Substructure abundance and the haloes of dwarfs

Raphaël Errani

News from the Dark meeting

Montpellier, 24 May 2018

abbreviated version for the web 1/15 Motivation: preventing artificial disruption of low-mass substructures

cosmological simulations resolve dwarf experiment II: J-factors ◦ ◦ galaxies with a finite number of particles, for a MW-like DM halo 11 500 e.g. at M 108 M , for Aquarius-A2 ∼ (Springel 2008), N 104 10 400

∼ ) 9 experiment I: MW-like host: NFW halo, 300 M kpc

◦ /

M/ 8 disc, bulge; dSph satellite, γ = 1, 200 d

8 lg ( 5 10 M , a = 1 kpc; polar orbit 7 × 100 rp = 2adisc 1 6 3 0 N = 10 3 N = 104 5 N = 10 2 8 J = dΩ dr % 1 > 10 M DM 10− ZZ 0

) 2 9 m > 10 M / > J m (

2 N 10− 10

lg > 10 M 1

3 10− 0 2 4 6 8 10 12 0 16 17 18 19 t [Gyrs] 2 4 5 lg J(< 0.5◦)/GeV c− cm− no convergence for low N! low-mass substructures might (see van den Bosch 2018: produce the dominant effect! up to 80 per cent artificial disruption) 2/15 i) Substructure abundance in Milky Way-like haloes: Numerical setup this project: assembly of a MW-like halo through single accreted satellites with equal numerical resolution over many orders of magnitude in mass (motivated by Bullock & Johnston 2005) first application: how does the presence of a disc alter the abundance of DM substructures as a function of the satellite DM profile (cusp/core)? host: spherical NFW halo, evolution fitted to ◦ Aq-A2 run (Buist & Helmi 2015) optional: axisymmetric disc of mass co-moving ◦ 0.1 M200(z) (Miyamoto & Nagai 1975) NFW halo satellites: structural and orbital parameters from MN disc 2a ◦ Aq-A2 tree at zinfall 20a 8 M200 > 10 M , 960 in total ◦ r from mass-concentration relation ◦ 200 (Prada 2012) fix N-body: 2 106 particles (CCCP-II: 107) ◦ × ρc 1 Mpc ρ r ( ) = 3 (r/a + rc/a)(r/a + 1) superbox, multi-grid PM code, (dx2) cusp r = 0, core r > 0 ◦ O c c (Fellhauer 2000) injected in host potential at zinfall ◦ dx = 2 r 2/64 (CCCP-II: 2 r−2/128 ) ◦ − dt = min 1 Myr, tdyn(r 2)/400 − 3/15  Controlled simulations

selected individual cuspy satellites at z = 0, box width 1 Mpc

4/15 Controlled simulations

no disc no disc with disc

200 13 50

12 6 − 100 25 11 kpc 2

0 0 10 M / cusp /kpc z i 9

-25 2 DM

-100 ρ h

8 lg -50 -200 7

200 50

100 25

0 0 core /kpc z -25 -100

-50 -200

-200 -100 0 100 200 -50 -25 0 25 50 -50 -25 0 25 50 x/kpc x/kpc x/kpc

5/15 Substructure abundance at z = 0

1000 as a function of mass: z = 0, rp < r200

masses estimated by iteratively fitting ) 100 ◦ Hernquist profiles to particles of each < M satellite (limits impact of extra-tidal ( M200(zinfall) N 10 cusp, no disc features) cusp, disc core, no disc no surviving cored substructures with core, disc ◦ M 2.5 106 M 1 ≤ ×

shape of the mass spectrum does not ) 100

◦

change between models M

cored models have 2 times less M/ ◦ ∼

substructures than cuspy ones d lg( 10 N/

including a disc reduces the total d ◦ number of substructures by 20 per cent ∼ 106 107 108 109 1010 M/M

6/15 Substructure abundance at z = 0

1000 z = 0

as a function of the galactocentric dis- ) 100 p tance rp of the first pericentric passage: < r (

N 10 no cored substructures with rp 8 kpc 6 a = 21 kpc r ◦ . d 200 for large rp the number of satellites per ◦ pericentre bin converges to similar values 1 for all models the difference between the models is 100 kpc)

◦ /

largest for satellites on orbits that p r penetrate the disc (rp 6ad): zinfall, no disc . z d lg( 10 infall, disc factor 4 between cusp/core, cusp, no disc

∼ N/ factor 2 between no disc/disc d cusp, disc . core, no disc core, disc 1 4 10 100

rp/kpc RE, J. Peñarrubia, C. Laporte & F. Gómez, arXiv:1608.01849

7/15 ii) The haloes of Milky Way dwarfs: dynamical mass estimates

Using the Jeans equations? 2 2 2 Rσ (r) d ln ν?(r) d ln σ (r) σ M(< r) = r + r + 2β(r) where β 1 r (e.g. BT87) G d ln r d ln r ≡ − σ2 mass - anisotropy degeneracy:  ⊥ β(r) is (practically) inaccessible to observations (but: 3D motions in Sculptor, Massari+18) ◦ β(r) does not need to be a monotonic function of r, and might vary between different stellar ◦ populations within the same dwarf Read+17 show that with 104 and Jeans analysis, β(r) can’t be recovered robustly ◦

Projected Virial theorem: (e.g. Merrifield+90, more recently Agnello+12, Richardson+14) no mass - anisotropy degeneracy ! 2Klos + Wlos = 0 ◦ systematic biases of inferred masses follow ◦ Pressure term: directly from the assumptions on the DM ∞ 2 2 and stellar density profiles 2Klos = 2π Σ?σlosRdR σlos ≡ h i σ2 is a sum over all stars and does not 0 ◦h losi Z require data to be binned: can be robustly Potential term for spherical systems: computed also for systems with a low 4πG ∞ number of stars (uncertainties for low number Wlos = rν?(r)M(< r)dr − 3 0 of tracers: Laporte+18) Mass and dispersion areZ related by: 1 2 with 1 1 M(< R) = G− µ R σlos µ(R) = GM(< R) R− Wlos− h i − 8/15 Minimum variance values for λ, µ

Which choice of constants for λ, µ minimizes Given an observed half-light radius Rh the uncertainty on the inferred masses motivates to write (e.g. Amorisco+12): introduced by our ignorance of the segregation 1 2 Rh/rmax Mest(< λRh) = G− µ λRh σlos ◦ h i the central slope γ of the DM profile ? ◦ µ is a function of segregation Rh/rmax! Marginalize over segregation and γ (flat priors): For DM α, β, γ density profiles 1 1 { } µ(λ) = d(Rh/rmax) dγ µ γ α (γ β)/α h i r − r − Z0 Z0 %(r) = %s 1 + 2 2 rs rs variance = µ(λ) µ(λ)   h   i h i − h i and Plummer 2, 5, 0 stellar tracers: minimum variance: λ¯ = 1.8, µ¯ = 3.5 { } 4 5 µγ i λ = 1, ν? Plummer =0 3 hµ i 2 los 4 γ=1

σ h i

h µ

h h i 2 cusp /R s

) 3 h Minimum variance

α, β, γ i ± ¯ { } µ λ = 1.8, µ¯ = 3.5 < R h 2 ( 1 NFW 1, 3, 1 { } Dehnen, cusp 1, 4, 1 Walker+ 2009

GM { } Tidal, cusp 1, 5, 1 1 Wolf+ 2010

= core { } Dehnen, core 1, 4, 0 Amorisco+ 2011

µ 0.5 { } Tidal, core 1, 5, 0 Campbell+ 2016 { } 0 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 R /r λ h max 9/15 Consistency test using mock dwarf galaxies

We assign mass-to-light ratios at infall to the DM particles of our MW-halo re-simulations to trace the tidal evolution of an embedded stellar population (see Bullock & Johnston 2005)

a) Min. var. Cusp γ = 1 b) Walker+ 2009 true 1.5 c) Wolf+2010 1.5

λ, a

/M b )

h 1 c 1 c a < λR ( b M 0.5 0.5 Core γ = 0

true 1.5 b 1.5 a λ, c /M )

h 1 1 a c < λR (

M b 0.5 0.5 0.1 1 0 0.5 1 Rh/rmax (z = 0) N/Nmax

Minimum variance estimator gives accurate masses within 10% for both cuspy and cored ∼ systems 10/15 Mean densities of Milky Way dwarfs vs controlled simulations

R and σ2 of Milky Way dwarfs taken from McConnachie 2012 ◦ h h losi Enclosed masses M(< 1.8 Rh) estimated using the minimum-variance estimator ◦ 1 3 Mean density: %(< 1.8 R ) = M(< 1.8 R )(4π/3)− (1.8 R )− ◦ h h i h h Compared against our cuspy and cored simulated haloes: (Aq-A2 re-simulations, 107 particles per satellite):

Cusp γ = 1 Core γ = 0 Sagittarius dSph 10 Fornax M I 1.0 1.0 max Sculptor M 0.1 Leo II /M max Sextans (I) 3 9 max 0.1 /M

− 0.01 Carina Ursa Minor , max

0 kpc Draco

, Canes Venatici (I) 8 0 M Crater 2

/ 0.01 i

) Bootes (I)

< r 7 Leo IV (

% Ursa Major (I) h

lg Canes Venatici II 6 Ursa Major II Coma Berenices Bootes II 5 Segue II 0.01 0.1 1 0.01 0.1 1 Segue (I) r / kpc r / kpc

Ultra-faint dwarfs require core sizes much smaller than the DM scale radius 11/15 (Total) DM halo masses of Milky Way dwarfs

Observed R + σ2 + 2 parameter halo model r , v degeneracy curves: h h losi → max max Cusp γ = 1 Core γ = 0 Sagittarius dSph Fornax 10 Sculptor Leo II Sextans (I) Carina Ursa Minor Draco Canes Venatici (I) Crater 2 kpc

/ Leo T Hercules

max 1 Bootes (I) r Leo IV Ursa Major (I) Leo V Canes Venatici II Ursa Major II Coma Berenices Bootes II Willman 1 Segue II 0.1 10 10 Segue (I) 1 1 vmax/km s− vmax/km s− breaking the degeneracy: we fit the observed dispersions σ2 to simulated haloes h losi ∞ 2 4πG σ = Wlos = rν?(r)M(< r) dr h los,simi − 3 Z0 by selecting the halo which minimizes 2 2 2 2 1 2 2 crosses ++++ in figure χ σ2 = σlos σlos,sim var− σlos σlos,sim h losi h i − h i h i − h i → 12/15   Consistency test using mock dwarf galaxies

Cusp Core

2 200 σlos fit Min.h i var.

10 Walker+09 / 150 Wolf+10 = 1 0 N , 100 max /r

0 50 , h R 0 200 20 / 150 = 1 0 , N 100 max /r 0

, 50 h R 0 0.1 1 10 0.1 1 10 Mtot/Mtrue Mtot/Mtrue

The (total) halo masses inferred using direct σ2 -fits for the mock catalogue are unbiased. h losi 13/15 Stellar mass - halo mass relation for satellite galaxies

8 Cusp Ultra-faint dwarfs: anti-correlation of Moster+10 Sgr For Behroozi+13 stellar mass - halo mass Sawala+15 7 Leo I 1.0 0.1 Scl 0.01 Possible causes: ,0 6 max Leo II /M Sex (I), Car Mmax Binary motion inflates the observed velocity

CVen (I) Dra,UMi

M Cra 2 Leo T ◦ /

? 5 dispersion M Boo (I)Her lg Leo IV UMa (I) Contamination by foreground stars Leo V 4 CVen II ◦ CBer UMa II e.g. Adén+09: σlos for Hercules 7 km/s → 4 km/s i l1o II Will 1Boo 3 Seg II Systems not in equilibrium Seg (I) ◦ Aq-A2 merger does not contain haloes 2 ◦ 4 5 6 7 8 9 10 11 12 8 representative of ultra-faints (cosmic variance?) Core Moster+10 Sgr For Behroozi+13 7 Sawala+15 Leo I Use the virial theorem to avoid mass - anisotropy 0.1 1.0 Scl 0.01 ◦ degeneracy: M(< λR ) = G 1µλR σ2 6 ,0 Leo II h − h los /Mmax Sex (I) Mmax Car h i CVen (I) UMi,Dra λ = 1.8, µ = 3.5 for minimum-variance mass M Cra 2 Leo T /

? 5 ◦

M estimates Boo (I)Her lg Leo IV Leo V UMa (I) Direct fits of 2 allow to infer the (total) halo 4 CVen II σlos CBer UMa II ◦ h i mass Boo II Will 1 3 Seg II Something odd is going on with ultra-faints Seg (I) ◦ 2 RE, J. Peñarrubia, M. Walker, arXiv:1805.00484 4 5 6 7 8 9 10 11 12 lg Mtot/M 14/15 8 We reliably resolve low-mass substructures: e.g. for haloes with M(zinfall) = 10 M , we

have mp 10 M , and we follow the dynamical evolution of substructure with the same ∼ numerical resolution spanning many orders of magnitude in mass and size.

(future) applications: dynamical properties of DM: abundances (E+16), annihilation signals, J-factors ◦ structure of stellar haloes: abundance and distribution of ultra-faints, ◦ number of streams in the solar neighbourhood, mass-luminosity relation for Milky Way dwarfs (E+18) formation mechanisms for ultra-diffuse galaxies (see C+18 arXiv:1805.06896), convolve our models with Gaia-uncertainties; ◦ predictions on the number and properties of detectable faint streams and remnant progenitors

web: www.roe.ac.uk/~raer, mail: [email protected]

15/15