We review recent determinations of the present-day mass function (PDMF) and initial mass function (IMF) in various components of the Galaxy—disk, spheroid, young, and globular clusters—and in conditions characteristic of early star formation. As a general feature, the IMF is found to depend weakly on the environment and to be well described by a power-law form forM , and a lognormal form below, except possibly for m!1 early star formation conditions. The disk IMF for single objects has a characteristic mass around M , m!0.08 c and a variance in logarithmic mass , whereas the IMF for multiple systems hasM , and . j!0.7 m!0.2 j!0.6 c The extension of the single MF into the brown dwarf regime is in good agreement with present estimates of L- and T-dwarf densities and yields a disk brown dwarf number density comparable to the stellar one, n!n! BD " pc !3 .T he IMF of young clusters is found to be consistent with the disk fi eld IMF, providing the same correction 0.1 for unresolved binaries, confirming the fact that young star clusters and disk field stars represent the same stellar population. Dynamical effects, yielding depletion of the lowest mass objects, are found to become consequential for ages!130 Myr. The spheroid IMF relies on much less robust grounds. The large metallicity spread in the local subdwarf photometric sample, in particular, remains puzzling. Recent observations suggest that there is a continuous kinematic shear between the thick-disk population, present in local samples, and the genuine spheroid one. This enables us to derive only an upper limit for the spheroid mass density and IMF. Within all the uncertainties, the latter is found to be similar to the one derived for globular clusters and is well represented also by a lognormal form with a characteristic mass slightly larger than for the disk, M , ,e xcluding as ignif icant population of m!0.2-0.3 c brown dwarfs in globular clusters and in the spheroid. The IMF characteristic of early star formation at large redshift remains undetermined, but different observational constraints suggest that it does not extend below!1M , .T hese results suggest a characteristic mass for star formation that decreases with time, from conditions prevailing at large redshift to conditions characteristic of the spheroid (or thick disk) to present-day conditions.Theseconclusions,however, remain speculative, given the large uncertainties in the spheroid and early star IMF determinations. These IMFs allow a reasonably robust determination of the Galactic present-day and initial stellar and brown dwarf contents. They also have important galactic implications beyond the Milky Way in yielding more accurate mass-to-light ratio determinations. The mass-to-light ratios obtained with the disk and the spheroid IMF yield values 1.8-1.4 times smaller than for a Salpeter IMF, respectively, in agreement with various recent dynamical determinations. This general IMF determination is examined in the context of star formation theory. None of the theories based on a Jeans-type mechanism, where fragmentation is due only to gravity, can fulfill all the observational constraints on star formation and predict a large number of substellar objects. On the other hand, recent numerical simulations of compressible turbulence, in particular in super-Alfvenic conditions, seem to reproduce both qualitatively and quantitatively the stellar and substellar IMF and thus provide an appealing theoretical foundation. In this picture, star formation is induced by the dissipation of large-scale turbulence to smaller scales through radiative MHD shocks, producing filamentary structures. These shocks produce local nonequilibrium structures with large density contrasts, which collapse eventually in gravitationally bound objects under the combined influence of turbulence and gravity. The concept of a single Jeans mass is replaced by a distribution of local Jeans masses, representative of the lognormal probability density function of the turbulent gas. Objects below the mean thermal Jeans mass still have a possibility to collapse, although with a decreasing probability.

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Galactic stellar and substellar initial mass function

A universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation.



In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M⊙ and near 0.08 M⊙. Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter.



Determinations of the power-law indices α are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Δα≈0.5 between 0.1 and 1 M⊙ than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Mendez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.

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On the variation of the initial mass function

▪ Abstract Stellar clusters are born embedded within giant molecular clouds (GMCs) and during their formation and early evolution are often only visible at infrared wavelengths, being heavily obscured by dust. Over the past 15 years advances in infrared detection capabilities have enabled the first systematic studies of embedded clusters in galactic molecular clouds. In this article we review the current state of empirical knowledge concerning these extremely young protocluster systems. From a survey of the literature we compile the first extensive catalog of galactic embedded clusters. We use the catalog to construct the mass function and estimate the birthrate for embedded clusters within ∼2 kpc of the sun. We find that the embedded cluster birthrate exceeds that of visible open clusters by an order of magnitude or more indicating a high infant mortality rate for protocluster systems. Less than 4–7% of embedded clusters survive emergence from molecular clouds to become bound clusters of Pleiades age. Th...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/ladalada.pdf

Embedded Clusters in Molecular Clouds

We review progress over the past decade in observations of large-scale star formation, with a focus on the interface between extragalactic and Galactic studies. Methods of measuring gas contents and star-formation rates are discussed, and updated prescriptions for calculating star-formation rates are provided. We review relations between star formation and gas on scales ranging from entire galaxies to individual molecular clouds.

Star Formation in the Milky Way and Nearby Galaxies

▪ Abstract The Local Group dwarf galaxies offer a unique window to the detailed properties of the most common type of galaxy in the Universe. In this review, I update the census of Local Group dwarfs based on the most recent distance and radial velocity determinations. I then discuss the detailed properties of this sample, including (a) the integrated photometric parameters and optical structures of these galaxies, (b) the content, nature, and distribution of their interstellar medium (ISM), (c) their heavy-element abundances derived from both stars and nebulae, (d) the complex and varied star-formation histories of these dwarfs, (e) their internal kinematics, stressing the relevance of these galaxies to the “dark matter problem” and to alternative interpretations, and (f) evidence for past, ongoing, and future interactions of these dwarfs with other galaxies in the Local Group and beyond. To complement the discussion and to serve as a foundation for future work, I present an extensive set of basic observ...

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Dwarf galaxies of the local group

We quantify the complex interdependence of stellar binarity, the stellar mass-luminosity relation, the mass function, the colour-magnitude relation and Galactic disc structure, all of which must be understood when analysing star-count data and stellar luminosity functions. We derive a mass-M V relation and a model for the change of stellar luminosity with changes in chemical abundance and age. Combination of this with detailed modelling of all astrophysical and observational contributions to the Malmquist scatter allows us to model star-count data without approximating Malmquist corrections. We show for the first time that a single mass function and normalization explain the stellar distribution towards both Galactic poles, as well as the distribution of stars within a distance of 5.2 pc of the Sun

The distribution of low-mass stars in the Galactic disc

WE have detected a large, extended group of comoving stars in the direction of the Galactic Centre, which we interpret as belonging to a dwarf galaxy that is closer to our own Galaxy than any other yet known. Located in the constellation of Sagittarius, and on the far side of the Galactic Centre, it has not previously been seen because of the large number of foreground stars (in the Milky Way) in that direction. Following convention, we propose to call it the Sagittarius dwarf galaxy. Its properties are similar to those of the eight other dwarf spheroidal companions to the Milky Way, and it is comparable in size and luminosity to the largest of them— the Fornax system. The Sagittarius dwarf is elongated towards the plane of the Milky Way, suggesting that it is undergoing some tidal disruption before being absorbed by the Milky Way.

A dwarf satellite galaxy in Sagittarius

New light on faint stars – III. Galactic structure towards the South Pole and the Galactic thick disc

We apply the Jeans equation to estimate masses for eight of the brightest dwarf spheroidal (dSph) galaxies. For Fornax, the dSph with the largest kinematic data set, we obtain a model-independent constraint on the maximum circular velocity, V max = 20+4 –3 km s–1. Although we obtain only lower limits of V max 10 km s–1 for the remaining dSphs, we find that in all cases the enclosed mass at the projected half-light radius is well constrained and robust to a wide range of halo models and velocity anisotropies. We derive a simple analytic formula that estimates M(r half) accurately with respect to results from the full Jeans analysis. Applying this formula to the entire population of Local Group dSphs with published kinematic data, we demonstrate a correlation such that M(r half) ∝ r 1.4±0.4 half, or in terms of the mean density interior to the half-light radius, ρ ∝ r –1.6±0.4 half. This relation is driven by the fact that the dSph data exhibit a correlation between global velocity dispersion and half-light radius. We argue that tidal forces are unlikely to have introduced this relation, but tides may have increased the scatter and/or altered the slope. While the data are well described by mass profiles ranging over a factor of 2 in normalization (V max ~ 10-20 km s–1), we consider the hypothesis that all dSphs are embedded within a "universal" dark matter halo. We show that in addition to the power law M ∝ r 1.4, viable candidates include a cuspy "Navarro-Frenk-White" halo with V max ~ 15 km s–1 and scale radius r 0 ~ 800 pc, as well as a cored halo with V max ~ 13 km s–1 and r 0 ~ 150 pc. Finally, assuming that their measured velocity dispersions accurately reflect their masses, the smallest dSphs now allow us to resolve dSph densities at radii as small as a few tens of pc. At these small scales, we find mean densities as large as ρ 5 M ☉ pc–3 (200 GeV cm–3).

http://iopscience.iop.org/article/10.1088/0004-637X/704/2/1274/pdf

A Universal Mass Profile for Dwarf Spheroidal Galaxies

Les donnees photometriques et spectroscopiques pour un echantillon de naines K en direction du pole galactique sud sont analysees en utilisant la technique de modelisation des fonctions de distribution decrite dans l'article I des memes auteurs (1989, Mon. Not. R. astr. Soc., 239). La densite de masse superficielle de la masse identifiee peut egalement etre obtenue en integrant la population stellaire pres du Soleil a travers la loi de force derivee et en y rajoutant la quantite observee de gaz interstellaire. La densite de masse superficielle totale du disque galactique derivee de l'analyse dynamique est comparee a la densite de masse superficielle totale identifiee pres du Soleil

Gerard Gilmore

Papers

The distribution of low-mass stars in the Galactic disc

A dwarf satellite galaxy in Sagittarius

New light on faint stars – III. Galactic structure towards the South Pole and the Galactic thick disc

A Universal Mass Profile for Dwarf Spheroidal Galaxies

The mass distribution in the galactic disc -II. Determination of the surface mass density of the galactic disc near the Sun.