Properties of Cold Dark Matter Halos at z>6

We compute the properties of dark matter halos with mass ${10}^{6.5}-{10}^9\text{msun}$ at redshift $z=6-11$ in the standard cold dark matter cosmological model, utilizing a very high resolution N-body simulation. We find that dark matter halos in these mass and redshift ranges are significantly biased over matter with a bias factor in the range 2-6. The dark matter halo mass function displays a slope of $2.05\pm 0.15$ at the small mass end. We do not find a universal dark matter density profile. Instead, we find a significant dependence of the central density profile of dark matter halos on halo mass and epoch with ${\alpha }_0=0.4-1.0$; the high-mass ($M\ge {10}^8\text{msun}$) low-redshift ($z\sim 6$) halos occupy the high end of the range and low-mass ($M\sim 10^{7}\msun$)high-redshift($z\sim 11$) halos occupy the low end. Additionally, for fixed mass and epoch there is a significant dispersion in ${\alpha }_0$ due to the stochastic assembly of halos. Our results fit a relationship of the form ${\alpha }_0=0.75((1+z)\mathrm{/}7.0{)}^{-1.25}(M\mathrm{/}{10}^7\text{msun}{)}^{0.11(1+z)\mathrm{/}7.0}$ with a dispersion about this fit of $\pm 0.5$ and no systematic dependence of variance correlated with environment. The median spin parameter of dark matter halos is $0.03-0.04$ but with a large lognormal dispersion of $\sim 0.4$. Various quantities are tabulated or fitted with empirical formulae.