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

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.

/pdf/on-the-variation-of-the-initial-mass-function-30qbs7h433.pdf

On the variation of the initial mass function

The Kepler mission was designed to determine the frequency of Earth-sized planets in and near the habitable zone of Sun-like stars. The habitable zone is the region where planetary temperatures are suitable for water to exist on a planet’s surface. During the first 6 weeks of observations, Kepler monitored 156,000 stars, and five new exoplanets with sizes between 0.37 and 1.6 Jupiter radii and orbital periods from 3.2 to 4.9 days were discovered. The density of the Neptune-sized Kepler-4b is similar to that of Neptune and GJ 436b, even though the irradiation level is 800,000 times higher. Kepler-7b is one of the lowest-density planets (~0.17 gram per cubic centimeter) yet detected. Kepler-5b, -6b, and -8b confirm the existence of planets with densities lower than those predicted for gas giant planets.

/pdf/kepler-planet-detection-mission-introduction-and-first-5xbrdhycdy.pdf

Kepler Planet-Detection Mission: Introduction and First Results

Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source, robust, efficient, thread-safe libraries for a wide range of applications in computational stellar astrophysics. A one-dimensional stellar evolution module, MESAstar, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very low mass to massive stars, including advanced evolutionary phases. MESAstar solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. State-of-the-art modules provide equation of state, opacity, nuclear reaction rates, element diffusion data, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own explicitly defined public interface to facilitate independent development. Several detailed examples indicate the extensive verification and testing that is continuously performed and demonstrate the wide range of capabilities that MESA possesses. These examples include evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets to very old ages; the complete evolutionary track of a 1 M ☉ star from the pre-main sequence (PMS) to a cooling white dwarf; the solar sound speed profile; the evolution of intermediate-mass stars through the He-core burning phase and thermal pulses on the He-shell burning asymptotic giant branch phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; the complete evolutionary tracks of massive stars from the PMS to the onset of core collapse; mass transfer from stars undergoing Roche lobe overflow; and the evolution of helium accretion onto a neutron star. MESA can be downloaded from the project Web site (http://mesa.sourceforge.net/).

https://iopscience.iop.org/article/10.1088/0067-0049/192/1/3/pdf

Modules for Experiments in Stellar Astrophysics (MESA)

▪ 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 have computed stellar evolutionary models for stars in a mass range characteristic of Cepheid variables ($3<m/\Msol<12$) for different metallicities representative of the Galaxy and the Magellanic Clouds populations. The stellar evolution calculations are coupled to a linear non adiabatic stability analysis to get self-consistent mass-period-luminosity relations. The period - luminosity relation as a function of metallicity is analysed and compared to the recent EROS observations in the Magellanic Clouds. The models reproduce the observed width of the instability strips for the SMC and LMC. We determine a statistical P-L relationship, taking into account the evolutionary timescales and a mass distribution given by a Salpeter mass function. Excellent agreement is found with the SMC PL relationship determined by Sasselov et al. (1997). The models reproduce the change of slope in the P-L relationship near $P\sim 2.5$ days discovered recently by the EROS collaboration (Bauer 1997; Bauer et al. 1998) and thus explain this feature in term of stellar evolution. Some discrepancy, however, remains for the LMC Cepheids. The models are also in good agreement with Beat Cepheids observed by the MACHO and EROS collaborations. We show that most of the 1H/2H Beat Cepheids have not yet ignited central helium burning; they are just evolving off the Main Sequence toward the red giant branch.

http://arxiv.org/pdf/astro-ph/9804061.pdf

Cepheid models based on self-consistent stellar evolution and pulsation calculations: the right answer?

Stellar convection is a non-local process responsible for the transport of heat and chemical species. It can lead to enhanced mixing through convective overshooting and excitation of internal gravity waves (IGWs) at convective boundaries. The relationship between these processes is still not well understood and requires global hydrodynamic simulations to capture the important large-scale dynamics. The steep stratiﬁcation in stellar interiors suggests that the radial extent of such simulations can aﬀect the convection dynamics, the IGWs in the stably stratiﬁed radiative zone, and the depth of the overshooting layer. We investigate these eﬀects using two-dimensional global simulations performed with the fully compressible stellar hydrodynamics code MUSIC. We compare eight diﬀerent radial truncations of the same solar-like stellar model evolved over approximately 400 convective turnover times. We ﬁnd that the location of the inner boundary has an insigniﬁcant eﬀect on the convection dynamics, the convective overshooting and the travelling IGWs. We relate this to the background conditions at the lower convective boundary which are unaﬀected by the truncation, as long as a signiﬁcantly deep radiative layer is included in the simulation domain. However, we ﬁnd that extending the outer boundary by only a few percent of the stellar radius signiﬁcantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The eﬀect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratiﬁcation and the given luminosity.

Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model

Dept. of Physics & Astronomy, Wichita State University, Wichita, KS 67226-0032,USAABSTRACTBrown dwarfshavemasses intermediateto stars andplan-ets, but their atmospheres can span planetary plasma con-ditions as they cool over time. They are more directlyobservable than the currently known extrasolar planets.In this paper, we provide a brief summary of the atmo-spheric propertiesof browndwarfs, and applythis knowl-edge to predict the thermal and spectral properties of ex-trasolar planets.1.INTRODUCTIONSince their ﬁrst discovery in the Pleiades (Teide 1 byRebolo et al. 1995) and in the solar neighborhood(Gliese 229b by Nakajima et al. 1995), brown dwarfsare found by the dozen mostly by photometric sky sur-veys (e.g. DENIS, 2MASS, and SLOAN). Most browndwarfs have been found within 50 parsecs. For some, ac-curate distances can be established by parallax, and goodresolution (R ) optical and near-infraredspectra areoften obtained. Over the years, models of atmospheresand interiors have continued to improve in their ability todescribe the global properties of brown dwarfs (Lunineet al. 1989, Burrows et al. 1993, Allard & Hauschildt1995, Tsuji et al. 1996, Chabrier et al. 2000, Allard et al.2001, to name a few). Consequently, brown dwarfs arefairly well understood and can serve as a stepping stoneto understand extrasolar giant planets.2.BROWNDWARFSFigures 1 and 2 summarize what we have learned of theoverall spectral properties of brown dwarfs from the stel-lar to the planetary temperaturerange. The topmost spec-trum is that of a low mass M dwarf star (M/M

Atmospheres of extrasolar giant planets and brown dwarfs

In the poster presented in Cool Star 15, we analyzed the effect of disk accretion on the evolution of very low mass pre-main sequence stars and young brown dwarfs and the resulting uncertainties on the determination of masses and ages. We use the Lyon evolutionary 1-D code assuming a magnetospheric accretion process, i.e., the material falls covering a small area of the radiative surface, and we take into account the internal energy added from the accreted material as a free parameter $\epsilon$. Even if the approach to this problem is phenomenological, our formalism provides important hints about characteristics of disk accretion, which are useful for improved stellar interior calculations. Using the accretion rates derived from observations our results show that accretion does not affect considerably the position of theoretical isochrones as well as the luminosity compared with standard non-accreting models. See more discussions in a forthcoming paper by Gallardo, Baraffe and Chabrier (2008).

Evolution of very low mass pre-main sequence stars and young brown dwarfs under accretion: A phenomenological approach

We present evolutionary models for low mass stars and brown dwarfs ($m \le 1.2 \msol$) based on recent improvement of the theory: equation of state, atmosphere models, ... We concentrate on early evolutionary phases from the initial deuterium burning phase to the zero-age Main Sequence. Evolutionary models for young brown dwarfs are also presented. We discuss the uncertainties of the present models. We analyse the difficulties arising when comparing models with observations for very young objects, in particular concerning the problem of reddening.

Isabelle Baraffe

Papers

Cepheid models based on self-consistent stellar evolution and pulsation calculations: the right answer?

Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model

Atmospheres of extrasolar giant planets and brown dwarfs

Evolution of very low mass pre-main sequence stars and young brown dwarfs under accretion: A phenomenological approach

Pre-Main Sequence Models for Low-Mass Stars and Brown Dwarfs