Do sub-millimeter galaxy number counts provide evidence for a top-heavy IMF?

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Theoretical models have had difficulty matching the observed number density of sub-millimeter galaxies (SMGs), causing some authors (e.g., Baugh et al. 2005) to suggest that SMGs provide evidence for a top-heavy initial mass function (IMF). To test this claim, we have, for the first time, combined high-resolution 3-D hydrodynamic simulations of isolated and merging massive, gas-rich galaxies, radiative transfer, and a semi-empirical merger rate model to predict the number density of SMGs. Our model can reproduce the observed SMG number density even when using a standard (Kroupa) IMF. The agreement is due to a combination of relatively long sub-mm duty cycles for mergers (a few times 10⁸ years for our most massive models), which owe to our combination of high-resolution 3-D hydrodynamic simulations and dust radiative transfer; sufficient number densities of massive, gas-rich mergers; and the decrease in sub-mm counts observed by recent deep/wide surveys (e.g., Austermann et al. 2010) relative to previous surveys. Our results suggest that the observed SMG number counts do not provide evidence for a top-heavy IMF at high redshift.