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Rewinding streams Adrian Price-Whelan Kathryn Johnston (Columbia University) adrn/streams + David Hogg, Barry Madore, Steve Majewski, Dan Foreman-Mackey, Ana Bonaca, Andreas Küpper, David Law, Marla Geha arXiv:1308.2670 Thursday, August 22, 13

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Thursday, August 22, 13

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Thursday, August 22, 13

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10% heavier correct Thursday, August 22, 13

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10% heavier correct Thursday, August 22, 13

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↵ D µl µb vr Gaia Spitzer ground Thursday, August 22, 13

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RR Lyrae - Standard candles - Bright: ~F/A type, MV ~ 0.5 - Distinct, large-amplitude light curve - Found in substructure (Sagittarius, Orphan, TriAnd...) - PL relation in Mid-IR = 2% distance error Thursday, August 22, 13

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0.1 km/s 1.0 km/s 10.0 km/s 100.0 km/s 1 kpc 10 kpc 100 kpc Gaia RR Lyrae Tangential velocity error Heliocentric distance Thursday, August 22, 13

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0.1 km/s 1.0 km/s 10.0 km/s 100.0 km/s 1 kpc 10 kpc 100 kpc Gaia RR Lyrae Heliocentric distance 35 kpc 10.0 km/s Tangential velocity error Thursday, August 22, 13

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Madore & Freedman 2012 Catelan et al. 2004 P-L relation for RR Lyrae Absolute Mag. Period V K Thursday, August 22, 13

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Ground-based RV - Correct for pulsation (~100 km/s) - Take multiple spectra - Match to ephemeris, e.g. velocity curve Sesar (2012) Thursday, August 22, 13

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Gaia ↵ vl vb ϵ ~ 10 km/s ϵ ~ 80 µas RR Lyrae at 35 kpc Spitzer d ϵ ~ 700 pc ground vr ϵ ~ 10 km/s Thursday, August 22, 13

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p( ~ X0 | ~ ✓, ¯ ¯ ⌃, ~ !0, t⇤) 6D position of star potential parameters satellite shape 6D position of satellite time star is unbound Thursday, August 22, 13

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p( ~ X0 | ~ ✓, ¯ ¯ ⌃, ~ !0, t⇤) = N( ~ X | ~ !, ¯ ¯ ⌃) t⇤ full orbit of star orbit of progenitor Thursday, August 22, 13

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Can get orbit of stars & satellite by integrating backwards: Treat stars, satellite as test particles ~ X0, (✓) ! ~ X(t) ~ !0, (✓) ! ~ !(t) Thursday, August 22, 13

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As an initial test, we assume: 1) we know exactly 2) 3) satellite is a spherical 6D Gaussian: ~ !0 ¯ ¯ ⌃ = 0 B B B B B B @ r2 tide r2 tide r2 tide 2 v 2 v 2 v 1 C C C C C C A rtide = rtide(t = t⇤) t⇤ = arg min t || ~ X(t) ~ !(t)|| Thursday, August 22, 13

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p( ~ X0 | ~ ✓, ¯ ¯ ⌃, ~ !0, t⇤) p( ~ X0 | ~ ✓) assumptions Thursday, August 22, 13

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Assumes N-body e ects are small p( ~ X0 0 , ~ X1 0 , . . . ~ Xm 0 | ~ ✓) = m Y j p( ~ Xj 0 | ~ ✓) Thursday, August 22, 13

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p(~ ✓ | ~ X0) / p( ~ X0 | ~ ✓)p(~ ✓) Thursday, August 22, 13

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−80 −60 −40 −20 0 20 40 −40 −20 0 20 40 60 Law & Majewski (2010) ~75 kpc ~50 kpc Sagittar-ish Stream Thursday, August 22, 13

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Find Maximum A Posteriori parameters for many samples ✓MAP = arg max ✓ p ( ✓ | { ~ X0 }m) Thursday, August 22, 13

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Applied to simulated observations of Law & Majewski 2010 1.30 1.38 1.46 115 122 129 1.28 1.36 1.44 92 97 102 [deg] [km/s] Thursday, August 22, 13

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Applied to simulated observations of Law & Majewski 2010 1.30 1.38 1.46 115 122 129 1.28 1.36 1.44 92 97 102 [deg] [km/s] Thursday, August 22, 13

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q1 = 1.37 ± 0.03 q z = 1.36 ± 0.04 = 96.6 ± 1.3 v halo = 121.5 ± 2.5 km/s Thursday, August 22, 13

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streams debris Thursday, August 22, 13

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Next: - properly marginalize over unbinding time - missing data (stars and progenitor) - inference without a progenitor - multiple streams - contamination Thursday, August 22, 13

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Z d~ !0p(~ !0)d¯ ¯ ⌃p(¯ ¯ ⌃)dt⇤p(t⇤)p( ~ X0 | ~ ✓, ¯ ¯ ⌃, ~ !0, t⇤) p( ~ X0 | ~ ✓) = ⇡ 1 n n X i p( ~ X0 | ~ ✓, t⇤ i ) Er...the right way ouch ln L / m X j ln n X i p( ~ Xj 0 | ~ ✓, t⇤ i ) Thursday, August 22, 13