The Metal Abundances across Cosmic Time ($\mathcal{M}\mathcal{A}\mathcal{C}\mathcal{T}$) 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 $\log (\mathrm{SFR})\propto \alpha \log (M_{\star }/M_{\odot })+\beta z$ 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.

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