Effect of substructure on tidal streams Denis Erkal University of - - PowerPoint PPT Presentation

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Effect of substructure on tidal streams Denis Erkal University of - - PowerPoint PPT Presentation

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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 )

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SLIDE 1

Effect of substructure

  • n tidal streams

Denis Erkal

University of Surrey Halo Substructure and Dark Matter Searches
 , IFT Madrid, June 29th 2018

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SLIDE 2

Milky Way Substructure

Aquarius, Springel et al. 2008

200 kpc Stars No Stars Mass (M) Halo mass function 1010 104

Image credit:ESA/Hubble & NASA

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SLIDE 3
  • Stars stripped at tidal radius
  • Once in the stream, each star

follows an orbit

  • Stream roughly follows an orbit

x (kpc) y (kpc) radial offset (kpc) tangential

  • ffset

(kpc)

Tidal Streams from Globular Clusters

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SLIDE 4

Tidal Streams from Globular Clusters

Smooth Potential Lumpy Potential

Interaction with substructure

Ibata et al. 2002, Johnston et al. 2002

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SLIDE 5
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SLIDE 6

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 7

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 8

Analytic Toy Model for Gaps

Setup

  • Stream on circular orbit
  • No position/velocity

dispersion

  • Plummer sphere perturber
  • Arbitrary spherical host

potential

  • Arbitrary impact geometry

Approach

  • Impulse approximation for

velocity kicks

  • Compute resulting orbits at

first order

  • Compute resulting stream

shape

  • Similar to Carlberg 2013,

Yoon, Johnston, Hogg 2011

Stream Perturber

b

Erkal & Belokurov 2015a

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SLIDE 9

Cartoon of Gap Formation

Orbital Mechanics 101 Gap Formation (also in Space)

Gap!

1) Flyby

ρ ψ ψ ρ

3) Expansion

ρ ψ

4) Gap

ρ ψ

2) Compression

ρ ψ

5) Caustic 1) Flyby

ρ ψ ψ ρ

3) Expansion

ρ ψ

4) Gap

ρ ψ

2) Compression 1) Flyby

ρ ψ ψ ρ

3) Expansion

ρ ψ

2) Compression 1) Flyby

ρ ψ ρ ψ

2) Compression 1) Flyby

ρ ψ

1) Flyby

Tangential Throw Radial Throw

Oscillations!

Earth Earth

aka Football in Space

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SLIDE 10

N-body example

  • Stream generated by progenitor on circular
  • rbit at 10kpc
  • NFW host potential
  • 108 M Plummer sphere, 250pc scale

radius

  • Direct impact on stream

Density along stream Sky angle (o) Gap density Time in Gyr Gap size (o) Time in Gyr

~1/t ~t1/2 ~t

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SLIDE 11

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

Time Time Gap size Gap density ~t1/2 ~1/t

Sanders, Bovy, Erkal 2016

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SLIDE 12

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 13

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 14

Streams around the MW

Shipp et al. 2018

Streams in DES

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SLIDE 15

Streams around the MW

Pal 5, Odenkirchen et al. 2002 Ibata et al. 2016 Tri/Psc - Bonaca et al. 2012 Martin et al. 2014 GD1, Grillmair & Dinatos 2006

~ 15 globular cluster streams around MW

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SLIDE 16

How many subhaloes fly near the stream?

  • Flux through cylinder around stream (same

approach as Yoon et al. 2011, Carlberg 2012)

v

s

z x y

r

|v |dt stream l bmax

Nenc ~ (number density)x(stream length)x(stream age)

  • Also get velocity distribution

Erkal, Belokurov, Bovy, Sanders 2016

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SLIDE 17

How many subhaloes fly near the stream?

  • Pal 5
  • ~3.4 Gyr old (Kuepper et al. 2015)
  • # 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)

105-106 M: ~26 within 2 rs 106-107 M: ~10 within 2 rs 107-108 M: ~4 within 2 rs

Ibata et al. 2016 Erkal, Belokurov, Bovy, Sanders 2016

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SLIDE 18

How many gaps are created?

  • Use gap size and gap depth from model
  • Subhalo properties from VLII (Diemand et al. 2008)
  • Match M-vmax relation with Plummer spheres
  • Know number of interactions, sample properties of flyby, get

distribution of gap properties

Angle along stream Stream density fcut

Erkal, Belokurov, Bovy, Sanders 2016

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SLIDE 19

Properties of Gaps

  • Distribution of gap sizes for LCDM spectrum from 105-108 M

Gap size Normalized distribution Guides the scale on which to search for gaps

Erkal, Belokurov, Bovy, Sanders 2016

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SLIDE 20

So… how many gaps?

GD1 0.6 gaps with f < 75% Tri/Psc 1.6 gaps with f < 75%

~3 gaps expected in all three streams

Density threshold Number of gaps deeper than threshold Pal 5 0.7 gaps with f < 75%

Erkal, Belokurov, Bovy, Sanders 2016

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SLIDE 21

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 22

Outline

  • How do gaps grow/evolve?
  • How many gaps are expected in the known

streams around the Milky Way?

  • Gaps in known streams
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SLIDE 23

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

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SLIDE 24 −5 −4 −3 −2 −1 1 φ2 () Leading Trailing

Fiducial Model

N-body Data 2 4 6 8 Linear Density (arcmin1) epicyclic overdensities 0.0 0.1 0.2 0.3 0.4 w () −80 −60 −40 vr (km/s) −5 −4 −3 −2 −1 1 φ2 () Leading Trailing

Fiducial Model

N-body Data 2 4 6 8 Linear Density (arcmin1) epicyclic overdensities 0.0 0.1 0.2 0.3 0.4 w () −80 −60 −40 vr (km/s)
  • How should unperturbed

stream look?

  • Equal amounts of material

in leading and trailing arm

  • Symmetric density since no

significant distance gradient (Ibata et al 2016)

  • Relatively smooth density

along stream with little small scale structure

  • Epicyclic over densities

near progenitor

Gaps in Pal 5

Erkal, Koposov, Belokurov 2017 Angle along stream Radial velocity Width Density Perp angle Ibata et al 2016

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SLIDE 25 −5 −4 −3 −2 −1 1 φ2 () Leading Trailing

Fiducial Model

N-body Data 2 4 6 8 Linear Density (arcmin1) epicyclic overdensities 0.0 0.1 0.2 0.3 0.4 w () −80 −60 −40 vr (km/s) −5 −4 −3 −2 −1 1 φ2 () Leading Trailing

Perturbation by subhaloes

N-body Data 2 4 6 8 Linear Density (arcmin1) ∼ 106M flyby ∼ 107.7M flyby 0.0 0.1 0.2 0.3 0.4 w () −80 −60 −40 vr (km/s)
  • 2 gaps
  • ~ 2 degrees (106-107 M)
  • ~ 9 degrees (107-108 M)
  • Observed width is more

uniform

Gaps in Pal 5

Angle along stream Radial velocity Width Density Perp angle Erkal, Koposov, Belokurov 2017 106-107 M ~ 9-18 keV thermal relic WDM Expected 0.7 gaps so ~3x LCDM

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SLIDE 26
  • Alternative mechanisms
  • GMCs (Amorisco+ 2016): 106-107 M

within solar circle (Rice + 2016), 0.65 gaps expected

  • Globular clusters: < 1/6 rate

expected from subhaloes (Erkal, Koposov, Belokurov 2017)

  • MW Bar: Rotating bar creates

differential torque along stream (Erkal, Koposov, Belokurov 2017,
 Pearson et al. 2017)

  • MOND can create asymmetries in

tidal streams (Thomas, Famaey, Ibata 2017,Wu+2010)

Gaps in Pal 5

−5 −4 −3 −2 −1 1 φ2 ()

Perturbation by Milky Way bar

2 4 6 8 Linear Density 0.0 0.1 0.2 0.3 0.4 w () −80 −60 −40 vr (km/s)

Angle along stream Radial velocity Width Density Perp angle Erkal, Koposov, Belokurov 2017

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SLIDE 27
  • 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

Gaps in Pal 5

Data Realizations

Bovy, Erkal, Sanders 2017

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SLIDE 28
  • Tested with N-body streams
  • Pal 5 consistent with 1.5-9 LCDM,


consistent with gap counting

Gaps in Pal 5

Bovy, Erkal, Sanders 2017

N-body inference Pal 5 inference

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SLIDE 29

Gaps in GD-1

  • 55
  • 50
  • 45
  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

ϕ1 (deg)

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 ∆ϕ2 (deg) 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 N

∆ϕ 15 20 25 30 35 40 45 50

  • 55
  • 50
  • 45
  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

density (stars/deg2) ϕ1 (deg)

CFHT data Simulation

Stream


  • n sky

Stream
 density Angle along stream

  • Hard to interpret since no progenitor
  • Wiggles and density variations
  • Still working on interpretation

Angle along stream

de Boer + 2018

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SLIDE 30

Gaps in GD-1

∆ϕ 15 20 25 30 35 40 45 50

  • 55
  • 50
  • 45
  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

density (stars/deg

2

) ϕ1 (deg)

Stream
 density Angle along stream

Price-Whelan & Bonaca 2018

Gaps confirmed with Gaia

de Boer + 2018

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SLIDE 31

Gaps in GD-1

Stream density Stream observables Progenitor disruption creates a gap

Erkal & Gieles in prep.

Angle along stream Angle along stream

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SLIDE 32

Recovering Subhalo Properties

  • Gap properties depends on 7d parameter

space:

  • Subhalo mass
  • Scale radius
  • 3 velocities
  • Impact parameter
  • Time since impact
  • Can we constrain these from observations of

a gap?

z x y b α (w ,w ,w )

x y z

(0,v ,0)

y

To galaxy center

Stream M,rs

Erkal & Belokurov 2015b

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SLIDE 33

Stream observables

Angle along stream Distance Declination angle Radial velocity Tangential velocity Vertical velocity Density

  • Analytic model predicts 6d shape of perturbed stream

107 M, rs=250 pc

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SLIDE 34

Inference with emcee

Mass Velocity rs b time Velocity rs b time

{

107 M, rs=250 pc

LSST Errors

Erkal & Belokurov 2015b

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SLIDE 35

Observational Strategy

  • Measure density and centroid along stream
  • Look for density variation with accompanying 


wiggle

  • Follow up with radial velocities
  • Develop tools to model gaps in real streams
  • Fit gap!





√ √- Pal 5 GD-1 √ In progress In progress √-

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SLIDE 36

Sagittarius stream in Gaia

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SLIDE 37

Conclusions

  • Kicks from subhaloes change orbital periods and create gaps
  • Expect ~1 deep gap per long stream
  • Pal 5 contains 2 gaps and is consistent with ~ 3x LCDM
  • Small gap consistent with 106-107 M subhalo, > 9-18 keV WDM
  • GD-1 has 3 gaps (1 from progenitor?), ~ 3x LCDM
  • Next step: perform inference for observed gaps
  • Can be used for constraints on any DM model