The stellar initial mass function is a critical property influencing almost all aspects of star and galaxy evolution, and it has been the focus of a prodigious wealth of research spanning more than 60 years. This review has adopted a particular emphasis on the growing range of observational approaches to inferring or constraining the IMF, and exploring their strengths, weaknesses and apparent conflicts.
I have pedantically recommended that unambiguous terminology be adopted, echoing similar pleas dating back twenty years, and argued for the use of a standard nomenclature convention to minimise ambiguity (§ 2.2 and 2.3).
I have explored the issue of a “universal” IMF, and raised concerns about the Occam's Razor default toward “universality.” This is accompanied by a recommendation that the most general scenario, that the IMF is not “universal,” rather than the simplest, be taken as the baseline assumption (§ 2.4). This baseline approach should lead to a clearer presentation in the literature around degrees of uncertainty and the physical parameter ranges being probed, to aid in defining the extent of any possible IMF variation.
Relying heavily on previous reviews where available, I have summarised results from a selection of studies that infer the IMF, spanning the scale of stellar clusters to galaxies and galaxy populations, along with simulations that model it (§§ 3 - 7). This was followed by the introduction of a general and self-consistent approach (§ 8). This approach makes the temporal and spatial dependencies of the stellar mass function explicit, ξ(m, t, V), leading to clear distinctions between ξs, ξg, and ξc representative of the spatial scale of stellar clusters, galaxies and cosmic census probes of galaxy populations. These quantities should not in general be expected to be the same and should not be conflated or compared.
Using this self-consistent approach, a selection of new diagnostic diagrams were introduced to explore the IMF shapes from a selection of published results (§ 9), complementing and extending the “alpha plot” (Scalo, 1998, Kroupa, 2002, Bastian et al., 2010). These diagnostics were used to assess the degree to which published IMF properties are consistent or not. If the cIMF evolves, the degree of evolution only needs to be mild in order to resolve the SFH/SMD constraint. The gIMF, in contrast, does seem to show some evidence for a bimodality in the IMF shape for star forming galaxies and the progenitors of low redshift passive galaxies. There is scope now to begin presenting the many sIMF measurements in diagnostic diagrams similar to these in order to further quantitatively explore possible dependencies on a range of physical conditions.
This review has, inevitably, been limited in many ways. I have endeavoured to capture the current state of the field through summarising representative work, in order to tease out where tensions actually exist. I have presented a general approach that may be of value in supporting simulations and models to more precisely compare against the most relevant observational constraints. It is my hope that this review provides a unifying perspective for this fundamental aspect of the formation and evolution of stars and galaxies.
I am deeply grateful to Jill Rathborne for extensive discussion and invaluable support through the development and writing of this review. I thank the two anonymous reviewers for detailed and positive feedback that helped improve and refine the discussion presented here. My thanks also to Dennis Zaritsky, Madusha Gunawardhana, Pieter van Dokkum, and Michele Cappellari for their willingness to share the original versions of the figures from their papers that are reproduced here. I thank Pavel Kroupa for his careful reading of this lengthy work, identification of otherwise overlooked references, and his input in refining the descriptions of the IGIMF method. I greatly appreciate numerous conversations with Madusha Gunawardhana that have helped inform this review, and I thank her also for providing Figure 4. I thank Matthew Colless for input on this project, and his advice, mentoring, and guidance on many others over the past decade. I thank Warrick Couch for his valuable support in encouraging me to pursue this project and for enabling me to manage my time while working on this review. I gratefully acknowledge input as well from the following colleagues in helping to refine various different elements of this review: Joss Bland-Hawthorn, Elisabete da Cunha, Gayandhi De Silva, Chris Evans, and Ned Taylor.
I thank the Editorial Board of PASA for giving me the opportunity to contribute this work to the Dawes Review series. I have found it incredibly rewarding to explore the many areas and subtleties of this fascinating field, and it has been a privilege to share my perspective on this fundamental topic.