It has been claimed in the recent literature that a non-trivial relation between the mass of the most-massive star, mmax, in a star cluster and its embedded star cluster mass (the mmax-Mecl relation) is falsified by observations of the most-massive s
tars and the Halpha luminosity of young star clusters in the starburst dwarf galaxy NGC 4214. Here it is shown by comparing the NGC 4214 results with observations from the Milky Way that NGC 4214 agrees very well with the predictions of the the mmax-Mecl relation and the integrated galactic stellar initial mass function (IGIMF) theory and that this difference in conclusions is based on a high degree of degeneracy between expectations from random sampling and those from the mmax-Mecl relation, but are also due to interpreting mmax as a truncation mass in a randomly sampled IMF. Additional analysis of galaxies with lower SFRs than those currently presented in the literature will be required to break this degeneracy.
Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR o
f a galaxy, it follows that galaxies which have or which formed with SFRs > 10 Msol yr^-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk- and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index beta of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.
Recent evidence based independently on spectral line strengths and dynamical modelling point towards a non-universal stellar Initial Mass Function (IMF), probably implying an excess of low-mass stars in elliptical galaxies with a high velocity disper
sion. Here we show that a time-independent bottom-heavy IMF is compatible neither with the observed metal-rich populations found in giant ellipticals nor with the number of stellar remnants observed within these systems. We suggest a two-stage formation scenario involving a time-dependent IMF to reconcile these observational constraints. In this model, an early strong star-bursting stage with a top-heavy IMF is followed by a more prolonged stage with a bottom-heavy IMF. Such model is physically motivated by the fact that a sustained high star formation will bring the interstellar medium to a state of pressure, temperature and turbulence that can drastically alter the fragmentation of the gaseous component into small clumps, promoting the formation of low-mass stars. This toy model is in good agreement with the different observational constrains on massive elliptical galaxies, such as age, metallicity, alpha-enhancement, M/L, or the mass fraction of the stellar component in low-mass stars.
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.
The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in
increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.
The question whether or not massive stars can form in isolation or only in star clusters is of great importance for the theory of (massive) star-formation as well as for the stellar initial mass function of whole galaxies (IGIMF-theory). While a seem
ingly easy question it is rather difficult to answer. Several physical processes (e.g. star-loss due to stellar dynamics or gas expulsion) and observational limitations (e.g. dust obscuration of young clusters, resolution) pose severe challenges to answer this question. In this contribution we will present the current arguments in favour and against the idea that all O stars form in clusters.
Star formation rates (SFR) larger than 1000 Msun/ yr are observed in extreme star bursts. This leads to the formation of star clusters with masses > 10^6 Msun in which crowding of the pre-stellar cores may lead to a change of the stellar initial mass
function (IMF). Indeed, the large mass-to-light ratios of ultra-compact dwarf galaxies and recent results on globular clusters suggest the IMF to become top-heavy with increasing star-forming density. We explore the implications of top-heavy IMFs in these very massive and compact systems for the integrated galactic initial mass function (IGIMF), which is the galaxy-wide IMF, in dependence of the star-formation rate of galaxies. The resulting IGIMFs can have slopes, alpha_3, for stars more massive than about 1 Msun between 1.5 and the Salpeter slope of 2.3 for an embedded cluster mass function (ECMF) slope (beta) of 2.0, but only if the ECMF has no low-mass clusters in galaxies with major starbursts. Alternatively, beta would have to decrease with increasing SFR >10 Msun/ yr such that galaxies with major starbursts have a top-heavy ECMF. The resulting IGIMFs are within the range of observationally deduced IMF variations with redshift.
The functional form of the galaxy-wide stellar initial mass function is of fundamental importance for understanding galaxies. So far this stellar initial mass function has been assumed to be identical to the IMF observed directly in star clusters. Bu
t because stars form predominantly in embedded groups rather than uniformly distributed over the whole galaxy, the galaxy-wide IMF needs to be calculated by adding all IMFs of all embedded groups. This integrated galactic stellar initial mass function (IGIMF) is steeper than the canonical IMF and steepens with decreasing SFR, leading to fundamental new insights and understanding of star forming properties of galaxies. This contribution reviews the existing applications of the IGIMF theory to galactic astrophysics, while the parallel contribution by Weidner, Pflamm-Altenburg & Kroupa (this volume) introduces the IGIMF theory.
Over the past years observations of young and populous star clusters have shown that the stellar initial mass function (IMF) can be conveniently described by a two-part power-law with an exponent alpha_2 = 2.3 for stars more massive than about 0.5 Ms
ol and an exponent of alpha_1 = 1.3 for less massive stars. A consensus has also emerged that most, if not all, stars form in stellar groups and star clusters, and that the mass function of these can be described as a power-law (the embedded cluster mass function, ECMF) with an exponent beta ~2. These two results imply that the integrated galactic IMF (IGIMF) for early-type stars cannot be a Salpeter power-law, but that they must have a steeper exponent. An application to star-burst galaxies shows that the IGIMF can become top-heavy. This has important consequences for the distribution of stellar remnants and for the chemo-dynamical and photometric evolution of galaxies. In this contribution the IGIMF theory is described, and the accompanying contribution by Pflamm-Altenburg, Weidner & Kroupa (this volume) documents the applications of the IGIMF theory to galactic astrophysics.
Context. The mass discrepancy in massive O stars represents a long-standing problem in stellar astrophysics with far-reaching implications for the chemical and dynamical feedback in galaxies. Aims. Our goal is to investigate this mass discrepancy by
comparing state-of-the-art model masses with model-independent masses determined from eclipsing binaries. Methods. Using stellar evolution models and a recent calibration of stellar parameters for O-star spectral sub-classes, we present a convenient way to convert observed solar metallicity O star spectral types into model masses, which we subsequently compare to our dynamical mass compilation. We also derive similar
