Effect of substructure on tidal streams Denis Erkal University of Surrey Halo Substructure and Dark Matter Searches , IFT Madrid, June 29th 2018
Milky Way Substructure Halo mass function Stars No Stars 200 kpc 10 4 10 10 Mass (M � ) Aquarius, Springel et al. 2008 Image credit:ESA/Hubble & NASA
Tidal Streams from Globular Clusters • Stars stripped at tidal radius • Once in the stream, each star follows an orbit • Stream roughly follows an orbit tangential y (kpc) offset (kpc) x (kpc) radial offset (kpc)
Tidal Streams from Globular Clusters Smooth Potential Lumpy Potential Interaction with substructure Ibata et al. 2002, Johnston et al. 2002
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Analytic Toy Model for Gaps Approach Setup Perturber • Impulse approximation for • Stream on circular orbit velocity kicks b • No position/velocity • Compute resulting orbits at dispersion first order • Compute resulting stream • Plummer sphere perturber shape • Arbitrary spherical host • Similar to Carlberg 2013, potential Yoon, Johnston, Hogg 2011 Stream • Arbitrary impact geometry Erkal & Belokurov 2015a
Cartoon of Gap Formation Orbital Mechanics 101 Gap Formation (also in Space) aka Football in Space 1) Flyby 1) Flyby 1) Flyby 1) Flyby 1) Flyby 1) Flyby Tangential Throw ρ ρ ρ ρ ρ ψ ψ ψ ψ ψ Earth 5) Caustic 2) Compression 2) Compression 2) Compression 2) Compression ρ ρ ρ ρ ρ ψ ψ ψ ψ ψ Gap! Radial Throw Earth 4) Gap 4) Gap 3) Expansion 3) Expansion 3) Expansion ρ ρ ρ ρ ρ Oscillations! ψ ψ ψ ψ ψ
N-body example Stream generated by progenitor on circular • orbit at 10kpc NFW host potential • Gap density ~1/t 10 8 M � Plummer sphere, 250pc scale • radius Direct impact on stream • Time in Gyr Density along Gap size ( o ) stream ~t 1/2 ~t Time in Gyr Sky angle ( o )
Same picture roughly holds for realistic streams • Simple model misses two important aspects: • Streams are not generally on circular orbits • Stream material has a distribution in E,L ~t 1/2 ~1/t Gap Gap size density Time Time Sanders, Bovy, Erkal 2016
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Streams around the MW Streams in DES Shipp et al. 2018
Streams around the MW ~ 15 globular cluster streams around MW GD1, Grillmair & Dinatos 2006 Pal 5, Odenkirchen et al. 2002 Tri/Psc - Bonaca et al. 2012 Ibata et al. 2016 Martin et al. 2014
How many subhaloes fly near the stream? • Flux through cylinder around stream (same approach as Yoon et al. 2011, Carlberg 2012) x y b max v stream s z |v |dt r l N enc ~ (number density)x(stream length)x(stream age) • Also get velocity distribution Erkal, Belokurov, Bovy, Sanders 2016
How many subhaloes fly near the stream? Pal 5 • ~3.4 Gyr old (Kuepper et al. 2015) • Ibata et al. 2016 # density of subhaloes scaled down from Aquarius (Springel et al. 2009) • length from observations (Odenkirchen et al. 2002) • disk depletes substructure by 3 (D’Onghia et al. 2010, Penarrubia et al. • 2010, Sawala et al. 2016) 10 5 -10 6 M � : ~26 within 2 r s 10 6 -10 7 M � : ~10 within 2 r s 10 7 -10 8 M � : ~4 within 2 r s Erkal, Belokurov, Bovy, Sanders 2016
How many gaps are created? Use gap size and gap depth from model • Subhalo properties from VLII (Diemand et al. 2008) • Match M-v max relation with Plummer spheres • Know number of interactions, sample properties of flyby, get • distribution of gap properties Stream density f cut Erkal, Belokurov, Bovy, Sanders 2016 Angle along stream
Properties of Gaps • Distribution of gap sizes for LCDM spectrum from 10 5 -10 8 M � Normalized distribution Guides the scale on Gap size which to search for gaps Erkal, Belokurov, Bovy, Sanders 2016
So… how many gaps? Pal 5 GD1 0.7 gaps with f < 75% 0.6 gaps with f < 75% Number of gaps deeper than threshold Density threshold Tri/Psc 1.6 gaps with f < 75% ~3 gaps expected in all three streams Erkal, Belokurov, Bovy, Sanders 2016
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Outline • How do gaps grow/evolve? • How many gaps are expected in the known streams around the Milky Way? • Gaps in known streams
Gaps in Pal 5 • Nearby cold/long stream (~ 1km/s dispersion, ~10 kpc long) • Progenitor still intact • Deep data with CFHT (Ibata et al 2016) • Proper motion for progenitor (Fritz & Kallivayalil 2015) • Radial velocities along stream (Odenkirchen et al 2009, Kuzma et al 2015) Belokurov/SDSS
Gaps in Pal 5 • How should unperturbed stream look? Ibata et al 2016 Fiducial Model Fiducial Model 1 1 • Equal amounts of material N-body N-body Leading Leading Trailing Trailing 0 0 Data Data Perp − 1 − 1 φ 2 ( � ) φ 2 ( � ) in leading and trailing arm − 2 − 2 angle − 3 − 3 − 4 − 4 − 5 − 5 epicyclic overdensities epicyclic overdensities 8 8 • Symmetric density since no Linear Density Linear Density (arcmin � 1 ) (arcmin � 1 ) 6 6 Density 4 4 significant distance 2 2 gradient (Ibata et al 2016) 0 0 0.4 0.4 Width 0.3 0.3 w ( � ) w ( � ) 0.2 0.2 • Relatively smooth density 0.1 0.1 0.0 0.0 along stream with little Radial − 40 − 40 v r (km/s) v r (km/s) small scale structure velocity − 60 − 60 − 80 − 80 • Epicyclic over densities Angle along stream near progenitor Erkal, Koposov, Belokurov 2017
Gaps in Pal 5 • 2 gaps Perturbation by subhaloes Fiducial Model • ~ 2 degrees (10 6 -10 7 M � ) 1 1 N-body N-body Leading Leading Trailing Trailing 0 0 Perp Data Data − 1 − 1 φ 2 ( � ) φ 2 ( � ) − 2 − 2 angle − 3 − 3 − 4 − 4 • ~ 9 degrees (10 7 -10 8 M � ) − 5 − 5 epicyclic overdensities ∼ 10 6 M � flyby ∼ 10 7.7 M � flyby 8 8 Linear Density Linear Density (arcmin � 1 ) (arcmin � 1 ) 6 6 Density 4 4 • Observed width is more 2 2 0 0 uniform 0.4 0.4 Width 0.3 0.3 w ( � ) w ( � ) 0.2 0.2 0.1 0.1 0.0 0.0 Radial − 40 − 40 v r (km/s) v r (km/s) velocity − 60 − 60 Expected 0.7 gaps so − 80 − 80 ~3x LCDM Angle along stream 10 6 -10 7 M � ~ 9-18 keV thermal relic WDM Erkal, Koposov, Belokurov 2017
Gaps in Pal 5 Alternative mechanisms • GMCs (Amorisco+ 2016): 10 6 -10 7 M � • Perturbation by Milky Way bar 1 within solar circle (Rice + 2016), 0.65 0 Perp − 1 gaps expected φ 2 ( � ) − 2 angle − 3 − 4 − 5 Globular clusters: < 1/6 rate • 8 Density 6 expected from subhaloes (Erkal, Density Linear 4 Koposov, Belokurov 2017) 2 0 0.4 Width 0.3 w ( � ) MW Bar: Rotating bar creates • 0.2 differential torque along stream 0.1 0.0 (Erkal, Koposov, Belokurov 2017, Radial − 40 Pearson et al. 2017) v r (km/s) velocity − 60 − 80 MOND can create asymmetries in • tidal streams (Thomas, Famaey, Ibata Angle along stream 2017,Wu+2010) Erkal, Koposov, Belokurov 2017
Gaps in Pal 5 Data Realizations • Alternative statistical approach • Measure power spectrum/bispectrum of density fluctuations (Bovy, Erkal, Sanders 2017) • Streams and perturbations generated in action- angle space (Sanders, Bovy, Erkal 2016) • Idea • Select normalization of LCDM subhaloes • Perturb stream with subhalo flybys • Keep if power/bispectrum on large scales matches data • Get constraint on LCDM normalization Bovy, Erkal, Sanders 2017
Gaps in Pal 5 N-body inference • Tested with N-body streams Pal 5 inference • Pal 5 consistent with 1.5-9 LCDM, consistent with gap counting Bovy, Erkal, Sanders 2017
Gaps in GD-1 CFHT data Simulation 0.8 1 0.6 0.95 0.4 0.9 0.2 0.85 Stream ∆ϕ 2 (deg) 0 0.8 N on sky -0.2 0.75 -0.4 0.7 -0.6 0.65 -0.8 0.6 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 ϕ 1 (deg) 50 Angle along stream 45 density (stars/deg 2 ) 40 Stream 35 density • Hard to interpret since no progenitor 30 25 • Wiggles and density variations 20 15 • Still working on interpretation -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 ϕ 1 (deg) Angle along stream de Boer + 2018 ∆ϕ
Gaps in GD-1 Gaps confirmed with Gaia Price-Whelan & Bonaca 2018 50 45 Stream ) 2 40 density (stars/deg 35 density 30 25 20 15 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 ϕ 1 (deg) Angle along stream de Boer + 2018 ∆ϕ
Gaps in GD-1 Progenitor disruption creates a gap Stream density Stream observables Angle along stream Angle along stream Erkal & Gieles in prep.
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