A Universal Stellar Initial Mass Function? A Critical Look at Variations
  Few topics in astronomy initiate such vigorous discussion as whether or not
the initial mass function (IMF) of stars is universal, or instead sensitive to
the initial conditions of star formation. The distinction is of critical
importance: the IMF influences most of the observable properties of stellar
populations and galaxies, and detecting variations in the IMF could provide
deep insights into the process by which stars form. In this review, we take a
critical look at the case for IMF variations, with a view towards whether other
explanations are sufficient given the evidence. Studies of the field, local
young clusters and associations, and old globular clusters suggest that the
vast majority were drawn from a "universal" IMF: a power-law of Salpeter index
($\Gamma=1.35$) above a few solar masses, and a log normal or shallower
power-law ($\Gamma \sim 0-0.25$) between a few tenths and a few solar masses
(ignoring the effects of unresolved binaries). The shape and universality of
the IMF at the stellar-substellar boundary is still under investigation and
uncertainties remain large, but most observations are consistent with a IMF
that declines ($\Gamma < -0.5$) well below the hydrogen burning limit.
Observations of resolved stellar populations and the integrated properties of
most galaxies are also consistent with a "universal IMF", suggesting no gross
variations in the IMF over much of cosmic time. There are indications of
"non-standard" IMFs in specific local and extragalactic environments, which
clearly warrant further study. Nonetheless, there is no clear evidence that the
IMF varies strongly and systematically as a function of initial conditions
after the first few generations of stars.
