High-z dusty star-forming galaxies: a top-heavy initial mass function?
  Recent estimates point to abundances of z > 4 sub-millimeter (sub-mm)
galaxies far above model predictions. The matter is still debated. According to
some analyses the excess may be substantially lower than initially thought and
perhaps accounted for by flux boosting and source blending. However, there is
no general agreement on this conclusion. An excess of z > 6 dusty galaxies has
also been reported albeit with poor statistics. On the other hand, evidence of
a top-heavy initial mass function (IMF) in high-z starburst galaxies has been
reported in the past decades. This would translate into a higher sub-mm
luminosity of dusty galaxies at fixed star formation rate, i.e., into a higher
abundance of bright high-z sub-mm galaxies than expected for a universal
Chabrier IMF. Exploiting our physical model for high-z proto-spheroidal
galaxies, we find that part of the excess can be understood in terms of an IMF
somewhat top-heavier than Chabrier. Such IMF is consistent with that recently
proposed to account for the low 13C/18O abundance ratio in four dusty starburst
galaxies at z = 2-3. However, extreme top-heavy IMFs are inconsistent with the
sub-mm counts at z > 4.
