Calibrating the James Webb Space Telescope filters as star formation rate indicators

We have calibrated the 6.5 m James Webb Space Telescope (JWST) mid-infrared filters as star formation rate indicators, using JWST photometry synthesized from $Spitzer$ spectra of 49 low redshift galaxies, which cover a wider luminosity range than most previous studies. We use Balmer decrement corrected $\rm{H\alpha}$ luminosity and synthesized mid-infrared photometry to empirically calibrate the $Spitzer$, WISE and JWST filters as star formation rate indicators. Our $Spitzer$ and WISE calibrations are in good agreement with recent calibrations from the literature. While mid-infrared luminosity may be directly proportional to star formation rate for high luminosity galaxies, we find a power-law relationship between mid-infrared luminosity and star formation rate for low luminosity galaxies ($L_{\rm H\alpha} \leq 10^{43}~{\rm erg~s^{-1}}$). We find that for galaxies with a $\rm{H\alpha}$ luminosity of $\rm{10^{40}}~erg~s^{-1}$ (corresponding to a star formation rate of $\sim 0.055~{\rm M_\odot~yr^{-1}}$), the corresponding JWST mid-infrared $\nu L_{\nu}$ luminosity is between $\rm{10^{40.50}}$ and $\rm{10^{41.00}}~erg~s^{-1}$. Power-law fits of JWST luminosity as a function of $\rm{H\alpha}$ luminosity have indices between 1.17 and 1.32. We find that the scatter in the JWST filter calibrations decreases with increasing wavelength from 0.39 to 0.20 dex, although F1000W is an exception where the scatter is just 0.24 dex.