Mass/orbit 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 gravity? 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! density 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 d2Φ ⌃(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 velocities 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 = ⌫ Φ Jeans Equation r · − r tracer density € 2 P = ⌫ σv 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 β(r) 2 GM(r) +2 ⇥⇤r = ⇥ 2 dr ⇥ r − r ⇥2(r) θ = velocity anisotropy β(r)=1 2 − ⇥r (r) isotropic orbits: 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: β 2 − 0 2(β β0) 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 σz (R, r) ÊÊ -4000 0 500 1000 1500 2000 2500 line-of-sight velocity R 2 R kpc σz(R, r)= 1 β(r) σr(r) projected radius − r H L s ✓ ◆ Solution to Jeans equation of local dynamical equilibrium 2 z 1 1 dt GM(s) σ2(r)= exp 2 β(t) ⌫(s) ds R r r ⌫(r) t s2 Zr Zr very fast! Gary Mamon (IAP), 29 August 2016, Amsterdam-Paris-Stockholm