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 μm luminosity (L _ν,850) as a molecular gas mass (M _mol) estimator in galaxies between 0 < z < 9.5 for a broad range of masses. For our fiducial simulations, where we assume that the dust mass is linearly related to the metal mass, we find that empirical L _ν,850-M _mol calibrations accurately recover the molecular gas mass of our model galaxies and that the L _ν,850-dependent calibration is preferred. We argue that the major driver of scatter in the L _ν,850-M _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 _ν,850 from continuum emission at a different frequency contributes 10%-20% scatter to the L _ν,850-M _mol relation. This additional scatter arises from a combination of mismatches in assumed T _dust and β values, as well as the fact that the SEDs are not single-temperature blackbodies. However, this observationally induced scatter is a subdominant source of uncertainty. 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 ∼50% higher, the dust mass is significantly decreased for low-metallicity halos. As a result, the observationally calibrated L _ν,850-M _mol relation holds for massive galaxies, independent of the dust model, but below L _ν,850 ≲ 10²⁸ erg s^-1 (metallicities {log}}₁₀(Z/{Z}_⊙ )≲ -0.8) we expect that galaxies may deviate from literature observational calibrations by ≳0.5 dex.