Calibrating the star formation rate at $z \sim 1$ from optical data

Abstract

We present a star formation rate (SFR) calibration based on optical data that is consistent with average observed rates in both the red and blue galaxy populations at $z \sim 1$. The motivation for this study is to calculate SFRs for DEEP2 Redshift Survey galaxies in the $0.7 < z < 1.4$ redshift range, but our results are generally applicable to similar optically selected galaxy samples without requiring UV or IR data. Using SFR fits from UV/optical spectral energy distributions (SEDs) in the All-Wavelength Extended Groth Strip International Survey, we explore the behavior of rest-frame B-band magnitude, observed [O II] luminosity, and rest-frame color with SED-fit SFR for both red sequence and blue cloud galaxies. The resulting SFR calibration is based on three optical-band observables: $M_{B} , \big(U – B\big)$, and $\big(B – V\big)$. The best-fit linear relation produces residual errors of 0.3 dex rms scatter for the full color-independent sample with minimal correlated residual error in $L\big[O_{II}\big]$ or stellar mass. We then compare the calibrated $z \sim 1$ SFRs to two diagnostics that use $L\big[O_{II}\big]$ as a tracer in local galaxies and correct for dust extinction at intermediate redshifts through either galaxy $B$-band luminosity or stellar mass. We find that an$ L\big[O_{II}\big]-M_{B}$ SFR calibration commonly used in the literature agrees well with our calculated SFRs after correcting for the average B-band luminosity evolution in $L_{*}$ galaxies. However, we find better agreement with a local $L\big[O_{II}\big]$-based SFR calibration that includes stellar mass to correct for reddening effects, indicating that stellar mass is a better tracer of dust extinction for all galaxy types and less affected by systematic evolution than galaxy luminosity from $z = 1$ to the current epoch.