Submillimeter flux as a probe of molecular ISM mass in high-$z$ galaxies
  Recent long wavelength observations on the thermal dust continuum suggest
that the Rayleigh-Jeans (RJ) tail can be used as a time-efficient quantitative
probe of the dust and ISM mass in high-$z$ galaxies. We use high-resolution
cosmological simulations from the Feedback in Realistic Environment (FIRE)
project to analyze the dust emission of $M_*>10^{10}\;M_{\odot}$ galaxies at
$z=2-4$. Our simulations (MassiveFIRE) explicitly include various forms of
stellar feedback, and they produce the stellar masses and star formation rates
of high-$z$ galaxies in agreement with observations. Using radiative transfer
modelling, we show that sub-millimeter (sub-mm) luminosity and molecular ISM
mass are tightly correlated and that the overall normalization is in
quantitative agreement with observations. Notably, sub-mm luminosity traces
molecular ISM mass even during starburst episodes as dust mass and
mass-weighted temperature evolve only moderately between $z=4$ and $z=2$,
including during starbursts. Our finding supports the empirical approach of
using broadband sub-mm flux as a proxy for molecular gas content in high-$z$
galaxies. We thus expect single-band sub-mm observations with ALMA to
dramatically increase the sample size of high-$z$ galaxies with reliable ISM
masses in the near future.
