  The star formation rate (SFR) in high redshift galaxies is expected to be
time-variable due to competing physical processes. Such stochastic variability
might boost the luminosity of galaxies, possibly explaining the over-abundance
seen at $z\gtrsim 10$ by JWST. We aim at quantifying the amplitude and
timescales of such variability, and identifying the key driving physical
processes. We select 245 $z=7.7$ galaxies with stellar mass $5\times
10^{6}\lesssim M_\star/{\rm M}_\odot\lesssim 5\times 10^{10}$ from SERRA, a
suite of high-resolution, radiation-hydrodynamic cosmological simulations.
After fitting the average SFR trend, $\langle {\rm SFR} \rangle$, we quantify
the time-dependent variation, $\delta(t) \equiv \log [\rm SFR/\langle {\rm SFR}
\rangle]$ for each system, and perform a periodogram analysis to search for
periodicity modulations. We find that $\delta(t)$ is distributed as a zero-mean
Gaussian, with standard deviation $\sigma_\delta \simeq 0.24$ (corresponding to
a UV magnitude s.d. $\sigma_{\rm UV} \simeq 0.61$) that is independent of
$M_\star$. However, the modulation timescale increases with stellar mass:
$t_\delta \sim (9, 50, 100)\, \rm Myr$ for $M_\star \sim (0.1, 1, 5)\times
10^9\, {\rm M}_\odot$, respectively. These timescales are imprinted on the SFR
by different processes: (i) photoevaporation, (ii) supernova explosions, and
(iii) cosmological accretion/merging dominating in low, intermediate, and high
mass systems, respectively. The predicted SFR variations cannot account for the
required $z\gtrsim 10$ UV luminosity function boost. Other processes, such as
radiation-driven outflows clearing the dust, must then be invoked to explain
the enhanced luminosity of super-early systems.
