How Bursty is Star Formation at z>5?

Abstract

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 $M_*$ plane of galaxies at redshifts $z>5$. We find that the simplest model that fits the data has a quiescence period between bursts $Δt \sim 100$~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 $dN/dM_* \propto M_*^α$ with slope $α\sim -2$. 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 $M_* \sim 10^{10}$~M$_\odot$), roughly represent the distribution of masses formed in one burst.

Figures (4)

• Figure 1: The cyan points show $M_{UV}$ vs $M_\star$ for a model with $\xi = 1$, $\eta = 1$, and $\Delta t = 100 Myrs$ (Model A in Table \ref{['tab:models']}). Blue is for $\xi=1$, $\eta=0.5$ (Model B, displaced by -0.05 in log M for visibility purposes), and magenta for $\xi=0.5$ and $\eta=1$ (Model C, displaced by +0.05 in log M). Green is for with $\xi = 1$, $\eta = 1$, and $\Delta t = 50Myrs$ (Model D). We are only plotting models with apparent magnitude $m_{UV} \leq 30$ to simulate an observational limit. Each vertical line corresponds to a given number of bursts and the number of bursts is related to redshift but is not a one-to-one function of redshift because of the random distribution of starting redshifts. The vertical extent of each line is related to the burst length $\Delta t$. The observational points in red are from Morishita2024.
• Figure 2: $M_{UV}$ vs $M_\star$ for the galaxies in Morishita2024 compared to a model with a random distribution of $\xi$ and $\eta=0$ as described in the text (Model 20 in Table \ref{['tab:models']}). The redshift bins in each panel have the same cosmic volume.
• Figure 3: $M_{UV}$ vs $M_\star$ for the galaxies in Morishita2024 compared to a model with $\eta = 0$ and $\xi$ randomly distributed with $\alpha_\xi = -2$. Details are described in the text (Model 19 in Table \ref{['tab:models']}). The slope of luminosity function for this model is compatible with the observed one.
• Figure 4: log counts vs $M_{UV}$ for the models with $\eta=0$ and a random power-law distribution of $\xi$ (Model 1). The slope break around $M_{UV}\simeq-21$ is due to the adopted $\Delta t = 0.1$ and the dimming of a burst over the time $\Delta t$. The red lines show a broken power low fit to the LF with $\alpha_{faint}=-0.2$ and $\alpha_{bright}=-0.5$ at $z=5-6$, $\alpha_{faint}=-0.19$ and $\alpha_{bright}=-0.27$ at $z=6-8$, and $\alpha_{faint}=-0.2$ at higher z.