Is a top-heavy initial mass function needed to reproduce the
  submillimeter galaxy number counts?
  Matching the number counts and redshift distribution of submillimeter
galaxies (SMGs) without invoking modifications to the initial mass function
(IMF) has proved challenging for semi-analytic models (SAMs) of galaxy
formation. We adopt a previously developed SAM that is constrained to match the
z=0 galaxy stellar mass function and makes various predictions that agree well
with observational constraints; we do not recalibrate the SAM for this work. We
implement three prescriptions to predict the submillimeter flux densities of
the model galaxies; two depend solely on star formation rate, whereas the other
also depends on the dust mass. By comparing the predictions of the models, we
find that taking into account the dust mass, which affects the dust temperature
and thus influences the far-infrared spectral energy distribution, is crucial
for matching the number counts and redshift distribution of SMGs. Moreover,
despite using a standard IMF, our model can match the observed SMG number
counts and redshift distribution reasonably well, which contradicts the
conclusions of some previous studies that a top-heavy IMF, in addition to
taking into account the effect of dust mass, is needed to match these
observations. Although we have not identified the key ingredient that is
responsible for our model matching the observed SMG number counts and redshift
distribution without IMF variation- which is challenging given the different
prescriptions for physical processes employed in the SAMs of interest-our
results demonstrate that in SAMs, IMF variation is degenerate with other
physical processes, such as stellar feedback.
