CEERS: 7.7 ${\mu}$m PAH Star Formation Rate Calibration with JWST MIRI

We test the relationship between UV-derived star formation rates (SFRs) and the 7.7 ${\mu}$m polycyclic aromatic hydrocarbon (PAH) luminosities from the integrated emission of galaxies at z ~ 0 - 2. We utilize multi-band photometry covering 0.2 - 160 ${\mu}$m from HST, CFHT, JWST, Spitzer, and Herschel for galaxies in the Cosmic Evolution Early Release Science (CEERS) Survey. We perform spectral energy distribution (SED) modeling of these data to measure dust-corrected far-UV (FUV) luminosities, $L_{FUV}$, and UV-derived SFRs. We then fit SED models to the JWST/MIRI 7.7 - 21 ${\mu}$m CEERS data to derive rest-frame 7.7 ${\mu}$m luminosities, $L_{770}$, using the average flux density in the rest-frame MIRI F770W bandpass. We observe a correlation between $L_{770}$ and $L_{FUV}$, where log $L_{770}$ is proportional to (1.27+/-0.04) log $L_{FUV}$. $L_{770}$ diverges from this relation for galaxies at lower metallicities, lower dust obscuration, and for galaxies dominated by evolved stellar populations. We derive a "single-wavelength" SFR calibration for $L_{770}$ which has a scatter from model estimated SFRs (${{\sigma}_{{\Delta}SFR}}$) of 0.24 dex. We derive a "multi-wavelength" calibration for the linear combination of the observed FUV luminosity (uncorrected for dust) and the rest-frame 7.7 ${\mu}$m luminosity, which has a scatter of ${{\sigma}_{{\Delta}SFR}}$ = 0.21 dex. The relatively small decrease in ${\sigma}$ suggests this is near the systematic accuracy of the total SFRs using either calibration. These results demonstrate that the rest-frame 7.7 ${\mu}$m emission constrained by JWST/MIRI is a tracer of the SFR for distant galaxies to this accuracy, provided the galaxies are dominated by star-formation with moderate-to-high levels of attenuation and metallicity.