JWST/NIRSpec Balmer-line Measurements of Star Formation and Dust Attenuation at z~3-6

We present an analysis of the star-formation rates (SFRs) and dust attenuation properties of star-forming galaxies at $2.7\leq z<6.5$ drawn from the Cosmic Evolution Early Release Science (CEERS) Survey. Our analysis is based on {\it JWST}/NIRSpec Micro-Shutter Assembly (MSA) $R\sim1000$ spectroscopic observations covering approximately $1-5$$\mu$m. Our primary rest-frame optical spectroscopic measurements are H$\alpha$/H$\beta$ Balmer decrements, which we use as an indicator of nebular dust attenuation. In turn, we use Balmer decrements to obtain dust-corrected H$\alpha$-based SFRs (i.e., SFR(H$\alpha$)). We construct the relationship between SFR(H$\alpha$) and stellar mass ($M_*$) in three bins of redshift ($2.7\leq z< 4.0$, $4.0\leq z< 5.0$, and $5.0\leq z<6.5$), which represents the first time the star-forming main sequence has been traced at these redshifts using direct spectroscopic measurements of Balmer emission as a proxy for SFR. In tracing the relationship between SFR(H$\alpha$) and $M_*$ back to such early times ($z>3$), it is essential to use a conversion factor between H$\alpha$ and SFR that accounts for the subsolar metallicity prevalent among distant galaxies. We also use measured Balmer decrements to investigate the relationship between dust attenuation and stellar mass out to $z\sim6$. The lack of significant redshift evolution in attenuation at fixed stellar mass, previously confirmed using Balmer decrements out to $z\sim2.3$, appears to hold out to $z\sim 6.5$. Given the rapidly evolving gas, dust, and metal content of star-forming galaxies at fixed mass, this lack of significant evolution in attenuation provides an ongoing challenge to explain.