Evidence Supporting the Universality of the IMF

The stellar initial mass function (IMF) is an underlying distribution function which determines many important observables, from the number of ionizing photons in a population of some age and metallicity, through the creation rate of various chemical elements, to the mass to light ratio of a system. This significance, together with the empirical difficulty to determine the IMF robustly, and the near complete lack of any robust theoretical predictor, has allowed investigators freedom to treat the IMF as a continuously variable parameterisation of astrophysicists' ignorance of complexity. An ability to vary a parameter in a model is not the same as a true variation in a physical system. A more instructive approach is to use available data to constrain possible variations, and thereby to allow identification of those other aspects of an observed system whose understanding can be improved. Ideally, the most sensitive physical variable, or its parameterisation, should be the best constrained. A fundamental null hypothesis, which we defend here, is that the IMF is a universal invariant function, so that all apparent variations may be ascribed to other variables, and to irreducible statistical sampling fluctuations.