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Although the stellar initial mass function (IMF) has only been directly determined in star clusters it has been manifoldly applied on galaxy-wide scales. But taking the clustered nature of star formation into account the galaxy-wide IMF is…
Star-formation rates (SFRs) of galaxies are commonly calculated by converting the measured Halpha luminosities (L_Halpha) into current SFRs. This conversion is based on a constant initial mass function (IMF) independent of the total SFR. As…
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…
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…
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…
Theoretical and indirect observational evidences suggest that stellar initial mass function (IMF) increases with redshift. On the other hand star formation rates (SFR) may be as high as 100 $M_{\odot}$ yr$^{-1}$ in star burst galaxies.…
If all stars form in clusters and both the stars and the clusters follow a power law distribution which favours the creation of low mass objects, then the numerous low mass clusters will be deficient in high mass stars. Therefore, the mass…
The galaxy-wide stellar initial mass function (IGIMF) of a galaxy is thought to depend on its star formation rate (SFR). Using a catalogue of observational properties of early-type galaxies (ETGs) and a relation that correlates the…
The measured star-formation rates (SFRs) of galaxies comprise an important constraint on galaxy evolution and also on their cosmological boundary conditions. Any available tracer of the SFR depends on the shape of the mass-distribution of…
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…
The integrated galaxial initial mass function (IGIMF) is the relevant distribution function containing the information on the distribution of stellar remnants, the number of supernovae and the chemical enrichment history of a galaxy. Since…
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…
The stellar initial mass function (IMF) is commonly assumed to be an invariant probability density distribution function of initial stellar masses being represented by the canonical IMF. As a consequence the galaxy-wide IMF (gwIMF), defined…
[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…
Stars form in embedded star clusters which play a key role in determining the properties of a galaxy's stellar population. Physical mechanisms discussed in this paper are runaway stars shot out from young clusters, binary-star disruption in…
Recent observations indicate a lower Halpha to FUV ratio in dwarf galaxies than in brighter systems, a trend that could be explained by a truncated and/or steeper IMF in small galaxies. However, at low star formation rates (SFRs), the…
In this paper, we present a new derivation of the shape and evolution of the integrated galaxy-wide initial mass function (IGIMF), incorporating explicitly the effects of cosmic rays (CRs) as regulators of the chemical and thermal state of…
We investigate how a single generation galactic mass function (SGMF) depends on the existence of variations in the initial stellar mass functions (IMF) of stellar clusters. We show that cluster-to-cluster variations of the IMF lead to a…
We summarize recent observational and theoretical progress aimed at understanding the origin of the stellar initial mass function (IMF) with specific focus on galactic star-forming regions. We synthesize data from various efforts to…
The initial mass function (IMF) is one of the most important functions in astrophysics because it is key to reconstructing the cosmological matter cycle, understanding the formation of super-massive black holes, and deciphering the light…