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 processes that transform gas and dust in circumstellar disks into diverse exoplanets remain poorly understood. One key pathway is to study exoplanets as they form in their young ($\sim$few~Myr) natal disks. Extremely Large Telescopes (ELTs) such as GMT, TMT, or ELT, can be used to establish the initial chemical conditions, locations, and timescales of planet formation, via (1)~measuring the physical and chemical conditions in protoplanetary disks using infrared spectroscopy and (2)~studying planet-disk interactions using imaging and spectro-astrometry. Our current knowledge is based on a limited sample of targets, representing the brightest, most extreme cases, and thus almost certainly represents an incomplete understanding. ELTs will play a transformational role in this arena, thanks to the high spatial and spectral resolution data they will deliver. We recommend a key science program to conduct a volume-limited survey of high-resolution spectroscopy and high-contrast imaging of the nearest protoplanetary disks that would result in an unbiased, holistic picture of planet formation as it occurs.

Protoplanetary Disk Science Enabled by Extremely Large Telescopes

Angular Momentum Transport by Gravitational Torques in the Early Solar Nebula

The Solar System provides a unique fossil record of a single star formation event. Investigation of a variety of materials such as interplanetary dust, meteorites, and comets may provide us with information about physical processes which operate on scales totally inaccessible to study in observable star forming regions. However, our increasing ability to probe on-going star formation regions on subarc-second scales allows us to gather information about cosmogonic events on large scales. This paper investigates the overlap between the study of other star-forming regions and the Solar System.

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Star Formation and the Solar System

We have obtained precision astrometry of the planet hosting M dwarf GJ 317 in the framework of the Carnegie Astrometric Planet Search project. The new astrometric measurements give a distance determination of 15.3 pc, 65% further than previous estimates. The resulting absolute magnitudes suggest it is metal rich and more massive than previously assumed. This result strengthens the correlation between high metallicity and the presence of gas giants around low mass stars. At 15.3 pc, the minimal astrometric amplitude for planet candidate GJ 317b is 0.3 milliarcseconds (edge-on orbit), just below our astrometric sensitivity. However, given the relatively large number of observations and good astrometric precision, a Bayesian Monte Carlo Markov Chain analysis indicates that the mass of planet b has to be smaller than twice the minimum mass with a 99% confidence level, with a most likely value of 2.5 Mjup. Additional RV measurements obtained with Keck by the Lick-Carnegie Planet search program confirm the presence of an additional very long period planet candidate, with a period of 20 years or more. Even though such an object will imprint a large astrometric wobble on the star, its curvature is yet not evident in the astrometry. Given high metallicity, and the trend indicating that multiple systems are rich in low mass companions, this system is likely to host additional low mass planets in its habitable zone that can be readily detected with state-of-the-art optical and near infrared RV measurements.

Astrometry and radial velocities of the planet host M dwarf GJ 317: new trigonometric distance, metallicity and upper limit to the mass of GJ 317b

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Alan P. Boss

Papers

Protoplanetary Disk Science Enabled by Extremely Large Telescopes

Angular Momentum Transport by Gravitational Torques in the Early Solar Nebula

Star Formation and the Solar System

Astrometry and radial velocities of the planet host M dwarf GJ 317: new trigonometric distance, metallicity and upper limit to the mass of GJ 317b

Non-axisymmetric instability in three-dimensional accretion toroids