How Bursty is Star Formation at z>5?

Motivated by observational evidence from JWST and theoretical results from cosmological simulations, we use a simple parametric, phenomenological model to test to what extent bursty star formation with standard Initial Mass Function, no continuous star formation, no mergers, \mr{and no dust} can account for the observed properties in the $M_{UV}$ vs $M_{\ast }$ plane of galaxies at redshifts $z>5$. We find that the simplest model that fits the data has a quiescence period between bursts $\mathrm{\Delta }t\sim 100$~Myrs and the stellar mass in each galaxy grows linearly as a function of time from $z=12$ to $z=5$ (i.e., repeated bursts in each galaxy produce approximately equal mass in stars). The distribution of burst masses across different galaxies follows a power-law $dN\mathrm{/}d{M}_{\ast }\propto M_{\ast }^{\alpha }$ with slope $\alpha \sim -2$. At $z>9-10$ the observed galaxy population typically had only one or two bursts of stars formation, hence the observed stellar masses at these redshifts (reaching $M_{\ast }\sim {10}^{10}$~M${}_{\odot }$), roughly represent the distribution of masses formed in one burst.