We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included. Two-dimensional simulations of selfgravitating supersonic MHD turbulence, of supersonic self-gravitating hydrodynamic turbulence, and of decaying Burgers turbulence, produce in all cases filamentary density structures and evidence for a power-law density pdf with logarithmic slope around −1.7. This suggests that the functional form of the pdf and the general filamentary morphology are the signature of the nonlinear advection operator.These results do not support previous claims that the pdf is lognormal. A series of 1D simulations of forced supersonic polytropic turbulence is used to resolve the discrepancy. They suggest that the pdf is lognormal only for effective polytropic indices γ = 1 (or nearly lognormal for γ = 1 if the Mach number is sufficiently small), while power laws develop for densities larger than the mean if γ < 1. We evaluate the polytropic index for conditions relevant to the cool interstellar medium using published cooling functions and different heating sources, finding that a lognormal pdf may occur at densities between 10 3 and at least 10 4 cm −3 .Several applications are examined. First, we question a recent derivation of the IMF from the density pdf by Padoan, Nordlund & Jones because a) the pdf does not contain spatial information, and b) their derivation produces the most massive stars in the voids of the density distribution. Second, we illustrate how a distribution of ambient densities can alter the predicted form of the size distribution of expanding shells. Finally, a brief comparison is made with the density pdfs found in cosmological simulations.

We report on a sub-stellar companion search utilizing interferometric fringe-tracking astrometry acquired with Fine Guidance Sensor 3 (FGS 3) on the Hubble Space Telescope. Our targets were Proxima Centauri and Barnard's Star. We obtain absolute parallax values for Proxima Cen π abs = 0. ′′ 7687 ± 0. ′′ 0003 and for Barnard's Star π abs = 0. ′′ 5454 ± 0. ′′ 0003.Once low-amplitude instrumental systematic errors are identified and removed, our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 60 days for Proxima Cen. Between the astrometry and the Kürster et al. 1999 radial velocity results we exclude all companions with M > 0.8M Jup for the range of periods 1 < P < 1000 days. For Barnard's Star our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 150 days. Our null results for Barnard's Star are consistent with those of Gatewood (1995).

Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity, strengths) and dimensions. The existence of MFS implies an underlying multiplicative (or hierarchical, or cascade) process. Panoramic column density images of several nearby star-forming cloud complexes, constructed from IRAS data, are shown to exhibit such multifractal scaling, which we interpret as indirect but quantitative evidence for nested hierarchical structure. The relation between the dimensions of the subsets and their concentration strengths (the "multifractal spectrum") appears to satisfactorily order the observed regions in terms of the mixture of geometries present, from strong point-like concentrations, to line-like filaments or fronts, to space-filling diffuse structures. This multifractal spectrum is a global property of the regions studied, and does not rely on any operational definition of "clouds." The range of forms of the multifractal spectrum among the regions studied implies that the column density structures do not form a universality class, in contrast to indications for velocity and passive scalar fields in incompressible turbulence, providing another indication that the physics of highly compressible interstellar gas dynamics differs fundamentally from incompressible turbulence. There is no correlation between the geometrical properties of the regions studied and their level of internal star formation activity, a result that is also apparent from visual inspection. We discuss the viability of the multifractal spectrum as a measure of the structural "complexity" of the regions studied, and emphasize the problematic dependence of all structural descriptors on the subjective pre-selection of the region to be described. A comparison of IRAS 100 µm column density (not intensity) images with 13 CO, visual extinction, and C 18 O data suggests that structural details are captured by IRAS up to at least 30 magnitudes of visual extinction, except in the vicinity of embedded stars, and that lower-column density connective structure not seen by other methods is revealed.

An improved algorithm for the generation of gridded window brightness temperatures is presented. The primary data source is the International Satellite Cloud Climatology Project, level B3 data, covering the period from July 1983 to the present. The algorithm takes window brightness, temperatures from multiple satellites, both geostationary and polar orbiting, which have already been navigated and normalized radiometrically to the National Oceanic and Atmospheric Administration's Advanced Very High Resolution Radiometer, and generates 3-hourly global images on a 0.5Њ by 0.5Њ latitude-longitude grid. The gridding uses a hierarchical scheme based on spherical kernel estimators. As part of the gridding procedure, the geostationary data are corrected for limb effects using a simple empirical correction to the radiances, from which the corrected temperatures are computed. This is in addition to the application of satellite zenith angle weighting to downweight limb pixels in preference to nearer-nadir pixels. The polar orbiter data are windowed on the target time with temporal weighting to account for the noncontemporaneous nature of the data. Large regions of missing data are interpolated from adjacent processed images using a form of motion compensated interpolation based on the estimation of motion vectors using an hierarchical block matching scheme. Examples are shown of the various stages in the process. Also shown are examples of the usefulness of this type of data in GCM validation.

Several recent observational studies have shown that the clustering of young stars in local star-forming regions, and of Cepheids in the LMC, can be described by a power law two-point correlation function. We show by numerical simulations that the observed range in power law slopes can be accounted for by a model in which stellar winds drive expanding shells that are subjected to nonlinear fluid advection and interactions with other shells, and in which star formation occurs when a threshold shell column density is exceeded. The models predict how the power law slope should depend on the maximum age of the stellar sample and the average star formation rate, although a number of effects preclude a comparison with currently-available data. We also show how stellar migration flattens the power law slope below a scale that depends on the velocity dispersion and age of the sample, an effect which may explain the secondary breaks in the observed correlation functions of some regions at large separations. Problems with using the correlation function as a descriptor of clustering structure for statistically inhomogeneous data sets are discussed.