Dark-ages Reionization & Galaxy Formation Simulation II: Spin and concentration parameters for dark matter haloes during the Epoch of Reionization

Abstract

We use high resolution N-Body simulations to study the concentration and spin parameters of dark matter haloes in the mass range $10^8{\mathrm{M}}_{\odot }{h}^{-1}<\mathrm{M}<10^{11}{\mathrm{M}}_{\odot }{h}^{-1}$ and redshifts $5<z<10$, corresponding to the haloes of galaxies thought to be responsible for reionization. We build a sub-sample of equilibrium haloes and contrast their properties to the full population that also includes unrelaxed systems. Concentrations are calculated by fitting both NFW and Einasto profiles to the spherically-averaged density profiles of individual haloes. After removing haloes that are out-of-equilibrium, we find a $z>5$ concentration$-$mass ($c(M)$) relation that is almost flat and well described by a simple power-law for both NFW and Einasto fits. The intrinsic scatter around the mean relation is $\hat{I}”c_{\mathrm{vir}}\sim 1$ (or 20 per cent) at $z=5$. We also find that the analytic model proposed by Ludlow et al. reproduces the mass and redshift-dependence of halo concentrations. Our best-fit Einasto shape parameter, $\hat{I}\pm$, depends on peak height, $\hat{I}½$, in a manner that is accurately described by $\hat{I}\pm =0.0070\hat{I}{½}^2+0.1839$. The distribution of the spin parameter, $\hat{I}»$, has a weak dependence on equilibrium state; $\hat{I}»$ peaks at roughly $\sim 0.033$ for our relaxed sample, and at $\sim 0.04$ for the full population. The spin--virial mass relation has a mild negative correlation at high redshift.