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Observations have not yielded convincing results concerning the form of the stellar initial mass function (IMF) or its variations in space and time, so it is proposed that theoretical models may provide useful guidance. Several classes of…
We propose that the stellar initial mass function (IMF) is universal in the sense that its functional form arises as a consequence of the statistics of random supersonic flows. A model is developed for the origin of the stellar IMF, that…
One of the key observations regarding the stellar initial mass function (IMF) is its near-universality in the Milky Way (MW), which provides a powerful way to constrain different star formation models that predict the IMF. However, those…
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…
Deviations from a universal, MW-like, Stellar Initial Mass Function (IMF) have been reported for distant galaxies, although the physical reason behind the observed variations is still matter of ongoing debate. In this paper, we present an…
The stellar initial mass function (IMF) of early-type galaxies is the combination of the IMF of the stellar population formed in-situ and that of accreted stellar populations. Using as an observable the effective IMF $\alpha_{IMF}$, defined…
From time to time, and quite more frequently in recent years, claims appear favoring a variable Initial Mass Function (IMF), one way or another, either in time or space. In this chapter we add our two pennies of wisdom, illustrating how the…
The stellar initial-mass function (IMF) represents a fundamental quantity in astrophysics and cosmology, describing the mass distribution of stars from low to very-high masses. It is intimately linked to a wide variety of topics, including…
Observations of normal galactic star-forming regions suggest there is widespread near-uniformity in the initial stellar mass function (IMF) in spite of diverse physical conditions. Fluctuations may come largely from statistical effects and…
The stellar Initial Mass Function (IMF) seems to be close to universal in the local star-forming regions. However, this quantity of a newborn stellar population responds differently at gas metallicities $Z \sim$ $Z_\odot$ than $Z$ = 0. A…
It has frequently been suggested that the stellar IMF in galaxies was top-heavy at early times. This would be plausible physically if the IMF depends on a mass scale such as the Jeans mass that was higher at earlier times because of the…
Dust is important for star formation because it is the crucial component that couples gas to stellar radiation fields, allowing radiation feedback to influence gas fragmentation and thus the stellar initial mass function (IMF). Variations…
Observations with JWST have revealed an unexpected high abundance of bright z>10 galaxy candidates. We explore whether a stellar initial mass function (IMF) that becomes increasingly top-heavy towards higher redshifts and lower gas-phase…
The stellar initial mass function (IMF), which is often assumed to be universal across unresolved stellar populations, has recently been suggested to be "bottom-heavy" for massive ellipticals. In these galaxies, the prevalence of…
The combination of a finite time-scale for star formation, rapid early stellar evolution and rapid stellar-dynamical processes imply that the stellar IMF cannot be inferred for any star cluster independently of its age (the Cluster IMF…
We examine the cosmic evolution of a stellar initial mass function (IMF) in galaxies that varies with the Jeans mass in the interstellar medium, paying particular attention to the K-band stellar mass to light ratio (M/L_K) of present-epoch…
The manner in which the stellar initial mass function (IMF) scales with global galaxy properties is under debate. We use two hydrodynamical, cosmological simulations to predict possible trends for two self-consistent variable IMF…
The distribution of stellar masses that form in one star-formation event in a given volume of space is called the initial mass function (IMF). The IMF has been estimated from low-mass brown dwarfs to very massive stars. Combining IMF…
The current status of both the observational evidence and the theory of the stellar initial mass function (IMF) is reviewed, with particular attention to the two basic, apparently universal features shown by all observations of nearby…
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.…