ABSTRACT Extragalactic studies have demonstrated that there is a moderately tight (≈0.3 dex) relationship between galaxy stellar mass (M⋆) and star formation rate (SFR) that holds for star-forming galaxies at M⋆ ∼ 3 × 108–1011 M⊙, 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 narrow-band H α-selected galaxies with stellar masses between 106 and 1010 M⊙ (average of 108.2 M⊙) at z ≈ 0.07–0.5. These galaxies have sensitive ultraviolet (UV) to near-infrared photometric measurements and optical spectroscopy. The latter allows us to correct our H α SFRs for dust attenuation using Balmer decrements. Our study reveals that: (1) for low-SFR galaxies, our H α SFRs systematically underpredict compared to far-UV measurements, consistent with other studies; (2) at a given stellar mass (≈108 M⊙), log (specific SFR) evolves as A log (1 + z) with A = 5.26 ± 0.75, and on average, specific SFR increases with decreasing stellar mass; (3) the SFR–M⋆ relation holds for galaxies down to ∼106 M⊙ (∼1.5 dex below previous studies), and over lookback times of up to 5 Gyr, follows a redshift-dependent relation of log (SFR) ∝ α log (M⋆/M⊙) + β z with α = 0.60 ± 0.01 and β = 1.86 ± 0.07; and (4) the observed dispersion in the SFR–M⋆ relation at low stellar masses is ≈0.3 dex. Accounting for survey selection effects using simulated galaxies, we estimate that the true dispersion is ≈0.5 dex.

Deep rest-frame optical spectroscopy is critical for characterizing and understanding the physical conditions and properties of the ionized gas in galaxies. Here, we present a new spectroscopic survey called "Metal Abundances across Cosmic Time" or $\mathcal{MACT}$, which will obtain rest-frame optical spectra for $\sim$3000 emission-line galaxies. This paper describes the optical spectroscopy that has been conducted with MMT/Hectospec and Keck/DEIMOS for $\approx$1900 $z=0.1-1$ emission-line galaxies selected from our narrowband and intermediate-band imaging in the Subaru Deep Field. In addition, we present a sample of 164 galaxies for which we have measured the weak [OIII]$\lambda$4363 line (66 with at least 3$\sigma$ detections and 98 with significant upper limits). This nebular emission line determines the gas-phase metallicity by measuring the electron temperature of the ionized gas. This paper presents the optical spectra, emission-line measurements, interstellar properties (e.g., metallicity, gas density), and stellar properties (e.g., star formation rates, stellar mass). Paper II of the $\mathcal{MACT}$ survey (Ly et al.) presents the first results on the stellar mass--gas metallicity relation at $z\lesssim1$ using the sample with [OIII]$\lambda$4363 measurements.