  We analyze 88 independent high-resolution cosmological zoom-in simulations of
disk galaxies in the NIHAO simulations suite to explore the connection between
the atomic gas fraction and angular momentum of baryons throughout cosmic time.
The study is motivated by the analytic model of \citet{obreschkow16}, which
predicts a relation between the atomic gas fraction $f_{\rm atm}$ and the
global atomic stability parameter $q \equiv j\sigma / (GM)$, where $M$ and $j$
are the mass and specific angular momentum of the galaxy (stars+cold gas) and
$\sigma$ is the velocity dispersion of the atomic gas. We show that the
simulated galaxies follow this relation from their formation ($z\simeq4$) to
present within $\sim 0.5$ dex. To explain this behavior, we explore the
evolution of the local Toomre stability and find that $90\%$--$100\%$ of the
atomic gas in all simulated galaxies is stable at any time. In other words,
throughout the entire epoch of peak star formation until today, the timescale
for accretion is longer than the timescale to reach equilibrium, thus resulting
in a quasi-static equilibrium of atomic gas at any time. Hence, the evolution
of $f_{\rm atm}$ depends on the complex hierarchical growth history primarily
via the evolution of $q$. An exception are galaxies subject to strong
environmental effects.
