The MOSDEF Survey: Metallicity Dependence of PAH Emission at High Redshift and Implications for 24 μm Inferred IR Luminosities and Star Formation Rates at z ∼ 2

We present results on the variation of 7.7 μm 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 μm and Herschel/PACS 100 and 160 μm observations are used to derive rest-frame 7.7 μm 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 star formation rate [SFR]) and both metallicity and [O iii]/[O ii] ($O_{32}$) 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 $M_{\ast }<{10}^{10}{M}_{\odot }$, compared to the more massive ones. We demonstrate that commonly used conversions of $L_{7.7}$ (or 24 μm flux density, f ₂₄) to $L_{IR}$ underestimate the IR luminosity by more than a factor of 2 at $M_{\ast }\sim {10}^{9.6\text{--}10.0}{M}_{\odot }$. 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 $M_{\ast }⩽{10}^{10}$ 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.