November 10, 2005
We demonstrate that the mass of the most massive star in a cluster correlates non-trivially with the cluster mass. A simple algorithm according to which a cluster is filled up with stars that are chosen randomly from the standard IMF but sorted with increasing mass yields an excellent description of the observational data. Algorithms based on random sampling from the IMF without sorted adding are ruled out with a confidence larger than 0.9999. A physical explanation of this would be that a cluster forms by more-massive stars being consecutively added until the resulting feedback energy suffices to revert cloud contraction and stops further star formation. This has important implications for composite populations. For example, 10^4 clusters of mass 10^2 Msol will not produce the same IMF as one cluster with a mass of 10^6 Msol. It also supports the notion that the integrated galaxial IMF (IGIMF) should be steeper than the stellar IMF and that it should vary with the star-formation rate of a galaxy.
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September 8, 2009
We present a thorough literature study of the most-massive star, m_max, in several young star clusters in order to assess whether or not star clusters are populated from the stellar initial mass function (IMF) by random sampling over the mass range 0.01 < m < 150 M_sol without being constrained by the cluster mass, M_ecl. The data reveal a partition of the sample into lowest mass objects (M_ecl < 10^2 M_sol), moderate mass clusters (10^2 M_sol < M_ecl < 10^3 M_sol) and rich c...
November 23, 2022
The stellar initial mass function (IMF) is commonly interpreted to be a scale-invariant probability density distribution function (PDF) such that many small clusters yield the same IMF as one massive cluster of the same combined number of stars. Observations of the galaxy-wide IMF challenge this as dwarf galaxies do not form as many massive stars as expected. This indicates a highly self-regulated star formation process in which stellar masses are not stochastically sampled f...
July 25, 2005
Theoretical considerations lead to the expectation that stars should not have masses larger than about m_{max*}=60-120Msun, while the observational evidence has been ambiguous. Only very recently has a physical stellar mass limit near 150Msun emerged thanks to modern high-resolution observations of local star-burst clusters. But this limit does not appear to depend on metallicity, in contradiction to theory. Important uncertainties remain though. It is now also emerging that ...
May 7, 2007
Star formation happens in a clustered way which is why the star cluster population of a particular galaxy is closely related to the star formation history of this galaxy. From the probabilistic nature of a mass function follows that the mass of the most-massive cluster of a complete population, M_max, has a distribution with the total mass of the population as a parameter. The total mass of the population is connected to the star formation rate (SFR) by the length of a format...
March 28, 2013
Our understanding of stellar systems depends on the adopted interpretation of the IMF, phi(m). Unfortunately, there is not a common interpretation of the IMF, which leads to different methodologies and diverging analysis of observational data.We study the correlation between the most massive star that a cluster would host, mmax, and its total mass into stars, M, as an example where different views of the IMF lead to different results. We assume that the IMF is a probability d...
September 1, 2010
We attempt to evaluate whether the integrated galactic IMF (IGIMF) is expected to be steeper than the IMF within individual clusters through direct evaluation of whether there is a systematic dependence of maximum stellar mass on cluster mass. We show that the result is sensitive to observational selection biases and requires an accurate knowledge of cluster ages, particularly in more populous clusters. At face value there is no compelling evidence for non-random selection of...
November 20, 2013
A growing fraction of Simple Stellar Population (SSP) models, in an aim to create more realistic simulations capable of including stochastic variation in their outputs, begin their simulations with a distribution of discrete stars following a power-law function of masses. Careful attention is needed to create a correctly sampled Initial Mass Function (IMF) and in this contribution we provide a solid mathematical method called MASSCLEAN IMF Sampling for doing so. We then use o...
August 29, 2008
We have made a new compilation of observations of maximum stellar mass versus cluster membership number from the literature, which we analyse for consistency with the predictions of a simple random drawing hypothesis for stellar mass selection in clusters. Previously, Weidner and Kroupa have suggested that the maximum stellar mass is lower, in low mass clusters, than would be expected on the basis of random drawing, and have pointed out that this could have important implicat...
December 14, 2011
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 ...
September 30, 2004
As most if not all stars are born in stellar clusters the shape of the mass function of the field stars is not only determined by the initial mass function of stars (IMF) but also by the cluster mass function (CMF). In order to quantify this Monte-Carlo simulations were carried out by taking cluster masses randomly from a CMF and then populating these clusters with stars randomly taken from an IMF. Two cases were studied. Firstly the star masses were added randomly until the ...