Dark-ages Reionization & Galaxy Formation Simulation II: Spin and
  concentration parameters for dark matter haloes during the Epoch of
  Reionization
  We use high resolution N-Body simulations to study the concentration and spin
parameters of dark matter haloes in the mass range $10^8\, {\rm M}_{\odot}\,
h^{-1} < {\rm M} < 10^{11}\, {\rm
  M}_{\odot}\, h^{-1}$ 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 $\Delta c_{\rm{vir}}{\sim1}$ (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, $\alpha$, depends on peak height, $\nu$, in a
manner that is accurately described by $\alpha {=}0.0070\nu^2{+}0.1839$. The
distribution of the spin parameter, $\lambda$, has a weak dependence on
equilibrium state; $\lambda$ 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.
