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

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.

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Theory of Star Formation

New large-scale CO surveys of the first and second Galactic quadrants and the nearby molecular cloud complexes in Orion and Taurus, obtained with the CfA 1.2 m telescope, have been combined with 31 other surveys obtained over the past two decades with that instrument and a similar telescope on Cerro Tololo in Chile, to produce a new composite CO survey of the entire Milky Way. The survey consists of 488,000 spectra that Nyquist or beamwidth ( °) sample the entire Galactic plane over a strip 4°-10° wide in latitude, and beamwidth or ° sample nearly all large local clouds at higher latitudes. Compared with the previous composite CO survey of Dame et al. (1987), the new survey has 16 times more spectra, up to 3.4 times higher angular resolution, and up to 10 times higher sensitivity per unit solid angle. Each of the component surveys was integrated individually using clipping or moment masking to produce composite spatial and longitude-velocity maps of the Galaxy that display nearly all of the statistically significant emission in each survey but little noise. The composite maps provide detailed information on individual molecular clouds, suggest relationships between clouds and regions widely separated on the sky, and clearly display the main structural features of the molecular Galaxy. In addition, since the gas, dust, and Population I objects associated with molecular clouds contribute to the Galactic emission in every major wavelength band, the precise kinematic information provided by the present survey will form the foundation for many large-scale Galactic studies. A map of molecular column density predicted from complete and unbiased far-infrared and 21 cm surveys of the Galaxy was used both to determine the completeness of the present survey and to extrapolate it to the entire sky at |b| 5°), X shows little systematic variation with latitude from a mean value of (1.8 ± 0.3) × 1020 cm-2 K-1 km-1 s. Given the large sky area and large quantity of CO data analyzed, we conclude that this is the most reliable measurement to date of the mean X value in the solar neighborhood.

https://iopscience.iop.org/article/10.1086/318388/pdf

The Milky Way in Molecular Clouds: A New Complete CO Survey

CO line emission represents the most accessible and widely used tracer of the molecular interstellar medium. This renders the translation of observed CO intensity into total H2 gas mass critical to understand star formation and the interstellar medium in our Galaxy and beyond. We review the theoretical underpinning, techniques, and results of efforts to estimate this CO-to-H2 “conversion factor,” XCO, in different environments. In the Milky Way disk, we recommend a conversion factor XCO = 2×10 20 cm −2 (K km s −1 ) −1 with ±30% uncertainty. Studies of other “normal galaxies” return similar values in Milky Way-like disks, but with greater scatter and systematic uncertainty. Departures from this Galactic conversion factor are both observed and expected. Dust-based determinations, theoretical arguments, and scaling relations all suggest that XCO increases with decreasing metallicity, turning up sharply below metallicity ≈ 1/3–1/2 solar in a manner consistent with model predictions that identify shielding as a key parameter. Based on spectral line modeling and dust observations, XCO appears to drop in the central, bright regions of some but not all galaxies, often coincident with regions of bright CO emission and high stellar surface density. This lower XCO is also present in the overwhelmingly molecular interstellar medium of starburst galaxies, where several lines of evidence point to a lower CO-to-H2 conversion factor. At high redshift, direct evidence regarding the conversion factor remains scarce; we review what is known based on dynamical modeling and other arguments. Subject headings: ISM: general — ISM: molecules — galaxies: ISM — radio lines: ISM

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The CO-to-H2 Conversion Factor

The chemistry and dynamics of protoplanetary disks are likely to be intricately linked, with dynamical processes affecting the chemical composition and chemistry, in turn, controlling the ionization structure and hence the ability of a process such as the magnetorotational instability to drive turbulence. Here we present the results from chemical models of the outer disk, which include diffusive mixing driven by turbulence. We show that diffusion in the vertical direction can greatly affect the column densities of many molecules, increasing them by up to 2 orders of magnitude. Previous models have shown that disks consist of three chemically distinct layers, with the bulk of the observed molecular emission coming from a region between the cold midplane and the irradiated surface layers. Diffusion retains this structure, but increases the depth of the molecular layer, by bringing atoms and atomic ions formed by photodissociation in the layers into more shielded regions where the molecules can reform. The column densities of molecules whose abundances peak closer to the midplane, e.g., NH3 and N2H+, are not altered by diffusion. We find that diffusion does not affect the ionization fraction of the disk. We compare the calculated column densities to observations of DM Tau, LkCa 15, and TW Hya and find good agreement for many molecules for models with a diffusion coefficient of 1018 cm2 s-1.

Turbulence-driven Diffusion in Protoplanetary Disks: Chemical Effects in the Outer Regions

We compute the structure function scaling of a 2MASS extinction map of the Taurus molecular cloud complex. The scaling exponents of the structure functions of the extinction map follow Boldyrev's velocity structure function scaling of supersonic turbulence. This confirms our previous result based on a spectral map of 13CO J = 1-0 covering the same region and suggests that supersonic turbulence is important in the fragmentation of this star-forming cloud.

https://iopscience.iop.org/article/10.1086/345403/pdf

Structure Function Scaling of a 2MASS Extinction Map of Taurus

We present new observational data on the small-scale structure of the Taurus molecular cloud 1 (TMC-1) in the regime of 0.02-0.04 pc and 0.04-0.6 M☉. Our analysis is based on high-resolution, high-S/N, observations of an 8' × 8' area centered on the "cyanopolyyne peak" in the southeastern part of the TMC-1 ridge. The observations were made in the CCS 22 and 45 GHz transitions using NASA's Deep Space Network 70 m and 34 m telescopes at the Goldstone facility. The CCS emission in this region originates in three narrow components centered on LSR velocities of ~5.7, 5.9, and 6.1 km s-1. These components each represent a separate cylindrical feature elongated along the ridge. Among the three velocity components we identified a total of 45 clumps with a typical CCS column density of ~a few × 1013 cm-2, an H2 density of ~a few × 104 cm-3, and a mass in the range of 0.04-0.6 M☉. The statistical properties of these small-scale clumps are compared with those of the larger "NH3 cores" in cold clouds and "CS cores" in the hotter Orion region. The CCS clumps in TMC-1 are found to conform to Larson's scaling laws (relating observed line width to clump size) derived from the larger cores down to the small-scale regime (0.02 pc and 0.04 M☉). These clumps represent a regime in which microturbulence is small, amounting to ~10% of the thermal pressure inside a clump. Of the 45 clumps, only five appear to be gravitationally unstable to collapse. All unbound clumps have masses less than 0.2 M☉, while bound clumps have masses in the range 0.15-0.6 M☉. The 6.1 km s-1 velocity feature contains all the gravitationally unstable clumps and is the most likely site for future star formation.

Low-Mass Clumps in TMC-1: Scaling Laws in the Small-Scale Regime

Heating of Molecular-Hydrogen Clouds by Cosmic Rays and X-Rays

To study the role of protosellar jets and outflows in the time evolution of the parent cores and the protostars, the astronomical community needs a large enough database of infrared images of protostars at the highest spatial resolution possible to reveal the details of their morphology. Spitzer provides unprecedented sensitivity in the infrared to study both the jet and outflow features, however, its spatial resolution is limited by its 0.85 m mirror. Here, we use a high-resolution deconvolution algorithm, 'HiRes,' to improve the visualization of spatial morphology by enhancing resolution (to subarcsecond levels in the IRAC bands) and removing the contaminating side lobes from bright sources in a sample of 89 protostellar objects. These reprocessed images are useful for detecting (1) wide-angle outflows seen in scattered light, (2) morphological details of H{sub 2} emission in jets and bow shocks, and (3) compact features in MIPS 24 μm images as protostar/disk and atomic/ionic line emission associated with the jets. The HiRes FITS image data of such a large homogeneous sample presented here will be useful to the community in studying these protostellar objects. To illustrate the utility of this HiRes sample, we show how the opening angle of the wide-angle outflowsmore » in 31 sources, all observed in the HiRes-processed Spitzer images, correlates with age. Our data suggest a power-law fit to opening angle versus age with an exponent of ∼0.32 and 0.02, respectively, for ages ≤8000 yr and ≥8000 yr.« less

William D. Langer

Papers

Turbulence-driven Diffusion in Protoplanetary Disks: Chemical Effects in the Outer Regions

Structure Function Scaling of a 2MASS Extinction Map of Taurus

Low-Mass Clumps in TMC-1: Scaling Laws in the Small-Scale Regime

Heating of Molecular-Hydrogen Clouds by Cosmic Rays and X-Rays

HiRes DECONVOLVED SPITZER IMAGES OF 89 PROTOSTELLAR JETS AND OUTFLOWS: NEW DATA ON THE EVOLUTION OF THE OUTFLOW MORPHOLOGY*