[abridged] Stars are thought to be formed predominantly in clusters. The clusters are formed following a cluster initial mass function (CMF) similar to the stellar initial mass function (IMF). Both the IMF and the CMF favour low-mass objects. The numerous low-mass clusters will lack high mass stars. If the integrated galactic initial mass function originates from stars formed in clusters, the IGIMF could be steeper than the IMF. We investigate how well constrained this steepening is and how it depends on the choice of sampling method and CMF. We compare analytic sampling to several implementations of random sampling of the IMF, and different CMFs. We implement different IGIMFs into GALEV to obtain colours and metallicities for galaxies. 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 stellarmass. The number of O-stars detected by GAIA might help in judging on 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. As we still do not understand the details of star formation, one sampling method cannot be favoured over another. Also, the CMF at very low cluster masses is not well constrained observationally. These uncertainties need to be taken into account when using an IGIMF, with severe implications for galaxy evolution models and interpretations of galaxy observations.
Download