1. Possible Evidence of Thermodynamic Activity in Dark Matter Haloes

2. 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 +

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

4. Standard treatment of dark matter haloes N particle simulations

5. Navarro-Frenk-White Simulation-inspired density profiles: Einasto...and many others give reasonable fits to rotation curve data

6. 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

7. 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

8. 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. SteinhardtDavid N. SpergelPaul J. Steinhardt Phys.Rev.Lett. 84 (2000) 3760-3763 Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure Sean Tulin, Hai-Bo Yu, Kathryn M. Zurek, arXiv:1302.3898 Sean TulinHai-Bo YuKathryn M. ZurekarXiv:1302.3898 Is equilibrium possible?

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

10. 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

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. 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

19. NGC 2841 NGC 5055NGC 7331 NGC 2903NGC 2403NGC 3521 NGC 3198 Boltzmann fits

20. 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