Evolution of the dark matter phase-space density distributions of ΛCDM haloes

Abstract

We study the evolution of phase-space density during the hierarchical structure formation of Λ cold dark matter (CDM) haloes. We compute both a spherically averaged surrogate for phase-space density ( Q =Ρ/Σ 3 ) and the coarse-grained distribution function f ( x , v ) for dark matter (DM) particles that lie within ∼2 virial radii of four Milky Way sized dark matter haloes. The estimated f ( x , v ) spans over four decades at any radius. DM particles that end up within 2 virial radii of a Milky Way sized DM halo at z = 0 have an approximately Gaussian distribution in log ( f ) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value f peak corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by f peak ( z ) ∝ (1 + z ) 4.5 for z > 1 . The highest values of f (responsible for the skewness of the profile) are found at the centres of dark matter haloes and subhaloes, where f can be an order of magnitude higher than in the centre of the main halo. We confirm that Q ( r ) can be described by a power law with a slope of −1.8 ± 0.1 over 2.5 orders of magnitude in radius and over a wide range of redshifts. This Q ( r ) profile likely reflects the distribution of entropy ( K ≡Σ 2 /Ρ 2/3 DM ∝ r 1.2 ) , which dark matter acquires as it is accreted on to a growing halo. The estimated f ( x , v ) , on the other hand, exhibits a more complicated behaviour. Although the median coarse-grained phase-space density profile F ( r ) can be approximated by a power law, ∝ r −1.6±0.15 , in the inner regions of haloes (<0.6 r vir ) , at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high- f material associated with surviving subhaloes, as well as relatively unmixed material (probably in streams) resulting from disrupted subhaloes, which contribute a sizable fraction of matter at large radii.