The Metal Abundances across Cosmic Time ($\mathcal{MACT}$) Survey. III -- The relationship between stellar mass and star formation rate in extremely low-mass galaxies

Abstract

Extragalactic studies have demonstrated there is a moderately tight ($\approx$0.3 dex) relationship between galaxy stellar mass ($M_{\star}$) and star formation rate (SFR) that holds for star-forming galaxies at $M_{\star} \sim 3 \times 10^8$-10$^{11}~M_{\odot}$, i.e., the "star formation main sequence." However, it has yet to be determined whether such a relationship extends to even lower mass galaxies, particularly at intermediate or higher redshifts. We present new results using observations for 714 narrowband H$\alpha$-selected galaxies with stellar masses between $10^6$ and $10^{10}~M_{\odot}$ (average of $10^{8.2}~M_{\odot}$) at $z \approx$ 0.07-0.5. These galaxies have sensitive UV to near-infrared photometric measurements and optical spectroscopy. The latter allows us to correct our H$\alpha$ SFRs for dust attenuation using Balmer decrements. Our study reveals: (1) for low-SFR galaxies, our H$\alpha$ SFRs systematically underpredict compared to FUV measurements, consistent with other studies; (2) at a given stellar mass ($\approx $10$ ^{8}~M_{\odot}$), log(specific SFR) evolves as $ A \log(1+z) $ with $ A = 5.26 \pm 0.75 $, and on average, specific SFR increases with decreasing stellar mass; (3) the SFR-$M_{\star}$ relation holds for galaxies down to $\sim$10$^6~M_{\odot}$ ($\sim$1.5 dex below previous studies), and over lookback times of up to 5 Gyr, follows a redshift-dependent relation of $\log{({\rm SFR})} \propto \alpha \log(M_{\star}/M_{\odot}) + \beta z$ with $\alpha = 0.60 \pm 0.01$ and $\beta = 1.86 \pm 0.07$; and (4) the observed dispersion in the SFR-$M_{\star}$ relation at low stellar masses is $\approx$0.3 dex. Accounting for survey selection effects using simulated galaxies, we estimate the true dispersion is $\approx$0.5 dex.