On the Interpretation of Far-infrared Spectral Energy Distributions. I: The 850 μm 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$_{\rm \nu,850}$) 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$_{\rm \nu,850}$-M$_{\rm mol}$ calibrations accurately recover the molecular gas mass of our model galaxies, and that the L$_{\rm \nu,850}$-dependent calibration is preferred. We argue the major driver of scatter in the L$_{\rm \nu,850}$-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$_{\rm \nu,850}$ from continuum emission at a different frequency contributes $10-20\%$ scatter to the L$_{\rm \nu,850}$-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$_{\rm \nu,850}$-M$_{\rm mol}$ relation holds for massive galaxies, independent of the dust model, but below L$_{\rm \nu,850}\lesssim10^{28}$ 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.