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

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Supermassive black holes (BHs) have been found in 85 galaxies by dynamical modeling of spatially resolved kinematics. The Hubble Space Telescope revolutionized BH research by advancing the subject from its proof-of-concept phase into quantitative studies of BH demographics. Most influential was the discovery of a tight correlation between BH mass and the velocity dispersion σ of the bulge component of the host galaxy. Together with similar correlations with bulge luminosity and mass, this led to the widespread belief that BHs and bulges coevolve by regulating each other's growth. Conclusions based on one set of correlations from in brightest cluster ellipticals to in the smallest galaxies dominated BH work for more than a decade. New results are now replacing this simple story with a richer and more plausible picture in which BHs correlate differently with different galaxy components. A reasonable aim is to use this progress to refine our understanding of BH-galaxy coevolution. BHs with masses of 105−106M...

https://www.annualreviews.org/doi/suppl/10.1146/annurev-astro-082708-101811/suppl_file/aa51_kormendy_supmat.pdf

Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies

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

We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation—turbulence, magnetic fields, and self-gravity— are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Important problems include how GMCs form and evolve, what determines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The development of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes.

/pdf/theory-of-star-formation-sol2jzngnw.pdf

Theory of Star Formation

We propose a generalized model for stellar spin-down, disk accretion, and truncation, and the origin of winds, jets, and bipolar outflows from young stellar objects. We consider the steady state dynamics of accretion of matter from a viscous and imperfectly conducting disk onto a young star with a strong magnetic field. For an aligned stellar magnetosphere, shielding currents in the surface layers of the disk prevent stellar field lines from penetrating the disk everywhere except for a range of radii about pi = R(sub x), where the Keplerian angular speed of rotation Omega(sub x) equals the angular speed of the star Omega(sub *). For the low disk accretion rates and high magnetic fields associated with typical T Tauri stars, R(sub x) exceeds the radius of the star R(sub *) by a factor of a few, and the inner disk is effectively truncated at a radius R(sub t) somewhat smaller than R(sub x). Where the closed field lines between R(sub t) and R(sub x) bow sufficiently inward, the accreting gas attaches itself to the field and is funneled dynamically down the effective potential (gravitational plus centrifugal) onto the star. Contrary to common belief, the accompanying magnetic torques associated with this accreting gas may transfer angular momentum mostly to the disk rather than to the star. Thus, the star can spin slowly as long as R(sub x) remains significantly greater than R(sub *). Exterior to R(sub x) field lines threading the disk bow outward, which makes the gas off the mid-plane rotate at super-Keplerian velocities. This combination drives a magnetocentrifugal wind with a mass-loss rate M(sub w) equal to a definite fraction f of the disk accretion rate M(sub D). For high disk accretion rates, R(sub x) is forced down to the stellar surface, the star is spun to breakup, and the wind is generated in a manner identical to that proposed by Shu, Lizano, Ruden, & Najita in a previous communication to this journal. In two companion papers (II and III), we develop a detailed but idealized theory of the magnetocentrifugal acceleration process.

Magnetocentrifugally driven flows from young stars and disks. 1: A generalized model

We use three-dimensional (3D) numerical magnetohydrodynamic simulations to follow the evolution of cold, turbulent, gaseous systems with parameters chosen to represent conditions in giant molecular clouds (GMCs). We present results of three model cloud simulations in which the mean magnetic field strength is varied (B0 = 1.4-14 ?G for GMC parameters), but an identical initial turbulent velocity field is introduced. We describe the energy evolution, showing that (1) turbulence decays rapidly, with the turbulent energy reduced by a factor 2 after 0.4-0.8 flow crossing times (~2-4 Myr for GMC parameters), and (2) the magnetically supercritical cloud models gravitationally collapse after time ?6 Myr, while the magnetically subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of model snapshots with matched values of the Mach number ? 9,7,5. We show that the distributions of volume density and column density are both approximately log-normal, with mean mass-weighted volume density a factor 3-6 times the unperturbed value, but mean mass-weighted column density only a factor 1.1-1.4 times the unperturbed value. We introduce a spatial binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs) on the plane of the sky. We show that the average velocity dispersion for the distribution of ROCs is only weakly correlated with scale, similar to mean size-line width distributions for clumps within GMCs. We find that ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; we argue that the same difficulty may affect observed GMC clumps. We suggest that it may be possible to deduce the mean 3D size-line width relation using the lower envelope of the 2D size-line width distribution. We analyze magnetic field structure and show that in the high-density regime n 103 cm-3, total magnetic field strengths increase with density with logarithmic slope ~1/3-2/3. We find that mean line-of-sight magnetic field strengths may vary widely across a projected cloud and are not positively correlated with column density. We compute simulated interstellar polarization maps at varying observer orientations and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength, provided the dispersion in polarization angles is 25?.

https://www.kitp.ucsb.edu/sites/default/files/kitp/preprints/0004-637X_546_2_980.pdf

Density, velocity, and magnetic field structure in turbulent molecular cloud models

We report results of a three-dimensional, high resolution (up to 5123) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of the order of the flow crossing time or smaller, even in the presence of strong magnetic fields. About half of the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.

https://iopscience.iop.org/article/10.1086/311718/pdf

Dissipation in compressible magnetohydrodynamic turbulence

We report results of a three dimensional, high resolution (up to 512^3) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of order the flow crossing time or smaller, even in the presence of strong magnetic fields. About half the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.

https://arxiv.org/pdf/astro-ph/9809357.pdf

Eve C. Ostriker

Papers

Theory of Star Formation

Magnetocentrifugally driven flows from young stars and disks. 1: A generalized model

Density, velocity, and magnetic field structure in turbulent molecular cloud models

Dissipation in compressible magnetohydrodynamic turbulence

Dissipation in Compressible MHD Turbulence