The evolution of halos with masses around $M_\textrm{ h} \approx 10^{ 11}\; \textrm{ M}_\odot$ and $M_\textrm{ h} \approx 10^{ 12}\; \textrm{ M}_\odot$ at redshifts $z>9$ is examined using constrained N-body simulations. { The average specific mass accretion rates, $\dot{ M}_\textrm{ h} / M_\textrm{ h}$, exhibit minimal mass dependence and generally agree with existing literature. Individual halo accretion histories, however, vary substantially. } About one-third of simulations reveal an increase in $\dot{ M}_\textrm{ h}$ around $z\approx 13$. Comparing simulated halos with observed galaxies having spectroscopic redshifts, we find that for galaxies at $z\gtrsim9$, the ratio between observed star formation rate (SFR) and $\dot{ M}_\textrm{ h}$ is approximately $2\%$. This ratio remains consistent for the stellar-to-halo mass ratio (SHMR) but only for $z\gtrsim 10$. At $z\simeq 9$, the SHMR is notably lower by a factor of a few. At $z\gtrsim10$, there is an agreement between specific star formation rates (sSFRs) and $\dot{ M}_\textrm{ h} / M_\textrm{ h}$. However, at $z\simeq 9$, observed sSFRs exceed simulated values by a factor of two. It is argued that the mildly elevated SHMR in high-$z$ halos with $M_\textrm{ h} \approx 10^{ 11} M_{ \odot}$, can be achieved by assuming the applicability of the local Kennicutt-Schmidt law and a reduced effectiveness of stellar feedback due to deeper gravitational potential of high-$z$ halos of a fixed mass.
Categories: astro-ph.GA astro-ph.CO