Variations in integrated galactic initial mass functions due to sampling method and cluster mass function

Abstract

Context. Stars are thought to be formed predominantly in clusters. The star clusters are formed according to a cluster initial mass function (CMF) similar to the stellar initial mass function (IMF). Both the IMF and the CMF can be approximated by (broken) powerlaws, which favour low-mass objects. The numerous low-mass clusters will lack high mass stars compared to the underlying IMF, since the most massive star cannot be more massive than its host cluster. If the integrated galactic initial mass function (IGIMF, i.e. the total stellar mass function of all stars in a galaxy) originates from stars formed in star clusters, the IGIMF could be steeper than the IMF in clusters. Aims. We investigate how well constrained this steepening is and how it depends on the choice of sampling method and CMF. We investigate the observability of the IGIMF effect in terms of galaxy photometry and metallicities. Methods. We study various ways to sample the stellar IMF within star clusters and build up the IGIMF from these clusters. We compare analytic sampling to several implementations of random sampling of the IMF and different CMFs. We implement different IGIMFs into the galev evolutionary synthesis package to obtain colours and metallicities for galaxies.Results. Choosing different ways of sampling the IMF results in different IGIMFs. Depending on the lower cluster mass limit and the slope of the cluster mass function, the steepening varies between very strong and negligible. We find the size of the effect is continuous as a function of the power-law slope of the CMF if the CMF extends to masses smaller than the maximum stellar mass. The number of O-stars detected by GAIA will, if some uncertain factors are better understood, help to judge the importance of the IGIMF effect. The impact of different IGIMFs on integrated galaxy photometry is small, within the intrinsic scatter of observed galaxies. Observations of gas fractions and metallicities could rule out at least the most extreme sampling methods, if other sources of error are sufficiently understood. Conclusions. As we still do not understand the details of star formation and the sampling of the stellar IMF in clusters, one sampling method cannot be favoured over another. Also, the CMF at very low cluster masses is not well constrained observationally. These uncertainties therefore need to be taken into account when using an IGIMF, with severe implications for galaxy evolution models and interpretations of galaxy observations.

A possible solution to the [α/Fe]-σ problem in early-type galaxies within a hierarchical galaxy formation model

“…In fact, although our unprecedented rendition of this relation, the predicted slope obtained with our standard model is slightly shallower than the observed one. This aspect will be investigated in our future work, and may have its explanation in effects such as a possible IMF dependence on the SFR and/or a flatter IMF in starbursts (Recchi, Calura & Kroupa 2009; Calura et al 2010; Haas & Anders 2010). Some direct evidences in favour of the latter hypothesis come from observational studies of nuclear star clusters in the Milky Way (Bartko et al 2010).…”

SLUG – Stochastically Lighting Up Galaxies – II. Quantifying the effects of stochasticity on star formation rate indicators

“…Each cluster is then populated with stars drawn at random from the IMF, until the collective mass of the drawn stars is equal to the cluster mass. For the last star, SLUG implements a so-called stop-nearest method (Haas & Anders 2010), according to which the last drawn star is included only if keeping it makes the total effective mass of the cluster closer to the one drawn from the ICMF than leaving it out. Following this algorithm, the effective IMF (i.e.…”

Mass distributions of star clusters for different star formation histories in a galaxy cluster environment

“…A differentiation between the two types is very difficult because of the low number of high-mass SCs (e.g., Bastian 2008;Bastian et al 2012a). If the ECMF is indeed truncated, Haas & Anders (2010) did not expect the precise shape at the high-mass end to be important. They investigated how the choice of the sampling technique and the index of the ECMF alters the integrated galactic initial mass function (IGIMF) -the analogon of the IGECMF for stars instead of SCs.…”