We introduce a new method to measure the dispersion of mmax values of star clusters and show that the observed sample of mmax is inconsistent with random sampling from an universal stellar initial mass function (IMF) at a 99.9% confidence level. The
scatter seen in the mmax-Mecl data can be mainly (76%) understood as being the result of observational uncertainties only. The scatter of mmax values at a given Mecl 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.
Stars do not form continuously distributed over star forming galaxies. They form in star clusters of different masses. This nature of clustered star formation is taken into account in the theory of the integrated galactic stellar initial mass functio
n (IGIMF) in which the galaxy-wide IMF (the IGIMF) is calculated by adding all IMFs of young star clusters. For massive stars the IGIMF is steeper than the universal IMF in star clusters and steepens with decreasing SFR which is called the IGIMF-effect. The current SFR and the total Halpha luminosity of galaxies therefore scale non-linearly in the IGIMF theory compared to the classical case in which the galaxy-wide IMF is assumed to be constant and identical to the IMF in star clusters. We here apply for the first time the revised SFR-L_Halpha relation on a sample of local volume star forming galaxies with measured Halpha luminosities. The fundamental results are: i) the SFRs of galaxies scale linearly with the total galaxy neutral gas mass, ii) the gas depletion time scales of dwarf irregular and large disk galaxies are about 3 Gyr implying that dwarf galaxies do not have lower star formation efficiencies than large disk galaxies, and iii) the stellar mass buildup times of dwarf and large galaxies are only in agreement with downsizing in the IGIMF context, but contradict downsizing within the traditional framework that assumes a constant galaxy-wide IMF.
Star formation is mainly determined by the observation of H$alpha$ radiation which is related to the presence of short lived massive stars. Disc galaxies show a strong cutoff in H$alpha$ radiation at a certain galactocentric distance which has led to
the conclusion that star formation is suppressed in the outer regions of disc galaxies. This is seemingly in contradiction to recent UV observations (Boissier et al., 2007) that imply disc galaxies to have star formation beyond the Halpha cutoff and that the star-formation-surface density is linearly related to the underlying gas surface density being shallower than derived from Halpha luminosities (Kennicutt, 1998). In a galaxy-wide formulation the clustered nature of star formation has recently led to the insight that the total galactic Halpha luminosity is non-linearly related to the galaxy-wide star formation rate (Pflamm-Altenburg et al., 2007d). Here we show that a local formulation of the concept of clustered star formation naturally leads to a steeper radial decrease of the Halpha surface luminosity than the star-formation-rate surface density in quantitative agreement with the observations, and that the observed Halpha cutoff arises naturally.
Stars form in embedded star clusters which play a key role in determining the properties of a galaxys stellar population. Physical mechanisms discussed in this paper are runaway stars shot out from young clusters, binary-star disruption in clusters,
gas blow-out from clusters and the origin of thick galactic disks. I emphasise that the SNIa rate per low-mass star depends on the star-clusters formed in a galaxy and I discuss the IGIMF theory. Based on the IGIMF theory, the re-calibrated Halpha-luminosity--SFR relation implies dwarf irregular galaxies to have the same gas-depletion time-scale as major disk galaxies, suggesting a major change in our understanding of dwarf-galaxy evolution. The IGIMF-theory also naturally leads to the observed radial Halpha cutoff in disk galaxies without a radial star-formation cutoff. It emerges that the thorough understanding of the physics and distribution of star clusters may be leading to a major paradigm shift in our understanding of galaxy evolution.
This chapter is based on four lectures given at the Cambridge N-body school Cambody. The material covered includes the IMF, the 6D structure of dense clusters, residual gas expulsion and the initial binary population. It is aimed at those needing to
initialise stellar populations for a variety of purposes (N-body experiments, stellar population synthesis).
