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.

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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

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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

The Origin of the Moon

Models of the formation and evolution of the solar nebula.

The ability to make independent detections of the signatures of exoplanets with complementary telescopes and instruments brings a new potential for robust identification of exoplanets and precision characterization. We introduce PEXO, a package for Precise EXOplanetology to facilitate the efficient modeling of timing, astrometry, and radial velocity data, which will benefit not only exoplanet science but also various astrophysical studies in general. PEXO is general enough to account for binary motion and stellar reflex motions induced by planetary companions and is precise enough to treat various relativistic effects both in the solar system and in the target system. We also model the post-Newtonian barycentric motion for future tests of general relativity in extrasolar systems. We benchmark PEXO with the pulsar timing package TEMPO2 and find that PEXO produces numerically similar results with timing precision of about 1 ns, space-based astrometry to a precision of 1 $\mu$as, and radial velocity of 1 $\mu$m/s and improves on TEMPO2 for decade-long timing data of nearby targets, due to its consideration of third-order terms of Roemer delay. PEXO is able to avoid the bias introduced by decoupling the target system and the solar system and to account for the atmospheric effects which set a practical limit for ground-based radial velocities close to 1 cm/s. Considering the various caveats in barycentric correction and ancillary data required to realize cm/s modeling, we recommend the preservation of original observational data. The PEXO modeling package is available at GitHub (this https URL).

PEXO: a global modeling framework for nanosecond timing, microsecond astrometry, and {\mu}m/s radial velocities

Recent meteoritical analyses support an initial abundance of the short-lived radioisotope $^{60}$Fe that may be high enough to require nucleosynthesis in a core collapse supernova, followed by rapid incorporation into primitive meteoritical components, rather than a scenario where such isotopes were inherited from a well-mixed region of a giant molecular cloud polluted by a variety of supernovae remnants and massive star winds. This paper continues to explore the former scenario, by calculating three dimensional, adaptive mesh refinement, hydrodynamical code (FLASH 2.5) models of the self-gravitational, dynamical collapse of a molecular cloud core that has been struck by a thin shock front with a speed of 40 km/sec, leading to the injection of shock front matter into the collapsing cloud through the formation of Rayleigh-Taylor fingers at the shock-cloud intersection. These models extend the previous work into the nonisothermal collapse regime using a polytropic approximation to represent compressional heating in the optically thick protostar. The models show that the injection efficiencies of shock front material are enhanced compared to previous models, which were not carried into the nonisothermal regime and so did not reach such high densities. The new models, combined with the recent estimates of initial $^{60}$Fe abundances, imply that the supernova triggering and injection scenario remains as a plausible explanation for the origin of the short-lived radioisotopes involved in the formation of our solar system.

Alan P. Boss

Papers

The Origin of the Moon

Models of the formation and evolution of the solar nebula.

PEXO: a global modeling framework for nanosecond timing, microsecond astrometry, and {\mu}m/s radial velocities

Triggering Collapse of the Presolar Dense Cloud Core and Injecting Short-Lived Radioisotopes with a Shock Wave. V. Nonisothermal Collapse Regime

To B or not to B