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

A supernova is a likely source of short-lived radioisotopes (SLRIs) that were present during the formation of the earliest solar system solids. A suitably thin and dense supernova shock wave may be capable of triggering the self-gravitational collapse of a molecular cloud core while simultaneously injecting SLRIs. Axisymmetric hydrodynamics models have shown that this injection occurs through a number of Rayleigh-Taylor (RT) rings. Here we use the FLASH adaptive mesh refinement (AMR) hydrodynamics code to calculate the first fully three dimensional (3D) models of the triggering and injection process. The axisymmetric RT rings become RT fingers in 3D. While ~ 100 RT fingers appear early in the 3D models, only a few RT fingers are likely to impact the densest portion of the collapsing cloud core. These few RT fingers must then be the source of any SLRI spatial heterogeneity in the solar nebula inferred from isotopic analyses of chondritic meteorites. The models show that SLRI injection efficiencies from a supernova several pc away fall at the lower end of the range estimated for matching SLRI abundances, perhaps putting them more into agreement with recent reassessments of the level of 60Fe present in the solar nebula.

Supernova-Triggered Molecular Cloud Core Collapse and the Rayleigh-Taylor Fingers that Polluted the Solar Nebula

Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation

We present high-contrast Magellan adaptive optics (MagAO) images of HD 7449, a Sun-like star with one planet and a long-term radial velocity (RV) trend. We unambiguously detect the source of the long-term trend from 0.6-2.15 \microns ~at a separation of \about 0\fasec 54. We use the object's colors and spectral energy distribution to show that it is most likely an M4-M5 dwarf (mass \about 0.1-0.2 \msun) at the same distance as the primary and is therefore likely bound. We also present new RVs measured with the Magellan/MIKE and PFS spectrometers and compile these with archival data from CORALIE and HARPS. We use a new Markov chain Monte Carlo procedure to constrain both the mass ($> 0.17$ \msun ~at 99$\%$ confidence) and semimajor axis (\about 18 AU) of the M dwarf companion (HD 7449B). We also refine the parameters of the known massive planet (HD 7449Ab), finding that its minimum mass is $1.09^{+0.52}_{-0.19}$ \mj, its semimajor axis is $2.33^{+0.01}_{-0.02}$ AU, and its eccentricity is $0.8^{+0.08}_{-0.06}$. We use N-body simulations to constrain the eccentricity of HD 7449B to $\lesssim$ 0.5. The M dwarf may be inducing Kozai oscillations on the planet, explaining its high eccentricity. If this is the case and its orbit was initially circular, the mass of the planet would need to be $\lesssim$ 1.5 \mj. This demonstrates that strong constraints on known planets can be made using direct observations of otherwise undetectable long-period companions.

MagAO IMAGING OF LONG-PERIOD OBJECTS (MILO). I. A BENCHMARK M DWARF COMPANION EXCITING A MASSIVE PLANET AROUND THE SUN-LIKE STAR HD 7449*

The collapse and fragmentation of molecular cloud cores into binary and multiple protostar systems is a demanding computational problem, in part because of the large range of length scales involved. Truelove et al. proposed that the computational cell size Δx must be smaller than 1/4 of the Jeans length, λJ, if artificial (numerical) fragmentation is to be avoided. For a uniform Cartesian grid, Truelove et al.'s Jeans condition is equivalent to ensuring that the mass of a cell never exceeds ~1/64 of a Jeans mass. It is shown here that for a nonuniform spherical grid, artificial fragmentation can be avoided provided that the cell size of a cube with approximately the same volume as the spherical coordinate cell [Δx=(ΔxrΔxθΔx)1/3] is less than λJ/4 (i.e., that the mass inside each cell is much less than a Jeans mass), even if one of the three cell lengths (Δxr, Δxθ, or Δx) exceeds λJ/4. For a nonuniform grid, resolving a small fraction of a Jeans mass is less restrictive than resolving 1/4 of a Jeans length in each coordinate direction; resolving all three Jeans lengths is desirable but not necessary in order to avoid artificial fragmentation. The well-resolved collapse of an initially Gaussian-profile cloud is then followed with both isothermal and nonisothermal (Eddington approximation radiative transfer) thermodynamics and is shown to lead to fragmentation into a binary protostar system in both cases. The Jeans mass constraint appears to be a valuable indicator of physically realistic fragmentation.

The Jeans Mass Constraint and the Fragmentation of Molecular Cloud Cores

Forming giant planets by disk instability requires a gaseous disk that is massive enough to become gravitationally unstable and able to cool fast enough for self-gravitating clumps to form and survive. Models with simplified disk cooling have shown the critical importance of the ratio of the cooling to the orbital timescales. Uncertainties about the proper value of this ratio can be sidestepped by including radiative transfer. Three-dimensional radiative hydrodynamics models of a disk with a mass of 0.043 M ☉ from 4 to 20 AU in orbit around a 1 M ☉ protostar show that disk instabilities are considerably less successful in producing self-gravitating clumps than in a disk with twice this mass. The results are sensitive to the assumed initial outer disk (To ) temperatures. Models with To = 20 K are able to form a single self-gravitating clump, whereas models with To = 25 K form clumps that are not quite self-gravitating. These models imply that disk instability requires a disk with a mass of at least ~0.043 M ☉ inside 20 AU in order to form giant planets around solar-mass protostars with realistic disk cooling rates and outer-disk temperatures. Lower mass disks around solar-mass protostars must rely upon core accretion to form inner giant planets.

https://iopscience.iop.org/article/10.1088/2041-8205/725/2/L145/pdf

Alan P. Boss

Papers

Supernova-Triggered Molecular Cloud Core Collapse and the Rayleigh-Taylor Fingers that Polluted the Solar Nebula

Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation

MagAO IMAGING OF LONG-PERIOD OBJECTS (MILO). I. A BENCHMARK M DWARF COMPANION EXCITING A MASSIVE PLANET AROUND THE SUN-LIKE STAR HD 7449*

The Jeans Mass Constraint and the Fragmentation of Molecular Cloud Cores

Giant Planet Formation by Disk Instability in Low Mass Disks