The mmax–Mecl relation, the IMF and IGIMF: probabilistically sampled functions

Abstract

We introduce a new method to measure the dispersion of m max values of star clusters and show that the observed sample of m max is inconsistent with random sampling from an universal stellar initial mass function (IMF) at a 99.9% confidence level. The scatter seen in the m max -M ecl data can be mainly (76%) understood as being the result of observational uncertainties only. The scatter of m max values at a given M ecl are consistent with mostly measurement uncertainties such that the true (physical) scatter may be very small.Additionally, new data on the local star-formation regions Taurus-Auriga and L1641 in Orion make stochastically formed stellar populations rather unlikely. The data are however consistent with the local IGIMF (integrated galactic stellar initial mass function) theory according to which a stellar population is a sum of individual star-forming events each of which is described by well defined physical laws. Randomly sampled IMFs and henceforth scale-free star formation seems to be in contradiction to observed reality. 1 With 'form with a canonical IMF' it is meant that the form of the IMF of the star-forming region follows the canonical IMF but the upper mass limit is regulated by the mmax-M ecl relation. c 2013 RAS 2 C. Weidner et al.the canonical IMF. It should be pointed out here that the principal concept of the IGIMF -the galaxy-wide IMF (= IGIMF) of a galaxy is always the sum of all star-formation events within a galaxy -is in any case always true. The ingredients for the IGIMF as applied here are listed as follows:1. The IMF, ξ(m), within star clusters is assumed to be canonical (see Appendix B), 2. the CSFEs populate an embedded-cluster mass function (ECMF), which is assumed to be a power-law of the form, ξ ecl (M ecl ) = dN / dM ecl ∝ M −β ecl , 3. the relation between the most-massive star in a cluster, mmax, and the stellar mass of the embedded cluster, M ecl , 2006 Weidner et al. 2010), 4. the relation between the star-formation rate (SFR) of a galaxy and the most-massive young (< 10 Myr) star cluster, log 10 (M ecl,max ) = 0.746 × log 10 (SF R) + 4.93 .Uncertainties are only introduced by the details of star-formation. Properties like the slope of the embedded cluster mass function (ECMF) and its lower mass end (M ecl,min ) in dwarf galaxies or the top/bottom-heaviness of the IMF in the pc-scale star-formation events (Marks et al. 2012) are examples which need further studies. Therefore any models calculated within the IGIMF-theory contain uncertainties and can not be final. Conversely, it is possible to use observed relations and dependencies of galaxies to refine the understanding of the pc-scale star-formation events within the IGIMF-theory .However, the severity of the difference of the IGIMF to the underlying canonical IMF is strongly dependent on how stars form. Two extreme models can be discussed in the context of how stars should be sampled from the IMF. The first model, random sampling, assumes that the IMF is a probability density function. A star cluster is then an ens...

Dependency of Dynamical Ejections of O Stars on the Masses of Very Young Star Clusters

“…However, that is beyond the objectives of this study. In any case, the m max -M ecl relation is observationally well supported for young star clusters and star-forming regions in the Milky Way given the most recent data (Kirk & Myers 2011;Weidner et al 2013a).…”

“…The mass of the most massive star in the cluster, m max , is chosen from the maximum-stellar-masscluster-mass relation Weidner et al 2010Weidner et al , 2013aWeidner et al , 2014 . This procedure was adopted rather than optimal sampling introduced in Kroupa et al (2013) because the theoretical young cluster library of did not have this sampling method available.…”

“…It follows from an intuitive theoretical concept that the mass of a star-forming molecular cloud core is finite and that star formation is a self-regulated process (Adams & Fatuzzo 1996), and it follows from the data on young stellar populations (Weidner et al 2010(Weidner et al , 2013aKirk & Myers 2011). The existence of a physical m max -M ecl relation is thus taken to be established (Weidner et al 2014).…”

“…The existence of a physical m max -M ecl relation is thus taken to be established (Weidner et al 2014). Although the theory has been successful in describing the stellar contents of whole galaxies (e.g., Weidner et al 2013b), it has been debated if the relation exists (see Section 2.1 in Weidner et al 2013a for details) or if star formation is a purely stochastic process (e.g., Krumholz 2015). This is a fundamental issue for understanding galaxy-wide IMFs and how massive stars form, and we here thus stress that the data do not support the hypothesis that star formation is stochastic (see Section 7 of Kroupa 2015).…”

The little-studied cluster Berkeley 90 – III. Cluster parameters

“…Indeed, observations of clusters show that, in general, the mass of the most massive cluster member is a function of the cluster mass (Larson 1995;Elmegreen 1983;Weidner et al 2010). However, it is still unclear if this is simply a consequence of statistical sampling of the initial mass function (IMF) or a consequence of a deeper underlying principle (resulting in sorted sampling; Weidner et al 2013). Moreover, there is direct evidence of discs around some moderately massive stars (up to M * ∼ 25-30 M ; see Beltrán & de Wit 2016, for a review), supporting the idea of monolithic collapse.…”