A New Star-Formation Rate Calibration from Polycyclic Aromatic
  Hydrocarbon Emission Features and Application to High Redshift Galaxies
  We calibrate the integrated luminosity from the polycyclic aromatic
hydrocarbon (PAH) features at 6.2\micron, 7.7\micron\ and 11.3\micron\ in
galaxies as a measure of the star-formation rate (SFR). These features are
strong (containing as much as 5-10\% of the total infrared luminosity) and
suffer minimal extinction. Our calibration uses \spitzer\ Infrared Spectrograph
(IRS) measurements of 105 galaxies at $0 < z < 0.4$, infrared (IR) luminosities
of $10^9 - 10^{12} \lsol$, combined with other well-calibrated SFR indicators.
The PAH luminosity correlates linearly with the SFR as measured by the
extinction-corrected \ha\ luminosity over the range of luminosities in our
calibration sample. The scatter is 0.14 dex comparable to that between SFRs
derived from the \paa\ and extinction-corrected \ha\ emission lines, implying
the PAH features may be as accurate a SFR indicator as hydrogen recombination
lines. The PAH SFR relation depends on gas-phase metallicity, for which we
supply an empirical correction for galaxies with $0.2 < \mathrm{Z} \lsim
0.7$~\zsol. We present a case study in advance of the \textit{James Webb Space
Telescope} (\jwst), which will be capable of measuring SFRs from PAHs in
distant galaxies at the peak of the SFR density in the universe ($z\sim2$) with
SFRs as low as $\sim$~10~\sfrunits. We use \spitzer/IRS observations of the PAH
features and \paa\ emission plus \ha\ measurements in lensed star-forming
galaxies at $1 < z < 3$ to demonstrate the ability of the PAHs to derive
accurate SFRs. We also demonstrate that because the PAH features dominate the
mid-IR fluxes, broad-band mid-IR photometric measurements from \jwst\ will
trace both the SFR and provide a way to exclude galaxies dominated by an AGN.
