On the Cusp of the Dark Matter Sergey Mashchenko Hugh Couchman James Wadsley McMaster University ( Nature 3/8/06; Science 29/11/07 )

Outline The problem of “cusps” in standard CDM dark matter haloes Toy model for stellar feedback Self-consistent feedback in live, dwarf haloes The talk considers the interplay between gas (and the astrophysical processes connected with star formation) and collisionless dark matter in cosmic structure formation

The Cusp Problem in CDM Despite successes of ΛCDM on large and intermediate scales, serious issues remain on smaller, galactic and sub-galactic, scales. In particular: –Theory (simulation) predicts – with a fair degree of confidence – cuspy inner profiles ~ NFW –Observations show increasingly strong evidence for flat inner cores ~ Burkert

de Blok & Bosma, 2002 Battaglia et al., arXiv: Kinematic Status and mass content of The Sculptor dwarf spheroidal galaxy “…velocity dispersion profiles are best fitted by a cored dark matter halo with core radius R_c= 0.5kpc.”

Proposed solutions Observational problems –Beam smearing; non-circular motion etc. New physics –WDM; self-interacting DM –Modified gravity Solutions within standard ΛCDM (requires “heating” of dark matter) –Rotating bar –Passive evolution of cold lumps (e.g., El Zant et al., 2001) –Recoiling black holes –AGN –“Maximal stellar feedback”/“blowout” Ideas have variable traction… propose a mechanism that is a natural consequence of structure formation

Bulk gas motions in early dwarf galaxies – driven by supernovae and stellar winds - transfer kinetic energy to “heat” the dark matter –Plausible mechanism that must have been widespread in early, gas-rich dwarfs –Could likely have achieved significant gas compression in early (small concentration) haloes –Observe bulk motions of cold gas in present- day dwarfs that are mildly supersonic, have spatial scale similar to that of z>10 dwarfs (few 100pc) and have velocities similar to dark matter dispersion (~10km/s) Note: the naïve impact of cooling baryons is to make the cusp steeper

Sag DIG Young & Lo (1997) 500pc 3.2kpc Believed to be bulk motion resulting from star formation: ~ (10 km/s) 2 If sufficient gas can be concentrated and moved in bulk, the gravitational potential will fluctuate, resulting in the transfer of kinetic energy from baryons to dark matter. –For σ gas << σ dm, the dark matter will adjust adiabatically –For σ gas >> σ dm, the dark matter moves only in the time-averaged potential of the gas lumps –Would not expect sensitivity to gas density

Toy Model Challenging to do full hydro simulation of stellar-induced bulk motions in a live dark matter halo, so… DM halo: z ~ 10 dwarf galaxy (NFW M vir =10 9 M  ; r vir = 3kpc; r s = 850pc; 10 6 particles), and Model gas bulk motions by forced motion of extended rigid bodies moving through the centre of the halo: –Clumps 40pc; amplitude A=r s /2; speed 11km/s –For r ~ ½ gas within r = A Simple model allows access to, and control of, key parameters… N.B: early dwarfs were less concentrated and more gas rich than those at low redshift

Evolution of the DM density profile t =40 Myr t =80 Myr t =140 Myr V =11 km s -1 m vir =10 9 M  DM halo ~ 1 full period in DM halo – highly efficient Oscillation amplitude Must happen before halo is subsumed into next level of hierarchy SN ergs => 80/Myr at ε=10% => 0.01 M  /yr; gas depletion in 10 Gyr

ρ(r<A) 140 Myr 600 Myr h = A/2 M → M/2 240 Myr For M → M/4 cusp flattening after ~ 800 Myr

z Epoch of cusp removal by stellar feedback… phase-space density cannot increase in subsequent merger hierarchy m vir < 10 7 M  “blowout” – may contribute to effect; m vir > M  rotational support/large σ DM, small-scale turbulence

Z=150 Self-consistent cosmological simulations 4 Mpc (co-moving) Constrained cosmological simulations. Build-up of an isolated dwarf galaxy (~10 9 M  ) over z=10…5. 15 million particles (10 million hi-res). m DM = 1900 M  m gas = 370 M  m star = 120 M  ε = 12pc 1.1 × 10 7 dark 4.5 × 10 6 gas 4.5 × 10 5 star Z=5

Added physics… Jeans criterion + low-T metal cooling ( K, from Bromm et al. 2001) for star formation. Stochastic stellar feedback; model individual supernovae as point explosions. Delayed-cooling feedback (Thacker & Couchman; volume-weighted). Pressure (not density) is constant across the SPH smoothing kernel – but only for radiative cooling calculations (~ Ritchie & Thomas 2001). 6x10 5 cpu-hour run

ISM structure OldNew Critical to model low temperature cooling and to include a Jeans criterion in order to develop (more realistic) spatial star formation inhomogeneity

DM-only cosmological model Cosmological simulations of the formation of a dwarf galaxy. Dark matter only (no gas). Z=150…5

Cosmological simulations with gas dynamics and stellar feedback. Central 1.3 kpc of a forming dwarf galaxy. z = 9…5 Gas is in blue, stars are in yellow

Evolution of enclosed gas mass for different radii

Evolution of the central quantities (r=200 pc) F = ρ σ3σ3 Enclosed mass: Phase space density, r < 1.6kpc r < 100pc

Evolution of enclosed DM mass for different radii DM only simulations Simulations with feedback

Radial profiles DM core: 400 pc Stellar core: 300 pc η =(σ r 2 – σ t 2 )/ (σ r 2 + σ t 2 ) Isotropic velocity dispersion in core

Long-lived star clusters Distance from galactic centre: At birth (z~6.2): σ r = 37 pc After 200 Myr: σ r = 280 pc Orbits of “Globular Clusters” Stellar feedback also acts on GCs, and Impact of dynamical friction reduced by flat core (e.g., Fornax)

Stellar population gradients Have been observed in most dwarf spheroidal galaxies (in the Local Group). Older stars are more dispersed, more metal-poor, and kinematically warmer. Our model (gravitational heating by bulk gas motions) naturally explains the observed gradients: –Stars are born near the galactic center, and then gradually pushed outwards by the feedback. Age0360 Myr Radial extent365 pc637 pc Velocity disp.15.6 km s km s-1 [Fe/H]

Conclusions Gravitational resonant heating of matter appears to be an inevitable consequence of bulk gas motions driven by stellar feedback in early, gas-rich dwarfs. The result is: –Large dark matter cores –Stellar population gradients. –A distribution of long-lived globular clusters. –Low stellar density and a flat-cored distribution of stars in dSphs. –May also help resolve the “overabundance of satellites” problem –May be relevant to dark matter detections