On the Interpretation of Far-infrared Spectral Energy Distributions. I: The 850 $mu$m Molecular Mass Estimator

We use a suite of cosmological zoom galaxy formation simulations and dust radiative transfer calculations to explore the use of the monochromatic $850~mu m$ luminosity (L$_{rm u,850}$) as a molecular gas mass (M$_{rm mol}$) estimator in galaxies between $0 < z < 9.5$ for a broad range of masses. For our fiducial simulations, where we assume the dust mass is linearly related to the metal mass, we find that empirical L$_{rm u,850}$-M$_{rm mol}$ calibrations accurately recover the molecular gas mass of our model galaxies, and that the L$_{rm u,850}$-dependent calibration is preferred. We argue the major driver of scatter in the L$_{rm u,850}$-M$_{rm mol}$ relation arises from variations in the molecular gas to dust mass ratio, rather than variations in the dust temperature, in agreement with the previous study of Liang et al. Emulating a realistic measurement strategy with ALMA observing bands that are dependent on the source redshift, we find that estimating S$_{rm u,850}$ from continuum emission at a different frequency contributes $10-20%$ scatter to the L$_{rm u,850}$-M$_{rm mol}$ relation. This additional scatter arises from a combination of mismatches in assumed T$_{dust}$ and $beta$ values, as well as the fact that the SEDs are not single-temperature blackbodies.Finally we explore the impact of a dust prescription in which the dust-to-metals ratio varies with metallicity. Though the resulting mean dust temperatures are $sim50%$ higher, the dust mass is significantly decreased for low-metallicity halos. As a result, the observationally calibrated L$_{rm u,850}$-M$_{rm mol}$ relation holds for massive galaxies, independent of the dust model, but below L$_{rm u,850}lesssim10^{28}$ erg s$^{-1}$ (metallicities $log_{10}({rm Z}/{rm Z}_{odot})lesssim -0.8$) we expect galaxies may deviate from literature observational calibrations by $gtrsim0.5$ dex.