The Dawes Review 8: Measuring the Stellar Initial Mass Function

Abstract The birth of stars and the formation of galaxies are cornerstones of modern astrophysics. While much is known about how galaxies globally and their stars individually form and evolve, one fundamental property that affects both remains elusive. This is problematic because this key property, the birth mass distribution of stars, referred to as the stellar initial mass function, is a key tracer of the physics of star formation that underpins almost all of the unknowns in galaxy and stellar evolution. It is perhaps the greatest source of systematic uncertainty in star and galaxy evolution. The past decade has seen a growing variety of methods for measuring or inferring the initial mass function. This range of approaches and evolving definitions of the quantity being measured has in turn led to conflicting conclusions regarding whether or not the initial mass function is universal. Here I review this growing wealth of approaches, and highlight the importance of considering potential initial mass function variations, reinforcing the need to carefully quantify the scope and uncertainties of measurements. I present a new framework to aid the discussion of the initial mass function and promote clarity in the further development of this fundamental field.