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The initial mass function (IMF) succinctly characterizes a stellar population, provides a statistical measure of the end result of the star-formation process, and informs our under- standing of the structure and dynamical evolution of stellar clusters, the Milky Way, and other galaxies. Detecting variations in the form of the IMF could provide powerful insights into the processes that govern the formation and evolution of stars, clusters, and galaxies. In this contribution, we review measurements of the IMF in resolved stellar populations, and critically assess the evidence for systematic IMF variations. Studies of the field, local young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a universal IMF, suggesting no gross systematic variations in the IMF over a range of star formation environments, and much of cosmic time. We conclude by highlighting the complimentary roles that Gaia and the Large Synoptic Survey Telescope will play in future studies of the IMF in Galactic stellar populations.
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We present a method for investigating variations in the upper end of the stellar Initial Mass Function (IMF) by probing the production rate of ionizing photons in unresolved, compact star clusters with ages <~10 Myr and with different masses. We test this method by performing a pilot study on the young cluster population in the nearby galaxy NGC5194 (M51a), for which multi-wavelength observations from the Hubble Space Telescope are available. Our results indicate that the proposed method can probe the upper end of the IMF in galaxies located out to at least ~10 Mpc, i.e., a factor ~200 further away than possible by counting individual stars in young compact clusters. Our results for NGC5194 show no obvious dependence of the upper mass end of the IMF on the mass of the star cluster down to ~1000 M_sun, although more extensive analyses involving lower mass clusters and other galaxies are needed to confirm this conclusion.
The supermassive black hole at the center of the Milky Way plays host to a massive, young cluster that may have formed in one of the most inhospitable environments in the Galaxy. We present new measurements of the global properties of this cluster, including the initial mass function (IMF), age, and cluster mass. These results are based on Keck laser-guide-star adaptive optics observations used to identify the young stars and measure their Kp-band luminosity function as presented in Do et al. 2013. A Bayesian inference methodology is developed to simultaneously fit the global properties of the cluster utilizing the observations and extensive simulations of synthetic star clusters. We find that the slope of the mass function for this cluster is alpha = 1.7 +/- 0.2, which is steeper than previously reported, but still flatter than the traditional Salpeter slope of 2.35. The age of the cluster is between 2.5-5.8 Myr with 95% confidence, which is a younger age than typically adopted but consistent within the uncertainties of past measurements. The exact age of the cluster is difficult to determine since our results show two distinct age solutions (3.9 Myr and 2.8 Myr) due to model degeneracies in the relative number of Wolf-Rayet and OB stars. The total cluster mass is between 14,000 - 37,000 msun above 1 msun and it is necessary to include multiple star systems in order to fit the observed luminosity function and the number of observed Wolf-Rayet stars. The new IMF slope measurement is now consistent with X-ray observations indicating a factor of 10 fewer X-ray emitting pre-main-sequence stars than expected when compared with a Salpeter IMF. The young cluster at the Galactic center is one of the few definitive examples of an IMF that deviates significantly from the near-universal IMFs found in the solar neighborhood.
Few topics in astronomy initiate such vigorous discussion as whether or not the initial mass function (IMF) of stars is universal, or instead sensitive to the initial conditions of star formation. The distinction is of critical importance: the IMF influences most of the observable properties of stellar populations and galaxies, and detecting variations in the IMF could provide deep insights into the process by which stars form. In this review, we take a critical look at the case for IMF variations, with a view towards whether other explanations are sufficient given the evidence. Studies of the field, local young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a universal IMF: a power-law of Salpeter index ($Gamma=1.35$) above a few solar masses, and a log normal or shallower power-law ($Gamma sim 0-0.25$) between a few tenths and a few solar masses (ignoring the effects of unresolved binaries). The shape and universality of the IMF at the stellar-substellar boundary is still under investigation and uncertainties remain large, but most observations are consistent with a IMF that declines ($Gamma < -0.5$) well below the hydrogen burning limit. Observations of resolved stellar populations and the integrated properties of most galaxies are also consistent with a universal IMF, suggesting no gross variations in the IMF over much of cosmic time. There are indications of non-standard IMFs in specific local and extragalactic environments, which clearly warrant further study. Nonetheless, there is no clear evidence that the IMF varies strongly and systematically as a function of initial conditions after the first few generations of stars.
We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lognormal power law (MLP) distribution, the DPL distribution has a power law at the high mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power law decay also appears at the low mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e., rarely) stopping accretion at early times followed by outflow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object.
the present paper, we propose that the stellar initial mass distributions as known as IMF are best fitted by $q$-Weibulls that emerge within nonextensive statistical mechanics. As a result, we show that the Salpeters slope of $sim$2.35 is replaced when a $q$-Weibull distribution is used. Our results point out that the nonextensive entropic index $q$ represents a new approach for understanding the process of the star-forming and evolution of massive stars.
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