Biases on Initial Mass Function Determinations. II. Real Multiple Systems and Chance Superpositions1

Abstract

When calculating stellar initial mass functions (IMFs) for young clusters, one has to take into account that (1) most massive stars are born in multiple systems, (2) most IMFs are derived from data that cannot resolve such systems, and (3) multiple chance superpositions between members are expected to happen if the cluster is too distant. In this article I use numerical experiments to model the consequences of those phenomena on the observed color-magnitude diagrams and the IMFs derived from them. Real multiple systems affect the observed or apparent massive-star MF slope little but can create a significant population of apparently ultramassive stars. Chance superpositions produce only small biases when the number of superimposed stars is low but, once a certain number threshold is reached, they can affect both the observed slope and the apparent stellar upper mass limit. I apply these experiments to two well known massive young clusters in the Local Group, NGC 3603 and R136. In both cases I show that the observed population of stars with masses above 120 M can be explained by the effects of unresolved objects, mostly real multiple systems for NGC 3603 and a combination of real and chance-alignment multiple systems for R136. Therefore, the case for the reality of a stellar upper mass limit at solar or near-solar metallicities is strengthened, with a possible value even lower than 150 M . An IMF slope somewhat flatter than Salpeter or Kroupa with between À1.6 and À2.0 is derived for the central region of NGC 3603, with a significant contribution to the uncertainty arising from the imprecise knowledge of the distance to the cluster. The IMF at the very center of R136 cannot be measured with the currently available data but the situation could change with new HST observations.

A Universal Stellar Initial Mass Function? A Critical Look at Variations

“…If we consider that many determinations of the IMF start with monochromatic luminosity functions, we can guess that unresolved companions of a range of mass (and therefore added luminosity) could wreak havoc on the IMF. Indeed they do (Kroupa 2001;Chabrier 2003;Maíz Apellániz 2008), but correcting for this effect is difficult, because the impact of multiplicity on IMF studies is sensitive to both the binary fraction and the mass ratio of the systems involved. It is straightforward that a higher multiplicity fraction will produce a larger multiplicity correction, but the mass ratio dependence is somewhat more subtle: systems with high mass ratios are effective at "hiding" stars, and are also quite difficult to detect as a multiple system.…”

Exploring the consequences of pairing algorithms for binary stars

“…The measured mass distribution is often the distribution of single/primary masses f M 1,S (M), as it is not known which members are single and which are binary, which results in a measured mass distribution that is biased to higher masses with respect to the overall mass distribution f all (M), which, if measured just after star formation, is the IMF. As stellar masses are often derived from measured luminosities, the presence of unresolved binaries and crowding may further bias the measured (initial or presentday) mass distribution to higher masses (e.g., Vanbeveren 1982;Maíz Apellániz 2008;Weidner et al 2008). Over the last decade, considerable effort has been put into studying possible environmental dependences of the IMF (see, e.g., Elmegreen 2007;Kroupa 2008, for an overview and examples).…”

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

“…Vanbeveren (1982) investigated the IMFs of primaries and single stars analytically up to stars above 100 M ⊙ , but did not explicitly discuss any possible effects of unresolved binaries on the observed IMF. Only rather recently, the study by Maíz Apellániz (2008) explores the biases on the IMF introduced by unresolved binaries for massive stars. There a different colour is used ( U − V ) while in this contribution we resort to B − V , and only RP is studied by Maíz Apellániz (2008, see for details on binary pairing) while here we consider different viable q ‐distributions.…”

“…Only rather recently, the study by Maíz Apellániz (2008) explores the biases on the IMF introduced by unresolved binaries for massive stars. There a different colour is used ( U − V ) while in this contribution we resort to B − V , and only RP is studied by Maíz Apellániz (2008, see for details on binary pairing) while here we consider different viable q ‐distributions. This contribution can, therefore, be seen as an extension of these previous studies (Kroupa et al 1991, 1993; Sagar & Richtler 1991; Malkov & Zinnecker 2001; Thies & Kroupa 2007, 2008) to higher masses as well as a comparison to the Maíz Apellániz (2008) study.…”