The Burstiness of Star Formation at $z\sim 6$: A Huge Diversity in the Recent Star Formation Histories of Very UV-faint Galaxies

IRAC data have long implied that early ($z\gtrsim 6$) galaxies often have very high specific star formation rates (sSFR$\gtrsim$30 Gyr${}^{-1}$), but JWST data have shown that at least some early galaxies are forming stars far less vigorously. Here, we systematically analyze the recent star formation histories (SFHs) of a large ($N=368$) sample of $z\sim 6$ Lyman-break galaxies (LBGs) spanning $-22\lesssim M_{\mathrm{U}\mathrm{V}}\lesssim -16$ assembled from ACS+NIRCam imaging in the GOODS and Abell 2744 fields. We find that very low H$\alpha$-to-UV luminosity ratios ($L_{\mathrm{H}\alpha }\mathrm{/}{L}_{\mathrm{U}\mathrm{V}}$) and strong recent downturns in star formation rate (SFR) are $\approx$5$\times$ more common among the UV-faintest subset of our sample ($⟨M_{\mathrm{U}\mathrm{V}}⟩=-17.4$) compared to the brightest subset ($⟨M_{\mathrm{U}\mathrm{V}}⟩=-20.0$). The frequency of high $L_{\mathrm{H}\alpha }\mathrm{/}{L}_{\mathrm{U}\mathrm{V}}$ and strong recent SFR upturns is approximately constant with UV luminosity. We discuss how bursty SFHs naturally reproduce this much greater diversity in recent SFHs among very UV-faint galaxies. Using public NIRSpec/prism data, we newly confirm recent strong SFR downturns among three LBGs in our sample, and validate our photometric inferences on key SFH signatures among $z\sim 6$ LBGs in general. Our results imply that early galaxies frequently cycle through phases of rapid stellar mass assembly and other periods of much slower growth. This yields huge ($\gtrsim$1-2 mag) fluctuations in $M_{\mathrm{U}\mathrm{V}}$ on rapid ($\sim$10-30 Myr) timescales, helping explain the surprising abundance of $z>10$ galaxies. Finally, we caution that this burstiness causes all existing high-redshift samples (particularly line-selected samples) to be far less complete to galaxies with long recent phases of low sSFR than those currently undergoing a burst.