The MOSDEF Survey: Metallicity Dependence of the PAH Emission at High
  Redshift and Implications for 24 micron-inferred IR Luminosities and Star
  Formation Rates at z~2
  We present results on the variation of 7.7 micron Polycyclic Aromatic
Hydrocarbon (PAH) emission in galaxies spanning a wide range in metallicity at
z ~ 2. For this analysis, we use rest-frame optical spectra of 476 galaxies at
1.37 < z < 2.61 from the MOSFIRE Deep Evolution Field (MOSDEF) survey to infer
metallicities and ionization states. Spitzer/MIPS 24 micron and Herschel/PACS
100 and 160 micron observations are used to derive rest-frame 7.7 micron
luminosities (L(7.7)) and total IR luminosities (L(IR)), respectively. We find
significant trends between the ratio of L(7.7) to L(IR) (and to dust-corrected
SFR) and both metallicity and [OIII]/[OII] (O32) emission-line ratio. The
latter is an empirical proxy for the ionization parameter. These trends
indicate a paucity of PAH emission in low metallicity environments with harder
and more intense radiation fields. Additionally, L(7.7)/L(IR) is significantly
lower in the youngest quartile of our sample (ages of 500 Myr) compared to
older galaxies, which may be a result of the delayed production of PAHs by AGB
stars. The relative strength of L(7.7) to L(IR) is also lower by a factor of ~
2 for galaxies with masses $M_* < 10^{10}M_{\odot}$, compared to the more
massive ones. We demonstrate that commonly-used conversions of L(7.7) (or 24
micron flux density; f(24)) to L(IR) underestimate the IR luminosity by more
than a factor of 2 at $M_*$ ~ $10^{9.6-10.0} M_{\odot}$. We adopt a
mass-dependent conversion of L(7.7) to L(IR) with L(7.7)/L(IR)= 0.09 and 0.22
for $M_* < 10^{10}$ and $> 10^{10} M_{\odot}$, respectively. Based on the new
scaling, the SFR-$M_*$ relation has a shallower slope than previously derived.
Our results also suggest a higher IR luminosity density at z ~ 2 than
previously measured, corresponding to a ~ 30% increase in the SFR density.
