Distinguishing Between Warm and Cold Dark Matter

Transcription

1 Distinguishing Between Warm and Cold Dark Matter Center for Cosmology Aspen Workshop Neutrinos in Physics & Astrophysics 2/2/2007 Collaborators: James Bullock, Manoj Kaplinghat astro-ph/

2 Motivations Testing the CDM (WIMP) paradigm Predictions for well-motivated dark matter models Warm Dark Matter: Sterile neutrinos Dark matter from decays Early Decays ( 10 6 sec. ) Late Decays ( >10 12 sec. ) New observational tests of dark matter halo structure

3 CDM: Cosmological Consequences A nearly universal halo density profile scaling as 1/r in the central regions [Navarro et al 2004, Diemand et al 2004] Hundreds of dark matter-dominated Milky Way satellite galaxies [Klypin et al, Moore et al 1999] Dark mini-halos abundant in the central regions [Diemand et al 2006] Concentration of CDM halos set by the density of the universe when the halo formed [Bullock et al 2001]

4 CDM Predictions cusp core Simon et al. 2005

5 WDM: Cosmological Consequences Less dense dark matter halos. Expect constant central density cores Free streaming: Reduces the number of small halos Halos form later in the universe with reduced concentrations

6 Phase space densities Q = ρ/σ 3 [Hogan & Dalcanton 2000] CDM $ m Q CDM " 7 #10 14 cdm ' & ) % 100GeV ( 3 / 2 M sun pc *3 (km /s) *3 Neutrino WDM % m Q " 5 #10 $4 ' & kev ( * ) 4 M sun pc $3 (km /s) $3 Dark matter from decays (non-thermal) % 10 #3 Q "10 #6 ' & $m /m DM ( * ) 3 % zdecay ( ' * & 1000) 3 M sun pc #3 (km /s) #3

7 Phase space density limits Phase space elements mixed, or coarse grained, during halo formation. For fermions, h 3 f max = 1/2 [Tremaine-Gunn Bound] m ν > 170 ev (1 kpc/r c ) 3/4 (0.1 ρ/m solar pc -3 ) 1/8 g ν 1/4 Excess mass function is conserved: Applications to dark matter from decays [Kaplinghat 2005] Smallest, most dark matter-dominated galaxies expected to have the largest cores

8 Free-streaming CDM free streaming: structure down to earth mass scales. Radius of earth mass halos 0.01 pc WDM: Free-streaming scale depends on the mass of the sterile neutrino Dark matter from decays: Free-streaming length During radiation domination During matter domination

9 Power spectrum with dark matter from decays Lifetime: sec. Lifetime: sec. Full solution of Boltzmann equation gives: Neutrino WDM limits Critical scale: k 2 c s 2 η 1 Radiation-era decays: Q -1/3 Matter-era decays: Q -1/3 τ -1/3 Strigari, Kaplinghat, Bullock 2006

10 Lyman alpha constraints on WDM Narayan et al 2000 claim m WDM > 750 ev (Q > 10-4 ) Viel et al 2005 claim m WDM > 550 ev (Q > 5 x 10-5 ) New data and analysis. Seljak et al 2006; Viel et al 2006 For different constraints, take a detailed look at dwarf galaxies

11 Milky Way Dwarf Spheroidal Galaxies Some of the missing CDM galaxies? Exhibit no rotation DM dominated Information on DM halo from line of sight velocities

12 Parameters of dwarf galaxies Generally there are 5 parameters we must marginalize over To complete the mass-modeling, we must know the velocity anisotropy of the stars Equilibrium analysis with jeans equations gives:

13 Line of sight velocity dispersion Fornax Strigari et al Degeneracy with cores and cusps. Cannot distinguish WDM from CDM models

14 Next step: Proper motions of stars Typical errors on proper motions are about 5 km/s At < 100 kpc, this corresponds to accuracy < 10 micro-arcseconds/yr ϕ R

15 SIM PlanetQuest (Space Interferometry Mission) Adapted from: SIM Positional Error Circle (4µas) Hipparcos Positional Error Circle (0.64 mas) HST Positional Error Circle (~1.5 mas). Reflex Motion of Sun from 100pc (axes 100 µas) Parallactic Displacement of Galactic Center Apparent Gravitational Displacement of a Distant Star due to Jupiter 1 degree away

16 Characterizing constraints on the density profile Consider: Motivation: the velocity dispersion data constrain the slope of the density profile at a characteristic radius Strigari, Bullock, Kaplinghat ApJL 2007

17 Breaking the degeneracy

18 Targeting dwarf galaxies

19 Redefining the dwarf satellite problem

20 Future prospects Improved data from dwarf galaxies, rotation curves WDM N-body simulations will more accurately predict the relation between Q and core size Improved measurements of the power spectrum from 21cm and Lyman alpha Constraints on many interesting sneutrino/kk neutrino models from low energy neutrino background