/ modeling of spherical systems: from galaxy clusters to dwarf spheroidals

Andrea BIVIANO Antonio CAVA OATS, Trieste Univ. de Genève

Gwenaël BOUÉ Richard TRILLING IMCCE, Paris retiree

+ Chris GORDON (Christchurch, NZ), Radek WOJTAK (KIPAC, Stanford), Joe SILK (IAP…), Laura WATKINS (STScI), Matt WALKER (Pittsburgh), Justin READ (Sussex) ...

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 1 Basic Motivations

Nature of Dark Matter self-interacting? warm? need for modified ? annihilation cross-section

Dark Matter as a reference normalization, concentration, inner & outer slopes = f(halo mass)

Dark Matter as a constraint on galaxy formation same compared to simulations

Morphological evolution of galaxies in clusters log M/M⊙ = 15 orbital shapes of different galaxy types in clusters

Formation & evolution of dwarf spheroidal galaxies log M/M⊙ = 8.5 orbital shapes of different stellar types in dwarfs spheroidals

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 2 Dark Matter Standard Model DM is collisionless Aquarius DM Simulation Springel+08 Millennium DM Simulation Springel+05 300 kpc 300 Mpc Milky Way size

r −3

Navarro, Frenk & White 96 « NFW »

Navarro, Frenk & White 96 « NFW » −1 r x50 numerous subhalos 8-9 • low mass (10 M⦿) galaxies (dSph) dominated by Dark Matter • lower mass structures = dark! r −3

Cores if self-interacting DM cuspy dark matter halos (or baryonic feedback) Subhalos rare if warm DM particle

Gary Mamon (IAP), 29 August 2016,log Amsterdam-Paris-Stockholmradius (kpc) mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 3 Cosmological N-body simulations with gas

Gnedin et al. 04

Pontzen & Governato 12

−2 ρDM ∝ r

2 ρDM ∝ 1/r intermittent SN feedback

no feedback

dominant baryons → even cuspier dark matter halos intermittent SN feedback → cored dark matter halos Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 4 Motivations 2 If DM has • fairly large annihilation x-section • cuspy profiles (as in DM-only cosmo-sims) → ~ observable in γ-rays d2 ⌃(v) v dN flux density = J (✓) h i b dE d⌦ los m2 i dE DM i i X ✓ ◆ Astrophysics Particle Particle Physics Chemistry

1 2 1 1 2 r dr Jlos(✓)= ⇢ (r)ds = ⇢ (r) 2 2 2 2 2 4⇡D 2⇡D ✓ D pr ✓ D Z Z

Mass/Orbit modeling → J → calibration of Particle Physics term

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 5 γ-ray telescopes

H.E.S.S. (Namibia) Resolution 10’ VERITAS (Arizona) Resolution 6’-10’ MAGIC (Canary Islands)

Cherenkov Telescope Array (CTA): 10x more sensitive, wider energy-range 3x better angular resolution

Which targets for CTA? Lefranc, GM & Panci 16, JCAP, submitted

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 6 Dependence of line-of-sight γ-ray flux on DM slope & concentration at fixed DM virial mass

��� concentration�=�������

��� c=5 c=20 c=10 ��� ��� inner slope ��� γ=-1 ���� γ=-0.7 γ=-0.4 �� γ=-0.1 ����� ����� ����� ����� ����� ����� �

�/���� inner DM slope vs DM concentration degeneracy may be lifted

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 7 Basic methods to measure mass profiles

• Dynamics tracer line-of-sight Only dynamics is applicable to dwarf spheroidal galaxies • Hydrodynamics Dynamics also provides X-rays w/o or w SZ orbital shapes

• General relativity strong or weak gravitational lensing

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 8 Dark Matter = Total Matter – Visible Matter

DM

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 9 Internal kinematics: from phase space to local space see also Hamish Silverwood’s talk

f = f (r,v) ≡ distribution function = 6D phase space density Collisionless Boltzmann Equation ∂f ∂f + v⋅ ∇f − ∇Φ⋅ = 0 incompressible 6D fluid ∂t ∂v € v CBE d 3v Boltzmann ∫ j

€ P = ⌫ Jeans Equation r · r tracer density € 2 P = ⌫ v

Maxwell Jeans

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 10 Spherical stationary Jeans equation tracer density anisotropic dynamical pressure 2 d ⇥⇤r (r) 2 GM(r) +2 ⇥⇤r = ⇥ 2 dr ⇥ r r

⇥2(r) = anisotropy (r)=1 2 ⇥r (r)

isotropic : β = 0 radial orbits: β = 1 circular orbits: β → −∞

mass / anisotropy degeneracy MAD

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 11 2 classes of kinematical modeling e.g. chap. 5 of Courteau et al. RevModPhys 2014

• Jeans equations on moments of the observed LOS velocities in bins of projected radii

• Distribution functions on distribution of tracers in projected phase space

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 12 2 classes of kinematic modelling 1. Jeans analysis R r Data: surface density Σ, los velocity dispersion σlos (& kurtosis κlos) in bins of projected radius R 2 – model fit of los velocity dispersion M & β → Σ σlos Tremaine+94; Mamon & Łokas 05b 2 – model fit of los velocity dispersion & kurtosis M & β → Σ σlos & κlos Łokas 02; Richardson & Fairbairn 13 2 – Anisotropy inversion Σ σlos & M → β Binney & Mamon 82; Solanes & Salvador-Solé 90; Dejonghe & Merritt 92; ... 2 – Mass inversion Σ σlos & β → M Mamon & Boué 10; Wolf+10 2. Distribution function modeling

Data: distribution of tracers in projected phase space g(R,vlos)

– standard M & β & f(E,J) → g(R,vlos) Wojtak+09

– orbit modeling M & orbits → g(R,vlos) Schwarzschild 79; Syer & Tremaine 94; de Lorenzi+09

– elementary distribution funcs M & fi(E,J) → g(R,vlos) Merritt & Saha 93; Gerhard+98;

– MAMPOSSt M & β & f(v3D) → g(R,vlos) Mamon, Biviano & Boué 13

– caustics g(R,vlos) & β → M Diaferio & Geller 97 Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 13 R r Mass inversion Kinematic deprojection & mass inversion of spherical systems with known anisotropy Mamon & Boué 10; Wolf et al. 10

∞ $ R2 ' r dr anisotropic kinematic projection P(R) = 2 1− β p ∫ & 2 ) 2 2 R % r ( r − R 2 p = ν σr = dynamical pressure Binney & Mamon 82 2 P = Σ σlos = observed “projected pressure” € deprojection

GM & Boué 10: → simple β(r) ↓ insert dynamical pressure into Jeans equation → mass profile simple β(r): single integral!

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 14 Jeans analysis involves binning!

Richardson & Fairbairn 14 Sculptor

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 15 z Distribution function modeling R r

Density in projected phase space Dejonghe & Merritt 92 ∞ r dr +∞ +∞ & 1 ) g(R,v ) = 2 dv f v2 + Φ(r),J dv z ∫ 2 2 ∫ R ∫ '( 2 *+ θ R r − R −∞ −∞ what choice for f(E,J)?

€ ΛCDM halos: 2 0 2( 0) J f = f(E,J)=f (E) J 1+ E r2v2 a a ⇥ Wojtak, Łokas, GM, et al. 08

analysis in projection Wojtak, Łokas, GM, et al. 09 slow (triple integral)

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 16 MAMPOSSt: Modeling Anisotropy & Mass Profiles of Observed Spherical Systems Mamon, Biviano & Boué 13 PDF of distribution in projected phase space 4000 4⇡R 1 r⌫(r) Projected phase space Ê p(R, v )= h(v R, r)dr Ê z z Ê Ê 2000 Ê 2 2 Ê Ê N p | ÊÊ Ê Ê Ê p R r R ÊÊÊ Ê Ê Ê Ê ÊÊÊ Ê ÊÊ Ê Ê Ê ÊÊÊÊ Ê Ê Ê ÊÊ Ê ÊÊ Ê Ê ÊÊ Ê Ê ÊÊ Ê Ê Ê Z L Ê Ê ÊÊÊ Ê Ê Ê Ê Ê ÊÊ ÊÊ ÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê 1 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ÊÊÊ Ê Ê Ê Ê ÊÊÊÊÊÊ Ê ÊÊÊ Ê Ê Ê Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê - Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê ÊÊ Ê ÊÊÊ ÊÊ ÊÊÊ Ê Ê ÊÊ Ê Ê Ê Ê Ê s ÊÊÊÊ Ê Ê Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ÊÊ Ê ÊÊ Ê Ê Ê Ê ÊÊ Ê ÊÊ ÊÊÊÊ Ê ÊÊÊ Ê ÊÊ ÊÊ Ê Ê Ê ÊÊ ÊÊ ÊÊÊ Ê Ê Ê ÊÊ Ê ÊÊ ÊÊÊ Ê Ê ÊÊ ÊÊ Ê 0 Ê ÊÊÊÊÊÊÊ ÊÊÊÊ Ê ÊÊ Ê Ê ÊÊÊÊ Ê Ê ÊÊÊ ÊÊ ÊÊ ÊÊ ÊÊÊ ÊÊ Ê Ê Ê Ê Ê ÊÊ ÊÊ Ê ÊÊ ÊÊ Ê ÊÊ Ê ÊÊÊÊ ÊÊ ÊÊ ÊÊ Ê ÊÊ ÊÊÊ Ê Ê Ê ÊÊ Ê Ê ÊÊ km Ê Ê Ê Ê Ê ÊÊ ÊÊÊ ÊÊ Ê Ê Ê Ê Ê Ê Ê ÊÊÊ Ê ÊÊ Ê ÊÊ ÊÊ Ê Ê Gaussian 3D velocities: H ÊÊ Ê ÊÊÊÊ Ê Ê Ê ÊÊ Ê Ê ÊÊ ÊÊ Ê Ê Ê Ê Ê Ê Ê ÊÊÊ ÊÊ Ê ÊÊ Ê ÊÊ ÊÊÊÊ ÊÊ Ê ÊÊ Ê Ê ÊÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê v Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê ÊÊÊ ÊÊ ÊÊ Ê Ê Ê Ê ÊÊ Ê ÊÊÊ ÊÊ Ê Ê ÊÊ Ê ÊÊ Ê ÊÊ Ê ÊÊ Ê Ê Ê ÊÊ Ê ÊÊ ÊÊÊ Ê Ê Ê ÊÊ ÊÊ Ê Ê Ê Ê Ê Ê Ê ÊÊÊÊÊ Ê Ê Ê ÊÊÊÊ Ê Ê Ê Ê ÊÊÊ Ê ÊÊ Ê Ê Ê ÊÊ Ê Ê Ê 2 Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 1 v Ê Ê Ê Ê Ê Ê -2000 Ê Ê Ê z Ê Ê Ê ÊÊ h(v R, r)= exp ÊÊ Ê z 2 2 Ê | 2⇡z (R, r) 2 z (R, r) ÊÊ  -4000

0 500 1000 1500 2000 2500 line-of-sightvelocity R 2 R kpc z(R, r)= 1 (r) r(r) projected radius r H L s ✓ ◆ Solution to Jeans equation of local dynamical equilibrium 2 z 1 1 dt GM(s) 2(r)= exp 2 (t) ⌫(s) ds R r r ⌫(r) t s2 Zr  Zr very fast!

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 17 Applications to clusters of galaxies

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 18 Mass inversion of Coma cluster

virial radius

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: fromSDSS galaxy clusters to dwarfs 19 Coma cluster

• SDSS DR7 ~ 550 Red Sequence velocity-accordant member galaxies

• Spectroscopic Completeness ~ 0.95, independent of projected radius

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 20 Mass inversion of Coma cluster: Mass (circular velocity) profile

1600

1400

1200

" ML anisotropy 1 ! 1 r Mamon & Łokas 05 1000 = km sec ! 2 r + r 2 800 circ cir v v 600 1800

400 Trilling, Mamon & Biviano in prep. 1600

200 20 40 60 1400 80 " 1 r arcmin ! isotropic velocities 1200 km sec ! " ! cir circ 1000 v v

800

600 Trilling, Mamon & Biviano in prep.

20 40 60 80 not flat (→ not singular-isothermal) r arcmin

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 21 ! " Trilling, Mamon & Biviano in prep. ] ] ⊙

⊙ Mass follows RS /L /L

⊙ isotropicisotropic ⊙ ML anisotropy

[M ) r • light? [M ) ( r ( X-SZhot gas RS RS L L

)/ center: NGC 4874

• number? r )/ ( r

( NGC 4889

• stellar mass? M M

Trilling, Mamon & Biviano in prep.

Trilling, Mamon & Biviano in prep. ) ) r ( ]

⊙ isotropicisotropic ML anisotropy stars,RS ML anisotropy ) [M ) m

r isotropicisotropic ( )/

ML anisotropy r hotX-SZ gas

ML anisotropy ( RS

N center: NGC 4874 )/

r hotX-SZ gas ( NGC 4889 center: NGC 4874

M NGC 4889 M

mass follows RS galaxies (outside 0.1 rvir)

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 22 mass inversion of Coma cluster: slope of total density profile

0 isotropic velocities – 1 errors from bootstraps in radial bins 2 ML anisotropy – 2 ρ r

Ρ

r ⇢ ln

ln ln errors from bootstraps in radialln – 3 bins d

1 d d d NFW

– m=6 Einasto NFW 4

0 Hernquist

r ⇢

r m=6 Einasto Ρ

– 5

ln ln ln

ln Hernquist

d d d

d Trilling, Mamon & Biviano in prep. – 1 200 300 500 700 1000 1500 2000 r ((kpc)kpc) – 2

– 3 Trilling, Mamon & Biviano in prep.

150 200 300 500 700 1000 1500 2000 rr(kpc)kpc ML anisotropy → slopes consistent with NFW isotropic velocities → require outer slope steeper than NFW

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 23 MAMPOSSt analysis of Coma cluster

tracer scale radius NFW tracer Mamon & Biviano in prep

NFW mass

r virial radius = 1 r + r 2

MCMC virialradius (CosmoMC) mass scale radius

Uniform priors isotropic ML of log X in given range massscale radius vel. anisotropy 6 chains of 40k elements vel.anisotropy

GaryPreferred Mamon (IAP) ,outer 29 August velocity 2016, Amsterdam-Paris-Stockholm anisotropy of mtg,Coma Gouvieux, Red Mass/orbit Sequence modeling of galaxies: spherical systems: β=0.6 from galaxy (β∞ clusters⩾0: P to=97%) dwarfs 24 Analysis of stacked WINGS clusters

stack 29 regular clusters with ≥ 81 members • adopt Brightest Cluster Cluster (BCG) for center • remove interlopers of individual clusters (Clean method of Mamon+13) • scale projected radii to virial radii • scale line-of-sight velocities to virial velocity • final removal of interlopers

→ 3500 total galaxies

Run MAMPOSSt jointly on Ellipticals, S0s and Spirals

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 25 DM density profiles Assume free inner slope and fix outer slope to –3 (NFW)

Cava, GM & Biviano inner mass excess due to in prep neglected BCG

RegsigvNm81Aug16NFWgenOMgengentry9

inner slope consistent with NFW cusp or steeper

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 26 Orbital shapes (velocity anisotropy)

RegsigvNm81Aug16NFWgenOMgengentry9

Cava, GM & Biviano in prep

inner orbits consistent with isotropic for all galaxy types (S0 slightly radial) outer orbits: spirals = radial, ellipticals = slightly radial, S0s in between, closer to Es

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 27 Applications to dwarf spheroidal galaxies

Fornax dwarf spheroidal

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 28 current analysis of dSphs

generally assume Gaussian LOS velocities

Bonnivard+15, arXiv:1504.02048

see Andrea Chiappo’s talk

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 29 Modeling Fornax & Sculptor dwarfs

Jardel & Amorisco+13 Breddels+13 Richardson & Gebhardt 12 Fairbairn 14

2200+ stars in 2200 stars in 1300 stars in Data Fornax in 3 metal 1300 stars in Sculptor Fornax Sculptor populations

Jeans Method orbit Wolf pinch orbit (dispersion-kurtosis)

Assumptions cored or NFW σLOS=cst (not true (all DM for 1 of 3 pops !) spherical) disagreements! inner DM core or NFW (if very cored –1 ↔ –0.1 unconstrained slope low concentration)

inner: radial inner: slightly velocity inner: isotropic NA outer: tangential tangential anisotropy outer: radial outer: radial disagreements! Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 30 Towards better analyses of dSph galaxies γ • dSph galaxies are tidally truncated: ρstars(r) ∝ r exp(–r/rtid) Kazantzidis+04

• dSph may harbor dynamically important Black Holes

2 • σLOS is not Gaussian, but χ distributed → wider wings

• Fitting σLOS(R) only misses information → poorly constrains β, hence M(r)

Orbit modeling is best solution, but extremely slow MAMPOSSt is best compromise

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 31 7 2633 velocities LV = 1.9 x 10 Lsun Fornax data 2278 Fornax members Irwin & Hatzimiditriou 95 Fornax metallicity Milky Way metallicity 7 LV = 0.9 x 10 Lsun Walcher et al. 03 2 Re m = 0.7 Sersic distribution Walcher et al. 03; Battaglia et al. 06

ellipticity: 0.21 → 0.36 Battaglia et al. 06

main starburst: age = 5.4 Gyr Saviane et al. 00

Mstars/LV = 4.8 Walcher et al. 03 (uncertain) center: Battaglia et al. 06 data & MW flags: rejected outlier Walker et al. 09 Magellan/MMFS Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 32 Fornax: at least two populations 2267 member velocities metal-poor: W′ < 0.5A

metal-rich: W′ > 0.5A

W′ = ΣMg + 0.079(V–VHB)

see Battaglia+08; Walker & Penarrubia 11; Amorisco & Evans 12

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 33 Fornaxrrich modelled rpoor with truncated NFW

frich

Mstars

MDM(1.4kpc)

cDM cores & cusps allowed

γDM

Arich

Apoor BH mass can be important

MBH

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 34 Inner DM profile of Fornax dwarf depends on priors!

Mamon+15, 1410.7175

to be analyzed in full detail by Gohar DASHYAN … Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 35 Can we better constrain the nature of Dark Matter with new observations?

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 36 The Theia Mission

Astrometric satellite with 30x Gaia’s accuracy

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 37 Parallax & Proper Motion

proper motion

parallax 6 months later Earth Dec∆ (mas)

Sun

∆RA (mas)

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 38 Dark Matter (DM) in mock dwarf Spheroidal galaxies without & with proper motions Gaia Challenge: mocks from M. Walker; with J. Read & L. Watkins

Mass-orbit modeling (Jeans equation) of mock dSph galaxies → DM density profiles ) ) –3 PM+LOS fit –3 PM+LOS fit LOS only fit 101 LOS only fit 0 pc 10 isotropic velocities pc radial outer velocities dSph = DM-dominated ⦿ true ⦿ true

] L. Watkins ] 0 velocity dispersion:

3 3 10 1 10 pc pc σv ≈ 10 km/s

sun 1 10

[M 2 [M 10 ⇢ LOS only fit ⇢ LOS only fit

LOS+PM fit 2 LOS+PM fit cored DM mocks10 Theia proper motions 3 10 L. Watkins true true → ∆v = 3 km/s DMmassdensity (M 1 0 DMmassdensity (M 1 0 10 10 10 10 radiusr [kpc] (kpc) radiusr [kpc] (kpc) ) ) 102

–3 Theia proper motionsPM+LOS fit dramatically–3 reduce biasPM+LOS & fit uncertainty on inner DM slope! 101 LOS only fit LOS only fit pc true pc radial outer velocitiestrue ⦿ isotropic velocities ⦿ 101

] 0 ]

3 10 3 L. Watkins L. Watkins If cores found in ~all dSphs: pc pc 100

sun sun case for interacting DM 1 10 [M [M

⇢ LOS only fit ⇢ LOS only fit 1 10 2 LOS+PM fit LOS+PM fit 10 cuspy DM mocks calibration of DM annihilation x-section

true 2 true 10 from γ-ray obs of dSph galaxies

DMmassdensity (M 1 0 DMmassdensity (M 2 1 10 10 10 10 r [kpc] r [kpc] Gary Mamon (IAP), 29 Augustradius 2016, (kpc) Amsterdam-Paris-Stockholm mtg, Gouvieux,radius Mass/orbit (kpc) modeling of spherical systems: from galaxy clusters to dwarfs 39 Detecting subhalos in Milky Way • By perturbations of stellar orbits

Largest effect when subhalo passes through disk still visible after 1st passage

in disk Feldmann & Spolyar 15

Gaia can detect log M = 8 subhalos (rare: closest at 3 kpc) Theia (20 LOS in 2 yr) can unambiguously detect log M = 6.7 subhalos → avoid confusion with other perturbers If no subhalos found: case for Warm Dark Matter

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 40 Detecting subhalos in Milky Way • By micro-lensing

follow-ups of candidates from γ-ray observations or stellar perturbations

Erickcek & Law 11

If no subhalos found: case for Warm Dark Matter

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 41 Shape of outer Dark Matter halo of Milky Way using Hypervelocity stars • v > vesc • 10 known today • originate from Black Hole at Galactic Center ⇒ trajectories measure shape of MW potential

standard DM halo model

10 µas/yr accuracy required Gnedin+05

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 42 Conclusions

• Mass/orbit modeling can constrain nature of Dark Matter – resolved γ-rays with CTA – using proper motions with Theia if approved

• Often contradictory results by ≠ teams on same object with same data e.g. cusps vs cores in dSphs results = f(priors)

• Cluster DM profiles consistent with NFW (+NFW for outer BCG)

• Outer orbits in clusters of galaxies: – Spirals on more radial orbits – Ellipticals on quasi-isotropic orbits – Lenticulars in between (closer to Ellipticals)

Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm mtg, Gouvieux, Mass/orbit modeling of spherical systems: from galaxy clusters to dwarfs 43