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 discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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The Cosmological simulation code GADGET-2

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

/pdf/the-observation-of-gravitational-waves-from-a-binary-black-58srpupgg9.pdf

The Observation of Gravitational Waves from a Binary Black Hole Merger

Solar photospheric and meteoritic CI chondrite abundance determinations for all elements are summarized and the best currently available photospheric abundances are selected. The meteoritic and solar abundances of a few elements (e.g., noble gases, beryllium, boron, phosphorous, sulfur) are discussed in detail. The photospheric abundances give mass fractions of hydrogen (X ¼ 0:7491), helium (Y ¼ 0:2377), and heavy elements (Z ¼ 0:0133), leading to Z=X ¼ 0:0177, which is lower than the widely used Z=X ¼ 0:0245 from previous compilations. Recent results from standard solar models considering helium and heavy-element settling imply that photospheric abundances and mass fractions are not equal to protosolar abundances (representative of solar system abundances). Protosolar elemental and isotopic abundances are derived from photospheric abundances by considering settling effects. Derived protosolar mass fractions are X0 ¼ 0:7110, Y0 ¼ 0:2741, and Z0 ¼ 0:0149. The solar system and photospheric abundance tables are used to compute self-consistent sets of condensation temperatures for all elements. Subject headings: astrochemistry — meteors, meteoroids — solar system: formation — Sun: abundances — Sun: photosphere

/pdf/solar-system-abundances-and-condensation-temperatures-of-the-f7u38sk0l8.pdf

Solar System Abundances and Condensation Temperatures of the Elements

The presence of a Jupiter-mass companion to the star 51 Pegasi is inferred from observations of periodic variations in the star's radial velocity. The companion lies only about eight million kilometres from the star, which would be well inside the orbit of Mercury in our Solar System. This object might be a gas-giant planet that has migrated to this location through orbital evolution, or from the radiative stripping of a brown dwarf.

A Jupiter-Mass Companion to a Solar-Type Star

Analyses of primitive meteorites and cometary samples have shown that the solar nebula must have experienced a phase of large-scale outward transport of small refractory grains as well as homogenization of initially spatially heterogeneous short-lived isotopes. The stable oxygen isotopes, however, were able to remain spatially heterogeneous at the ~6% level. One promising mechanism for achieving these disparate goals is the mixing and transport associated with a marginally gravitationally unstable (MGU) disk, a likely cause of FU Orionis events in young low-mass stars. Several new sets of MGU models are presented that explore mixing and transport in disks with varied masses (0.016 to 0.13 M ☉) around stars with varied masses (0.1 to 1 M ☉) and varied initial Q stability minima (1.8 to 3.1). The results show that MGU disks are able to rapidly (within ~104 yr) achieve large-scale transport and homogenization of initially spatially heterogeneous distributions of disk grains or gas. In addition, the models show that while single-shot injection heterogeneity is reduced to a relatively low level (~1%), as required for early solar system chronometry, continuous injection of the sort associated with the generation of stable oxygen isotope fractionations by UV photolysis leads to a sustained, relatively high level (~10%) of heterogeneity, in agreement with the oxygen isotope data. These models support the suggestion that the protosun may have experienced at least one FU Orionis-like outburst, which produced several of the signatures left behind in primitive chondrites and comets.

https://iopscience.iop.org/article/10.1088/0004-637X/773/1/5/pdf

Mixing and transport of short-lived and stable isotopes and refractory grains in protoplanetary disks

The relatively high initial abundance of the shortlived radioisotope 26Al in calciumaluminiumrich refractory inclusions found in meteorites is inconsistent with forming the 26Al by irradiation in t...

Injection of newly synthesized elements into the protosolar cloud

A long-standing problem in the collisional accretion of terrestrial planets is the possible loss of m-size bodies through their inward migration onto the protostar as a result of gas drag forces. Such inward migration can be halted, and indeed even reversed, in a protoplanetary disk with local pressure maxima, such as marginally gravitationally unstable (MGU) phases of evolution, e.g., FU Orionis events. Results are presented for a suite of three-dimensional models of MGU disks extending from 1 to 10 AU and containing solid particles with sizes of 1 cm, 10 cm, 1 m, or 10 m, subject to disk gas drag and gravitational forces. These hydrodynamical models show that over disk evolution time scales of years or longer, during which over half the gaseous disk mass is accreted by the protostar, very few 1 and 10 m bodies are lost through inward migration: most bodies survive and orbit stably in the outer disk. A greater fraction of 1 and 10 cm particles are lost to the central protostar during these time periods, as such particles are more closely tied to the disk gas accreting onto the protostar, but even in these cases, a significant fraction survive and undergo transport from the hot inner disk to the cold outer disk, perhaps explaining the presence of small refractory particles in Comet Wild 2. Evidently MGU disk phases offer a means to overcome the m-sized migration barrier to collisional accumulation.

Orbital Survival of Meter-size and Larger Bodies During Gravitationally Unstable Phases of Protoplanetary Disk Evolution

Three-dimensional calculations of the formation of the presolar nebula from a slowly rotating cloud

We present the results of a large suite of three-dimensional models of the collapse of magnetic molecular cloud cores using the adaptive mesh refinement code Enzo2.2 in the ideal magnetohydrodynamics approximation. The cloud cores are initially either prolate or oblate, centrally condensed clouds with masses of 1.73 or 2.73 M ?, respectively. The radial density profiles are Gaussian, with central densities 20?times higher than boundary densities. A barotropic equation of state is used to represent the transition from low density isothermal phases, to high density optically thick phases. The initial magnetic field strength ranges from 6.3 to 100 ?G, corresponding to clouds that are strongly to marginally supercritical, respectively, in terms of the mass to magnetic flux ratio. The magnetic field is initially uniform and aligned with the clouds' rotation axes, with initial ratios of rotational to gravitational energy ranging from 10?4 to 0.1. Two significantly different outcomes for collapse result: (1) formation of single protostars with spiral arms, and (2) fragmentation into multiple protostar systems. The transition between these two outcomes depends primarily on the initial magnetic field strength, with fragmentation occurring for mass to flux ratios greater than about 14?times the critical ratio for prolate clouds. Oblate clouds typically fragment into several times more clumps than prolate clouds. Multiple, rather than binary, system formation is the general rule in either case, suggesting that binary stars are primarily the result of the orbital dissolution of multiple protostar systems.

http://iopscience.iop.org/article/10.1088/0004-637X/794/1/44/pdf

Alan P. Boss

Papers

Mixing and transport of short-lived and stable isotopes and refractory grains in protoplanetary disks

Injection of newly synthesized elements into the protosolar cloud

Orbital Survival of Meter-size and Larger Bodies During Gravitationally Unstable Phases of Protoplanetary Disk Evolution

Three-dimensional calculations of the formation of the presolar nebula from a slowly rotating cloud

Collapse and Fragmentation of Magnetic Molecular Cloud Cores with the Enzo AMR MHD Code. II. Prolate and Oblate Cores