Do sub-millimeter galaxy number counts provide evidence for a top-heavy
  IMF?
  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
10^8 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.
