Possible Evidence of Thermodynamic Activity in Dark Matter Haloes

Universal feature of galactic haloes : Flat rotation curves

Flat rotation curves naturally appear if source is a self-gravitating isothermal Boltzmann gas.

A coincidence?

Circular orbits +

Spherical symmetry +

Now recall basic thermo undergrad homework problem: find density profile of the

atmosphere

Standard treatment of dark matter haloes N particle simulations

Standard treatment of dark matter haloes N particle simulations

Navarro-Frenk-White

Simulation-inspired density profiles: Einasto

...and many others give reasonable fits to rotation curve data

Standard treatment of dark matter haloes N particle simulations

Navarro-Frenk-White

Simulation-inspired density profiles: Einasto

...and many others give reasonable fits to rotation curve data

Thermodynamics

Equilibrium thermodynamics not considered in standard treatment of dark matter haloes

• Relaxation times arising from gravitational interactions alone are too long (compared with the Hubble time) for thermodynamic equilibrium to be established.

• If interactions other than gravity are present among the dark matter particles, they are too weak to establish thermal equilibrium.

Bull%&t cluster

• Rotation curves not exactly flat

• But issues remain for simulations eg., cusp at r=0, missing satellite problem

• Strong bounds on dark matter-baryon interactions, -- not so for dark matter self-coupling

• Self-couplings ( with interaction times < 1/H ) can cure simulation issues Observational evidence for self-interacting cold dark matter, David N. Spergel, Paul J. Steinhardt Phys.Rev.Lett. 84 (2000) 3760-3763 Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure

Sean Tulin, Hai-Bo Yu, Kathryn M. Zurek, arXiv:1302.3898

• Is equilibrium possible?

A closer look at rotation curves: Using simplifying assumptions, both density and potential can be determined directly.

Newton

Poisson

NGC 2841

• Disk distance scale =3.5 kpc, data available up to 51.6 kpc (THINGS)• H gas mass is approximately 4% of the disk mass

Series fit using

NGC 5055• Disk distance scale =3.622 kpc, data available up to 44.4 kpc (THINGS)• H gas mass is approximately 12.6% of the disk mass

NGC 3521• Disk distance scale =3.3 kpc, data available up to 35.5 kpc (THINGS)• H gas mass is approximately 11% of the disk mass

NGC 7331

• Disk distance scale =3.2 kpc, data available up to 24 kpc (THINGS)• H gas mass is approximately 7% of the disk mass

NGC 2403• Disk distance scale =2.75 kpc, data available up to 24 kpc (THINGS)• H gas mass is approximately 19% of the disk mass

NGC 2903 • Disk distance scale =3 kpc, data available up to 31 kpc (THINGS)• H gas mass is approximately 7% of the disk mass

Series fit from 1 kpc to 31 kpc

NGC 3198 • Disk distance scale = 2.68 kpc, data available up to 38 kpc• H gas mass is approximately 29% of the disk mass

Moral: coincidence with Boltzmann gas for large portions of haloes - even though rotation curves not exactly flat.

A simple model for Boltzmann region

Assume:• spherical symmetry

• dynamics given by Emden eq.

• gravitational attraction to inner (baryonic) region determined by boundary conditions at r=R_g

• leads to three-parameter family of solutions

• get fits for

Breakdown of Boltzmann description at small and large distances

NGC 2841 NGC 5055 NGC 7331

NGC 2903 NGC 2403 NGC 3521

NGC 3198

Boltzmann fits

If similarity with a Boltzmann gas not a coincidence,

appears to indicate dark matter in thermal equilibrium.

What can this tell us about dark matter self-interactions?

many improvements possible:

• drop spherical symmetry• include H gas, disk contributions• extend to galaxy interior – test quantum statistics

CONCLUDING REMARKS