Statistical sampling from the stellar initial mass function (IMF) for all
star-forming regions in the Galaxy would lead to the prediction of ~1000 Msun
stars unless there is a rapid turn-down in the IMF beyond several hundred solar
masses. Such a turndown is not necessary for dense clusters because the number
of stars sampled is always too small. Here we explore several mechanisms for an
upper mass cutoff, including an exponential decline of the star formation
probability after a turbulent crossing time. The results are in good agreement
with the observed IMF over the entire stellar mass range, and they give a
gradual turn down compared to the Salpeter function above ~100 Msun for normal
thermal Jeans mass, M_J. The upper mass turn down should scale with M_J in
different environments. A problem with the models is that they cannot give both
the observed power-law IMF out to the high-mass sampling limit in dense
clusters, as well as the observed lack of supermassive stars in whole galaxy
disks. Either there is a sharper upper-mass cutoff in the IMF, perhaps from
self-limitation, or the IMF is different for dense clusters than for the
majority of star formation that occurs at lower density. Dense clusters seem to
have an overabundance of massive stars relative to the average IMF in a galaxy.Comment: 19 pages, 2 figures, Astrophysical Journal, Vol 539, August 10, 200