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.

/pdf/galactic-stellar-and-substellar-initial-mass-function-1fntlgtk9q.pdf

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.

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

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

/pdf/the-co-to-h2-conversion-factor-26tvppkvj7.pdf

The CO-to-H2 Conversion Factor

Carbon monoxide column densities are compared to visual extinctions toward field stars in the rho Oph and Taurus molecular cloud complexes. The relationship of C(0-18) column density to extinction is established, and new determinations for (C-13)O column densities are given for a range of visual extinctions extended to beyond 20 mag. A prescription for determining hydrogen column densities and masses of molecular clouds from observations of CO isotopes is presented and discussed critically. These measurements agree well with the predictions of gas phase chemistry models which include chemical fractionation and selective isotopic photodestruction. The functional dependence of the C(O-18) column density on extinction is characterized by two different regimes separated by a distinct transition observed to occur at 4 mag in both molecular cloud complexes, whereas the functional dependence of (C-13)O is quite different in the two regions. Some saturation is found to occur for C(O-18) emission at high visual extinction and use the rarer isotopic species C(O-17) and (C-13)(O-18) to correct for it.

The relationship between carbon monoxide abundance and visual extinction in interstellar clouds.

We develop the use of the population diagram method to analyze molecular emission in order to derive physical properties of interstellar clouds. We focus particular attention on how the optical depth affects the derived total column density and the temperature. We derive an optical depth correction factor that can be evaluated based on observations and that incorporates the effect of saturation on derived upper level populations. We present analytic results for linear molecules in local thermodynamic equilibrium (LTE). We investigate numerically how subthermal excitation influences the population diagram technique, studying how the determination of kinetic temperature is affected when the local density is insufficient to achieve LTE. We present results for HC3N and CH3OH, representative of linear and nonlinear molecules, respectively. In some cases, alternative interpretations to the standard optically thin and thermalized picture yield significantly different results for column density and kinetic temperature, and we discuss this behavior. The population diagram method can be a very powerful tool for determining physical conditions in dense clouds if proper recognition is given to effects of saturation and subthermal excitation. We argue that the population diagram technique is, in fact, superior to fitting intensities of different transitions directly, and we indicate how it can be effectively employed.

https://iopscience.iop.org/article/10.1086/307195/pdf

Population Diagram Analysis of Molecular Line Emission

Elementary Processes in Hydrogen-Helium Plasmas

A large-scale (C-13)O map (containing 33,000 spectra on a 1-arcmin grid) is presented for the giant molecular cloud located in the southern part of Ori which contains the Ori Nebula, NGC 1977, and the L1641 dark cloud complex. The overall structure of the cloud is filamentary, with individual features having a length up to 40 times their width. The northern portion of the cloud is compressed, dynamically relaxed, and supports massive star formation. In contrast, the southern part of the Ori A cloud is diffuse, exhibits chaotic spatial and velocity structure, and supports only intermediate- to low-mass star formation. This morphology may be the consequence of the formation and evolution of the Ori OB I association centered north of the molecular cloud. The entire cloud, in addition to the 5000-solar-mass filament containing both OMC-1 and OMC-2, exhibits a north-south velocity gradient. Implications of the observed cloud morphology for theories of molecular cloud evolution are discussed. 14 references.

Filamentary structure in the Orion molecular cloud

We analyze in detail the cooling produced by line emission from a variety of molecular and atomic species, including those observed as well as theoretically expected in dense interstellar clouds. At molecular hydrogen densities less than 3 x 10/sup 4/ cm/sup -3/ and kinetic temperatures between 10 K and 40 K, /sup 12/CO is the dominant coolant. At n (H/sub 2/) =3 x 10/sup -3/, however, C c, O/sub 2/, and the rarer isotopic species of carbon monoxide together contribute half of the total cooling. As n (H/sub 2/) is increased beyond 3 x 10/sup 4/ cm/sup -3/, a large number of species including water, hydrides, molecular ions, and less abundant diatomic molecules collectively dominate the cooling. The cooling per H/sub 2/ molecule, ..lambda../n (H/sub 2/), is only very weakly density-dependent for n (H/sub 2/) greater than a few times 10/sup 2/ cm/sup -3/. At a density of 4 x 10/sup 3/ cm/sup -3/, ..lambda..=2.6 x 10/sup -26/T/sub kin//sup 2.2/ ergs cm/sup -3/ s/sup -1/. The rate of energy transfer by dust-gas collisions results in infrared emission by dust grains being a significant coolant for the gas only for n (H/sub 2/) >1.5 x 10/sup 4/ cm/sup -3/. We evaluatemore » the contribution of a number of gas heating machanisms which may be present in interstellar clouds including heating by cosmic rays, H/sub 2/ formation, gravitational collapse, and magnetic ion-neutral slip heating. For clouds with kinetic temperatures approx.10 K, cosmic ray heating alone may be sufficient to balance the gas cooling for 3 x 10/sup 2/< or =n (H/sub 2/) < or =10/sup 4/ cm/sup -3/, these conditions being in good agreement with the observationally determined characteristics of dark clouds.« less

William D. Langer

Papers

The relationship between carbon monoxide abundance and visual extinction in interstellar clouds.

Population Diagram Analysis of Molecular Line Emission

Elementary Processes in Hydrogen-Helium Plasmas

Filamentary structure in the Orion molecular cloud

Molecular cooling and thermal balance of dense interstellar clouds