A New Star-Formation Rate Calibration from the Polycyclic Aromatic Hydrocarbon Emission Features: Application to High Redshift Lensed Galaxies

Our goal is to calibrate polycyclic aromatic hydrocarbon (PAH) luminosity in the mid-infrared (mid-IR) as a star-formation rate (SFR) indicator that can be used in galaxies that host active galactic nuclei (AGN), where every other SFR indicator is contaminated by the AGN. We use mid-IR spectroscopy from the \textit{Spitzer} Infrared Spectrograph (IRS) and optical spectroscopy from various instruments to calibrate the mid-IR PAH features using (L$_{{\mathrm{H}} \alpha}$ + 0.020$\times L_{24 \mu \mathrm{m}}$) equivalent to dust-corrected H$_{\alpha}$ measurements (Kennicutt et al. 2009). Our sample consists of 226 galaxies corresponding to a range of total IR luminosity, L$_{\mathrm{IR}}$ = L(8-1000$\mu$m) = 10$^{9}$-10$^{12} L_\odot$ over the redshift range from 0$<$ z $<$0.6. We find using a unity relation, fit to the star-forming only galaxies (118 galaxies), correlates linearly to (L$_{\mathrm{H} \alpha}$ + 0.020$\times$L$_{24 \mu \mathrm{m}}$) with a gaussian scatter of $<$0.15 dex. As a result, we present a SFR relation for the PAH luminosity with uncertainties. We then apply our relations to a sample of high-redshift lensed galaxies (1 $<$ z $<$ 3) with previously estimated SFRs from other SFR indicators that are consistent to our PAH SFRs within uncertainties.