Probing the Star Formation Main Sequence down to 10$^{7} M_\odot$ at $1 < z < 9$

The Main Sequence of Star-Forming Galaxies (SFGMS or MS) is a fundamental scaling relation that provides a global framework for studying galaxy formation and evolution, as well as insight into the complex star formation histories (SFHs) of individual galaxies. In this work, we combine large-area pre-JWST surveys (COSMOS2020, CANDELS), which probe high-$M_\star$ sources (${>10^9\,M_\odot}$), with SHARDS/CANDELS FAINT and JWST data from CANUCS, CEERS, JADES, and UNCOVER, to obtain a high-$z$, star formation rate (SFR) and stellar mass ($M_\star$) complete sample spanning both high- and low-$M_\star$ regimes. Completeness in both $M_\star$ and SFR is key to avoiding biases introduced by low-mass, highly star-forming objects. Our combined data set is 80% complete down to $10^{7.6}\,M_\odot$ at $z\sim1$ ($10^{8.8}\,M_\odot$ at $z\sim9$). The overall intrinsic MS slope (based on the SFR$_{100}$ and $M_\star$ derived with Dense Basis and nonparametric SFHs) shows little evolution up to $z\sim5$, with values $\sim0.7 - 0.8$. The slope in the low-$M_\star$ regime becomes steeper than that in the high-$M_\star$ end at least up to $z\sim5$, but the strength of this change is highly dependent on the assumptions made on the symmetry of the uncertainties in $M_\star$ and SFR. If real, the steepening suggests reduced star formation efficiency or declining gas content with decreasing $M_\star$. The transition between the low-$M_\star$ regime and the canonical MS occurs around $10^{9.5}\,M_\odot$, independent of $z$. This critical value may coincide with the assembly of galaxies' disks, which can provide a mechanism for self-regulation that stabilizes them against feedback. The intrinsic scatter is compatible with canonical estimates, also at low-$M_\star$, ranging from $0.2-0.3$ dex. This is indicative of rapid variations in star formation being averaged out over $\lesssim100$ Myr.