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 .
We close with suggestions for future work that might uncover more subtle IMF variations than those that could be discerned to date .