Using a sample of 299 Ha-selected galaxies at z~0.8, we study the relationship between galaxy stellar mass, gas-phase metallicity, and star formation rate (SFR), and compare to previous results. We use deep optical spectra obtained with the IMACS spectrograph at the Magellan telescope to measure strong oxygen lines. We combine these spectra and metallicities with (1) rest-frame UV-to-optical imaging, which allows us to determine stellar masses and dust attenuation corrections, and (2) Ha narrowband imaging, which provides a robust measure of the instantaneous SFR. Our sample spans stellar masses of 10^9 to 6*10^11 solar masses, SFRs of 0.4 to 270 solar masses per year, and metal abundances of 12+log(O/H)~8.3-9.1 (~0.4-2.6 solar metallicity). The correlations that we find between the Ha-based SFR and stellar mass (i.e., the star-forming main sequence), and between the stellar mass and metallicity, are both consistent with previous z~1 studies of star-forming galaxies. We then study the relationship between the three properties using various plane-fitting techniques (Lara-Lopez et al.) and a curve-fitting projection (Mannucci et al.). In all cases, we exclude strong dependence of the M-Z relation on SFR, but are unable to distinguish between moderate and no dependence. Our results are consistent with previous mass-metallicity-SFR studies. We check whether dataset limitations may obscure a strong dependence on the SFR by using mock samples drawn from the SDSS. These experiments reveal that the adopted signal-to-noise cuts may have a significant effect on the measured dependence. Further work is needed to investigate these results, and to test whether a fundamental metallicity relation or a fundamental plane describes star-forming galaxies across cosmic time.
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