CEERS: Increasing Scatter along the Star-Forming Main Sequence Indicates Early Galaxies Form in Bursts

We present the star-formation-rate -- stellar-mass (SFR-M$_\ast$) relation for galaxies in the CEERS survey at $4.5\leq z\leq 12$. We model the \jwst\ and \hst\ rest-UV and rest-optical photometry of galaxies with flexible star-formation histories (SFHs) using \bagpipes. We consider SFRs averaged from the SFHs over 10~Myr (\sfrten) and 100~Myr (\sfrcen), where the photometry probes SFRs on these timescales, effectively tracing nebular emission lines in the rest-optical (on $\sim10$~Myr timescales) and the UV/optical continuum (on $\sim100$ Myr timescales). We measure the slope, normalization and intrinsic scatter of the SFR-M$_\ast$ relation, taking into account the uncertainty and the covariance of galaxy SFRs and $M_\ast$. From $z\sim 5-9$ there is larger scatter in the $\sfrten-M_\ast$ relation, with $\sigma(\log \sfrcen)=0.4$~dex, compared to the $\sfrcen-M_\ast$ relation, with $\sigma(\log \sfrten)=0.1$~dex. This scatter increases with redshift and increasing stellar mass, at least out to $z\sim 7$. These results can be explained if galaxies at higher redshift experience an increase in star-formation variability and form primarily in short, active periods, followed by a lull in star formation (i.e. ``napping'' phases). We see a significant trend in the ratio $R_\mathrm{SFR}=\log(\sfrten/\sfrcen)$ in which, on average, $R_\mathrm{SFR}$ decreases with increasing stellar mass and increasing redshift. This yields a star-formation ``duty cycle'' of $\sim40\%$ for galaxies with $\log M_\ast/M_\odot\geq 9.3$, at $z\sim5$, declining to $\sim20\%$ at $z\sim9$. Galaxies also experience longer lulls in star formation at higher redshift and at higher stellar mass, such that galaxies transition from periods of higher SFR variability at $z\gtrsim~6$ to smoother SFR evolution at $z\lesssim~4.5$.