space = 5D energy surface Chaotic orbit:
67. Chaotically mixed ➞ uniform on energy surface ⇢E0 (x) / Z d3v (H E0) / p E0 ( x ) Price-Whelan et al. (2015) (projected into configuration space)
68. Globular cluster-like “debris” Ensembles E ⇡ 0.5% E0 Start at pericenter, evolve for 25 periods
69. “Distance” to fully-mixed state DKL( t ) = Z d x ⇢ ( x, t ) ln ⇢ ( x, t ) ⇢E0 ⇡ N X i ln ⇢ ( xi, tj) ⇢E0 Price-Whelan et al. (2015)
70. Price-Whelan et al. (2015) DKL Time Regular Chaotic }
71. Price-Whelan et al. (2015)
72. x z Price-Whelan et al. (2015)
73. What does chaos do to the observability of streams?
74. x z
76. Price-Whelan et al. (2015) Regular Chaotic
77. Chaos is generic to triaxial potentials Frequency diffusion seems to be predictive of observables, e.g., stream morphology More realistic potentials will be time- dependent, lumpy, multi-component, all of which may enhance chaos The mere existence of thin streams around the Milky Way places constraints on the potential