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When a detailed model of a stellar population is unavailable, it is most common to assume that stellar masses are independently and identically distributed according to some distribution: the universal initial mass function (IMF). However,…
Observations and N-body simulations both support a simple relation for the disruption time of a cluster as a function of its mass of the form: t_dis = t_4 * (M/10^4 Msun)^gamma. The scaling factor t_4 seems to depend strongly on the…
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…
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…
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…
The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium (ISM) conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large…
Statistical sampling from the stellar initial mass function (IMF) for all star-forming regions in the Galaxy would lead to the prediction of ~1000 Msun stars unless there is a rapid turn-down in the IMF beyond several hundred solar masses.…
The star cluster initial mass function is observed to have an inverse power law exponent around 2, yet there is no consensus on what determines this distribution, and why some variation is observed in different galaxies. Furthermore, the…
Clusters of galaxies are powerful cosmological probes, particularly if their masses can be determined. One possibility for mass determination is to study the cosmic microwave background (CMB) on small angular scales and observe deviations…
Massive stars define the upper limits of the star formation process, dominate the energetics of their local environs, and significantly affect the chemical evolution of galaxies. Their role in starburst galaxies and the early Universe is…
Mass segregation in a star cluster is studied in an analytical manner. We consider a two-component cluster, which consists of two types of stars with different masses. Plummer's model is used for the initial condition. We trace the overall…
The conditions required for massive star formation are debated, particularly whether massive stars must form in conjunction with massive clusters. Some authors have advanced the view that stars of any mass (below the total cluster mass) can…
Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation. If turbulence driven fragmentation is the mechanism responsible for their formation, we expect their stellar mass function…
In this chapter, we review some historical understanding and recent advances on the Initial Mass Function (IMF) and the Core Mass Function (CMF), both in terms of observations and theories. We focus mostly on star formation in clustered…
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…
The mass function of galaxy clusters is a sensitive tracer of the gravitational evolution of the cosmic large-scale structure and serves as an important census of the fraction of matter bound in large structures. We obtain the mass function…
The distribution of core radii of rich clusters in the Large Magellanic Cloud (LMC) systematically increases in both upper limit and spread with increasing cluster age. Cluster-to-cluster variations in the stellar initial mass function…
Star clusters are key components of galaxies, and the relationship between cluster radius and mass encodes information about cluster formation and evolution. Theoretical models predict that age and specific star formation rate (sSFR) should…
We present a study on the clustering of a stellar mass selected sample of 18,482 galaxies with stellar masses M*>10^10M(sun) at redshifts 0.4<z<2.0, taken from the Palomar Observatory Wide-field Infrared Survey. We examine the clustering…
We investigate the triggering of star formation and the formation of stellar clusters in molecular clouds that form as the ISM passes through spiral shocks. The spiral shock compresses gas into $\sim$100 pc long main star formation ridge,…