Nonlinear Criterion for the Stability of Molecular Clouds

Dynamically significant magnetic fields are routinely observed in molecular clouds, with mass-to-flux ratio lambda = (2 pi sqrt{G}) (Sigma/B) ~ 1 (here Sigma is the total column density and B is the field strength). It is widely believed that ``subcritical'' clouds with lambda < 1 cannot collapse, based on virial arguments by Mestel and Spitzer and a linear stability analysis by Nakano and Nakamura. Here we confirm, using high resolution numerical models that begin with a strongly supersonic velocity dispersion, that this criterion is a fully nonlinear stability condition. All the high-resolution models with lambda <= 0.95 form ``Spitzer sheets'' but collapse no further. All models with lambda >= 1.02 collapse to the maximum numerically resolvable density. We also investigate other factors determining the collapse time for supercritical models. We show that there is a strong stochastic element in the collapse time: models that differ only in details of their initial conditions can have collapse times that vary by as much as a factor of 3. The collapse time cannot be determined from just the velocity dispersion; it depends also on its distribution. Finally, we discuss the astrophysical implications of our results.Comment: 11 pages, 5 figure

Historical perspective on astrophysical MHD simulations

This contribution contains the introductory remarks that I presented at IAU Symposium 270 on ``Computational Star Formation" held in Barcelona, Spain, May 31 -- June 4, 2010. I discuss the historical development of numerical MHD methods in astrophysics from a personal perspective. The recent advent of robust, higher order-accurate MHD algorithms and adaptive mesh refinement numerical simulations promises to greatly improve our understanding of the role of magnetic fields in star formation.Comment: 11 pages, 5 figures, in "Computational Star Formation" held in Barcelona, Spain, May 31 - June 4, 2010", Eds. J. Alves, B. G. Elmegreen, J. M. Girart, V. Trimbl

Extending learning opportunities: a framework for self-evaluation in study support

The Extending Learning Opportunities (ELO) framework for selfevaluation in study support is a tool to use when quality assuring learning opportunities for children and young people outside of normal lesson time. This framework is a revised edition of the ELO (2009) DCSF publication. It provides a framework for all schools, and school consortiums including Complementary Supplementary Schools, Children’s Centres, Playing for Success (PfS) centres, Higher Education Institutions (HEIs) and organisations such as libraries, museums, galleries, theatres, including youth and community/volunteer projects that offer a structured learning programmes to young people, to extend and enhance their provision and so to improve their outcomes. It is based on self–evaluation and sets out criteria against which schools, HEIs and other organisations, can review their extended provision, the planning and practices which support it and the overall ethos which supports learning. The criteria, which take the form of Key Indicators, are at three levels: Emerged, Established and Advanced

Density, Velocity, and Magnetic Field Structure in Turbulent Molecular Cloud Models

We use 3D numerical MHD simulations to follow the evolution of cold, turbulent, gaseous systems with parameters representing GMC conditions. We study three cloud simulations with varying mean magnetic fields, but identical initial velocity fields. We show that turbulent energy is reduced by a factor two after 0.4-0.8 flow crossing times (2-4 Myr), and that the magnetically supercritical cloud models collapse after ~6 Myr, while the subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of snapshots with matched Mach numbers. The volume and column densities are both log-normally distributed, with mean volume density a factor 3-6 times the unperturbed value, but mean column density only a factor 1.1-1.4 times the unperturbed value. We use a binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs). The average velocity dispersion for the ROCs is only weakly correlated with scale, similar to the mean size-linewidth relation for clumps within GMCs. ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; the same difficulty may affect observed GMC clumps. We analyze magnetic field structure, and show that in the high density regime, total magnetic field strengths increase with density with logarithmic slope 1/3 -2/3. Mean line-of-sight magnetic field strengths vary widely across a projected cloud, and do not correlate with column density. We compute simulated interstellar polarization maps at varying orientations, and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength provided the dispersion in polarization angles is < 25 degrees.Comment: 56 pages, 25 figures; Ap.J., accepte

Imaging an Event Horizon: Mitigation of Source Variability of Sagittarius A*

The black hole in the center of the Galaxy, associated with the compact source Sagittarius A* (Sgr A*), is predicted to cast a shadow upon the emission of the surrounding plasma flow, which encodes the influence of general relativity in the strong-field regime. The Event Horizon Telescope (EHT) is a Very Long Baseline Interferometry (VLBI) network with a goal of imaging nearby supermassive black holes (in particular Sgr A* and M87) with angular resolution sufficient to observe strong gravity effects near the event horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that radio emission from Sgr A* exhibits vari- ability on timescales of minutes, much shorter than the duration of a typical VLBI imaging experiment, which usually takes several hours. A changing source structure during the observations, however, violates one of the basic assumptions needed for aperture synthesis in radio interferometry imaging to work. By simulating realistic EHT observations of a model movie of Sgr A*, we demonstrate that an image of the average quiescent emission, featuring the characteristic black hole shadow and photon ring predicted by general relativity, can nonetheless be obtained by observing over multiple days and subsequent processing of the visibilities (scaling, averaging, and smoothing) before imaging. Moreover, it is shown that this procedure can be combined with an existing method to mitigate the effects of interstellar scattering. Taken together, these techniques allow the black hole shadow in the Galactic center to be recovered on the reconstructed image.Comment: 10 pages, 12figures, accepted for publication in Ap

Analysis of Clumps in Molecular Cloud Models: Mass Spectrum, Shapes, Alignment and Rotation

Observations reveal concentrations of molecular line emission on the sky, called ``clumps,'' in dense, star-forming molecular clouds. These clumps are believed to be the eventual sites of star formation. We study the three-dimensional analogs of clumps using a set of self-consistent, time-dependent numerical models of molecular clouds. The models follow the decay of initially supersonic turbulence in an isothermal, self-gravitating, magnetized fluid. We find the following. (1) Clumps are intrinsically triaxial. This explains the observed deficit of clumps with a projected axis ratio near unity, and the apparent prolateness of clumps. (2) Simulated clump axes are not strongly aligned with the mean magnetic field within clumps, nor with the large-scale mean fields. This is in agreement with observations. (3) The clump mass spectrum has a high-mass slope that is consistent with the Salpeter value. There is a low-mass break in the slope at \sim 0.5 \msun, although this may depend on model parameters including numerical resolution. (4) The typical specific spin angular momentum of clumps is $4 \times 10^{22} {\rm cm^2 s^{-1}}$. This is larger than the median specific angular momentum of binary stars. Scaling arguments suggest that higher resolution simulations may soon be able to resolve the scales at which the angular momentum of binary stars is determined.Comment: 14 pages, 13 figures, to appear in 2003 July 20 Ap

Altered maternal profiles in corticotropin-releasing factor receptor 1 deficient mice

BACKGROUND: During lactation, the CNS is less responsive to the anxiogenic neuropeptide, corticotropin-releasing factor (CRF). Further, central injections of CRF inhibit maternal aggression and some maternal behaviors, suggesting decreased CRF neurotransmission during lactation supports maternal behaviors. In this study, we examined the maternal profile of mice missing the CRF receptor 1 (CRFR1). Offspring of knockout (CRFR1-/-) mice were heterozygote to offset possible deleterious effects of low maternal glucocorticoids on pup survival and all mice contained a mixed 50:50 inbred/outbred background to improve overall maternal profiles and fecundity. RESULTS: Relative to littermate wild-type (WT) controls, CRFR1-/- mice exhibited significant deficits in total time nursing, including high arched-back, on each test day. Consistent with decreased nursing, pups of CRFR1-deficient dams weighed significantly less than WT offspring. Licking and grooming of pups was significantly higher in WT mice on postpartum Day 2 and when both test days were averaged, but not on Day 3. Time off nest was higher for CRFR1-/- mice on Day 2, but not on Day 3 or when test days were averaged. Licking and grooming of pups did not differ on Day 2 when this measure was examined as a proportion of time on nest. CRFR1-/- mice showed significantly higher nest building on Day 3 and when tests were averaged. Mean pup number was almost identical between groups and no pup mortality occurred. Maternal aggression was consistently lower in CRFR1-/- mice and in some measures these differences approached, but did not reach significance. Because of high variance, general aggression results are viewed as preliminary. In terms of sites of attacks on intruders, CRFR1-/- mice exhibited significantly fewer attacks to the belly of the intruder on Day 5 and when tests were averaged. Performance on the elevated plus maze was similar between genotypes. Egr-1 expression differences in medial preoptic nucleus and c-Fos expression differences in bed nucleus of stria terminalis between genotype suggest possible sites where loss of gene alters behavioral output. CONCLUSION: Taken together, the results suggest that the presence of an intact CRFR1 receptor supports some aspects of nurturing behavior

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.Comment: To appear in Nature (30 August 2007 issue). 18 pages (in referee mode), 3 figures. Supplementary Information can be found at 0708.389

Black Hole Spin Evolution

We consider a subset of the physical processes that determine the spin j = a/M of astrophysical black holes. These include: (1) Initial conditions. Recent models suggest that the collapse of supermassive stars are likely to produce black holes with j ~ 0.7. (2) Major mergers. The outcome of a nearly equal mass black hole-black hole merger is not yet known, but we review the current best guesses and analytic bounds. (3) Minor mergers. We recover the result of Blandford & Hughes that accretion of small companions with isotropically distributed orbital angular momenta results in spindown, with j ~ M^{-7/3}. (4) Accretion. We present new results from fully relativistic magnetohydrodynamic accretion simulations. These show that, at least for one sequence of flow models, spin equilibrium (dj/dt = 0) is reached for j ~ 0.9, far less than the canonical value 0.998 of Thorne that was derived in the absence of MHD effects. This equilibrium value may not apply to all accretion flows, particularly thin disks. Nevertheless, it opens the possibility that black holes that have grown primarily through accretion are not maximally rotating.Comment: 22 pp, 4 figures, accepted to Ap