On the Cusp of the

Dark Matter

Sergey MashchenkoHugh CouchmanJames 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:0802.4220Kinematic Status and mass content ofThe Sculptor dwarf spheroidal galaxy

“…velocity dispersion profiles are best fitted by a cored dark matter halo with core radiusR_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:

<v2> ~ (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 σgas << σdm, the dark

matter will adjust adiabatically

– For σgas >> σdm, 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 Mvir=109 M; rvir = 3kpc; rs = 850pc; 106 particles), and

• Model gas bulk motions by forced motion of extended rigid bodies moving through the centre of the halo:– Clumps 40pc; amplitude A=rs/2;

speed 11km/s– For r < A, Mgas ~ Mdm => ~ 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

mvir=109 M

DM halo

~ 1 fullperiod in DM halo – highly efficient

Oscillationamplitude

Must happen before halo is subsumed into next level of hierarchy

SN 1051 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/2240 Myr

For M → M/4cusp flattening after ~ 800 Myr

z01030

Epoch of cusp removal by stellar feedback… phase-space density cannot increase in subsequent merger hierarchy

• mvir < 107 M “blowout” – may contribute to effect;

• mvir > 1010 M rotational support/large σDM, small-scale turbulence

Z=150

Self-consistent cosmological simulations4

Mpc

(co

-mov

ing)

Constrained cosmological simulations.

Build-up of an isolated dwarf galaxy (~109 M) over z=10…5.

15 million particles (10 million hi-res).

mDM= 1900 M

mgas= 370 M

mstar= 120 M

ε = 12pc

1.1 × 107 dark

4.5 × 106 gas

4.5 × 105 star

Z=5

Added physics…

• Jeans criterion + low-T metal cooling (10-104 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).

• 6x105 cpu-hour run

ISM structureOld New

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

Cosmologicalsimulations with gas dynamics and stellar feedback.

Central 1.3 kpcof a formingdwarf 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

σ3

Enclosedmass:

Phase spacedensity,

r < 1.6kpc

r < 100pc

Evolution of enclosed DM mass for different radii

DM onlysimulations

Simulationswith feedback

Radial profiles

DM core: 400 pc

Stellar core: 300 pc

η =(σr2 – σt

2)/

(σr2 + σt

2)

Isotropic velocity dispersion in core

Long-lived star clusters

Distance from galacticcentre:

• At birth (z~6.2): σr = 37 pc

• After 200 Myr:

σr = 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.

Age 0 360 Myr

Radial extent 365 pc 637 pc

Velocity disp. 15.6 km s-1 18.3 km s-1

[Fe/H] -1.33 -1.54

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