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 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

IR emission spectra are calculated for dust heated by starlight, for mixtures of amorphous silicate and graphitic grains, including varying amounts of PAH particles. The models are constrained to reproduce the average Milky Way extinction curve. The calculations include the effects of single-photon heating. Updated IR absorption properties for the PAHs are presented that are consistent with observed emission spectra, including those newly obtained by Spitzer. We find a size distribution for the PAHs giving emission band ratios consistent with the observed spectra of the Milky Way and other galaxies. Emission spectra are presented for a wide range of starlight intensities. We calculate how the efficiency of emission into different IR bands depends on PAH size; the strong 7.7 μm emission feature is produced mainly by PAH particles containing Umin. We present graphical procedures using Spitzer IRAC and MIPS photometry to estimate the parameters qPAH, Umin, and γ, the fraction fPDR of the dust luminosity coming from photodissociation regions with U > 100, and the total dust mass Mdust.

https://iopscience.iop.org/article/10.1086/511055/pdf

Infrared Emission from Interstellar Dust. IV. The Silicate-Graphite-PAH Model in the Post-Spitzer Era

We present an analysis of the intrinsic colors and temperatures of 5-30 Myr old pre-main sequence (pre-MS) stars using the F0 through M9 type members of nearby, negligibly reddened groups: η Cha cluster, TW Hydra Association, β Pic Moving Group, and Tucana-Horologium Association. To check the consistency of spectral types from the literature, we estimate new spectral types for 52 nearby pre-MS stars with spectral types F3 through M4 using optical spectra taken with the SMARTS 1.5m telescope. Combining these new types with published spectral types, and photometry from the literature (Johnson-Cousins BV IC, 2MASS JHKS and WISE W1, W2, W3, and W4), we derive a new empirical spectral type-color sequence for 5-30 Myr old pre-MS stars. Colors for pre-MS stars match dwarf colors for some spectral types and colors, but for other spectral types and colors, deviations can exceed 0.3 mag. We estimate effective temperatures (Teff) and bolometric corrections (BCs) for our pre-MS star sample through comparing their photometry to synthetic photometry generated using the BT-Settl grid of model atmosphere spectra. We derive a new Teff and BC scale for pre-MS stars, which should be a more appropriate match for T Tauri stars than often-adopted dwarf star scales. While our new Teff scale for pre-MS stars is within ≃100 K of dwarfs at a given spectral type for stars <G5, for G5 through K6, the pre-MS stars are ∼250 K cooler than their main sequence counterparts. Lastly, we present (1) a modern Teff, optical/IR color, and bolometric correction sequence for O9V-M9V MS stars based on an extensive literature survey, (2) a revised Qmethod relation for dereddening UBV photometry of OB-type stars, and (3) introduce two candidate spectral standard stars as representatives of spectral types K8V and K9V. Subject headings: open clusters and associations: individual(η Cha cluster, TW Hydra Association, β Pic Moving Group, Tucana-Horologium Association); — stars: pre-main sequence — stars: fundamental parameters (colors, temperatures)

https://iopscience.iop.org/article/10.1088/0067-0049/208/1/9/pdf

Intrinsic Colors, Temperatures, and Bolometric Corrections of Pre-Main Sequence Stars

The c2d Spitzer Legacy project obtained images and photometry with both IRAC and MIPS instruments for five large, nearby molecular clouds. Three of the clouds were also mapped in dust continuum emission at 1.1 mm, and optical spectroscopy has been obtained for some clouds. This paper combines information drawn from studies of individual clouds into a combined and updated statistical analysis of star-formation rates and efficiencies, numbers and lifetimes for spectral energy distribution (SED) classes, and clustering properties. Current star-formation efficiencies range from 3% to 6%; if star formation continues at current rates for 10 Myr, efficiencies could reach 15-30%. Star-formation rates and rates per unit area vary from cloud to cloud; taken together, the five clouds are producing about 260 M ☉ of stars per Myr. The star-formation surface density is more than an order of magnitude larger than would be predicted from the Kennicutt relation used in extragalactic studies, reflecting the fact that those relations apply to larger scales, where more diffuse matter is included in the gas surface density. Measured against the dense gas probed by the maps of dust continuum emission, the efficiencies are much higher, with stellar masses similar to masses of dense gas, and the current stock of dense cores would be exhausted in 1.8 Myr on average. Nonetheless, star formation is still slow compared to that expected in a free-fall time, even in the dense cores. The derived lifetime for the Class I phase is 0.54 Myr, considerably longer than some estimates. Similarly, the lifetime for the Class 0 SED class, 0.16 Myr, with the notable exception of the Ophiuchus cloud, is longer than early estimates. If photometry is corrected for estimated extinction before calculating class indicators, the lifetimes drop to 0.44 Myr for Class I and to 0.10 for Class 0. These lifetimes assume a continuous flow through the Class II phase and should be considered median lifetimes or half-lives. Star formation is highly concentrated to regions of high extinction, and the youngest objects are very strongly associated with dense cores. The great majority (90%) of young stars lie within loose clusters with at least 35 members and a stellar density of 1 M ☉ pc–3. Accretion at the sound speed from an isothermal sphere over the lifetime derived for the Class I phase could build a star of about 0.25 M ☉, given an efficiency of 0.3. Building larger mass stars by using higher mass accretion rates could be problematic, as our data confirm and aggravate the "luminosity problem" for protostars. At a given T bol, the values for L bol are mostly less than predicted by standard infall models and scatter over several orders of magnitude. These results strongly suggest that accretion is time variable, with prolonged periods of very low accretion. Based on a very simple model and this sample of sources, half the mass of a star would be accreted during only 7% of the Class I lifetime, as represented by the eight most luminous objects.

/pdf/the-spitzer-c2d-legacy-results-star-formation-rates-and-5ddczd4myk.pdf

The Spitzer c2d legacy results: star-formation rates and efficiencies; evolution and lifetimes

Using results and calibrations from a previous paper (Gullbring et al. 1997), we estimate disk accretion rates for pre-main-sequence stars in the Taurus and Chamaeleon I molecular cloud complexes. The median accretion rate for T Tauri stars of age ~1 Myr is ~10-8 M☉ yr-1; the intrinsic scatter at a given age may be as large as 1 order of magnitude. There is a clear decline of mass accretion rates with increasing age t among T Tauri stars. Representing this decline as tη, we estimate 1.5 η 2.8; the large uncertainty is due to the wide range of accretion rates at a given age, the limited age range of the sample, and errors in estimating stellar ages and accretion luminosities. Adopting values of η near the low end of this range, which are more likely given probable errors and the neglect of birthline age corrections, masses accreted during the T Tauri phase are roughly consistent with disk masses estimated from millimeter-wave dust emission. Similarity solutions for evolving, expanding disks are used to investigate observational constraints on disk properties employing a minimum of parameters. For an assumed power-law form of the disk viscosity with radius ν Rγ, η 1.5 corresponds to γ 1. The limit γ ~ 1 corresponds to a roughly constant α in the Shakura-Sunyaev (1973) viscosity parameterization; using current observed disk sizes, we estimate α ~ 10-2 (on scales ~10-100 AU). Much of the observed variation in mass accretion rates can be accounted for by varying initial disk masses between 0.01 and 0.2 M☉, but this result may be strongly affected by the presence of binary companion stars. These results emphasize the need for older samples of stars for studying disk evolution.

https://iopscience.iop.org/article/10.1086/305277/pdf

Accretion and the Evolution of T Tauri Disks

Intrinsic near-infrared excesses of T tauri stars: Understanding the classical T tauri star locus

We present new measurements of disk accretion rates for T Tauri stars in the Taurus molecular cloud complex. Our results are based on intermediate-resolution spectrophotometry from 3200 to 5200 A, which is used to derive the excess hot continuum emission produced by accretion onto the central star. Previous estimates of T Tauri accretion rates in the literature differ by as much as 1 order of magnitude; our measurements agree better with the lowest estimates, and we discuss the problems and systematic effects that led to the previous disagreement. In particular, we note that the stellar photospheric emission from nonaccreting T Tauri stars exhibits color anomalies compared to main-sequence stars; these anomalies make the estimated extinction depend upon the color index used. We argue that the V-R index is a reasonable compromise to match with optically derived spectral types, and that V-I and V-J are much more likely to be biased by cooler companion stars and starspots. We develop a calibration with which approximate mass accretion rates can be derived for T Tauri stars based on broadband photometry and spectral types, which should enable accretion rates to be estimated for large samples with greater ease.

https://iopscience.iop.org/article/10.1086/305032/pdf

Disk accretion rates for T tauri stars

We have examined one of the key predictions of the magnetospheric infall model for classical T Tauri stars (CTTS), namely, the formation of a shock on the stellar surface. We find that accretion column emission can successfully reproduce the main observational properties of the excess continuum that veils the absorption features in CTTS. This success adds further support to the magnetospheric infall model for disk accretion. We have calculated the structure and the spectral energy distribution of the emergent continuum emission from a shock at the base of the magnetospheric accretion column. We find that the spectral shape of the excess can be understood as optically thick emission from the heated photosphere below the shock, appearing mostly on the Paschen and Brackett continua, and optically thin emission from the preshock and attenuated postshock regions, dominating at wavelengths shorter than the Balmer threshold. The accretion luminosity and rate depend on two parameters: the energy flux of the accretion flow, , and the surface coverage of the column, f, with typical values log ~10.5-11.5, of the order or up to a factor of 10 higher than the intrinsic stellar flux, and f ~ 0.1%-1% of the surface area. The so-called continuum stars have accretion columns with similar energy fluxes than the less veiled, typical CTTS but with much larger surface emitting areas of f ≥ 10%. At near-infrared wavelengths, the predicted veiling from the accretion column for typical CTTS parameters is nearly constant and ≤0.1. Only for the "continuum stars" are significant amounts of near-infrared veiling from the accretion column expected. For accretion columns with low values of , the Paschen continuum emission has spectral features, rendering the usual deveiling procedures uncertain. Magnetospheric flow Balmer emission may also contribute to the excess for stars with low- columns. Finally, accretion column emission can successfully reproduce the observed correlation between the excess luminosity at the U band and the accretion luminosity. This correlation does not depend on the characteristics (mass, spectral type) of the underlying star, at least in the range M3-K5.

https://iopscience.iop.org/article/10.1086/306527/pdf

The Structure and Emission of the Accretion Shock in T Tauri Stars

We discuss the properties of an accretion disk around a star with parameters typical of classical T Tauri stars (CTTSs) and with the average accretion rate for these disks The disk is assumed steady and geometrically thin The turbulent viscosity coefficient is expressed using the α prescription, and the main heating mechanisms considered are viscous dissipation and irradiation by the central star The energy is transported by radiation, turbulent conduction, and convection We find that irradiation from the central star is the main heating agent of the disk, except in the innermost regions, R 5 AU) becomes less dense, optically thin, and almost vertically isothermal, with a temperature distribution T ∝ R-1/2 The decrease in surface density at the outer disk decreases the disk mass by a factor of 4 with respect to a purely viscous case In addition, irradiation tends to make the outer disk regions stable against gravitational instabilities

https://iopscience.iop.org/article/10.1086/305702/pdf

Nuria Calvet

Papers

Accretion and the Evolution of T Tauri Disks

Intrinsic near-infrared excesses of T tauri stars: Understanding the classical T tauri star locus

Disk accretion rates for T tauri stars

The Structure and Emission of the Accretion Shock in T Tauri Stars

Accretion Disks around Young Objects. I. The Detailed Vertical Structure