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Low-energy cosmic rays (CRs) are confined by self-generated MHD waves in the mostly neutral ISM. We show that the CR transport equation can be expressed as a continuity equation for the CR number density involving an effective convection velocity. Assuming balance between wave growth and ion-neutral damping, this equation gives a steady-state condition n_cr ~ n_i^1/2 up to a critical density for free streaming. This relation naturally accounts for the heretofore unexplained difference in CR ionization rates derived for dense diffuse clouds (McCall et al. 2003) and dark clouds, and predicts large spatial variations in the CR heating rate and pressure., 4 pages, 1 figure included, to appear in ApJ Letters (Corrections after ApJ proofs)

The star formation rate in galaxies should be related to the fraction of gas that can attain densities large enough for gravitational collapse. In galaxies with a turbulent interstellar medium, this fraction is controlled by the effective barotropic index $gamma = dlog P/dlog (rho)$ which measures the turbulent compressibility. When the cooling timescale is smaller than the dynamical timescale, gamma can be evaluated from the derivatives of cooling and heating functions, using the condition of thermal equilibrium. We present calculations of gamma for protogalaxies in which the metal abundance is so small that H_2 and HD cooling dominates. For a heating rate independent of temperature and proportional to the first power of density, the turbulent gas is relatively "hard", with $gamma >= 1$, at large densities, but moderately "soft", $gamma, 8 pages, 5 figures, Accepted for Publication in MNRAS

We discuss the temperature distribution in a two-dimensional, thermally unstable numerical simulation of the warm and cold gas in the Galactic disk, including the magnetic field, self-gravity, the Coriolis force, stellar energy injection and a realistic cooling function. We find that ~50% of the turbulent gas mass has temperatures in what would be the thermally unstable range if thermal instability were to be considered alone. This appears to be a consequence of there being many other forces at play than just thermal pressure. We also point out that a bimodal temperature pdf is a simple consequence of the form of the interstellar cooling function and is not necessarily a signature of discontinuous phase transitions., video address has been updated

We investigate numerically the role of thermal instability (TI) as a generator of density structures in the interstellar medium (ISM), both by itself and in the context of a globally turbulent medium. Simulations of the instability alone show that the condenstion process which forms a dense phase (``clouds'') is highly dynamical, and that the boundaries of the clouds are accretion shocks, rather than static density discontinuities. The density histograms (PDFs) of these runs exhibit either bimodal shapes or a single peak at low densities plus a slope change at high densities. Final static situations may be established, but the equilibrium is very fragile: small density fluctuations in the warm phase require large variations in the density of the cold phase, probably inducing shocks into the clouds. This result suggests that such configurations are highly unlikely. Simulations including turbulent forcing show that large- scale forcing is incapable of erasing the signature of the TI in the density PDFs, but small-scale, stellar-like forcing causes erasure of the signature of the instability. However, these simulations do not reach stationary regimes, TI driving an ever-increasing star formation rate. Simulations including magnetic fields, self-gravity and the Coriolis force show no significant difference between the PDFs of stable and unstable cases, and reach stationary regimes, suggesting that the combination of the stellar forcing and the extra effective pressure provided by the magnetic field and the Coriolis force overwhelm TI as a density-structure generator in the ISM. We emphasize that a multi-modal temperature PDF is not necessarily an indication of a multi-phase medium, which must contain clearly distinct thermal equilibrium phases., 18 pages, 11 figures. Submitted to ApJ

We propose that galactic shocks propagating through interstellar density fluctuations provide a mechanism for the intermittent replenishment, or "pumping," of the supersonic motions and internal density enhancements observed pervasively within cool atomic and molecular interstellar structures, without necessarily requiring the presence of self-gravity, magnetic fields, or young stars. The shocks are assumed to be due to a variety of galactic sources on a range of scales. An analytic result for the kinematic vorticity generated by a shock passing through a radially-stratified two-dimensional isobaric model cloud is derived, assuming that the Mach number is not so large that the cloud is disrupted, and neglecting the shock curvature and cloud distortion. Two-dimensional lattic gas hydrodynamic simulations at modest Mach numbers were used to verify the analytic result. The induced internal velocities are initially a significant fraction of the shock speed divided by the square root of the density contrast, accounting for both the observed linewidth amplitudes and the apparent cloud-to-cloud linewidth-density scaling. The linewidth-size relation could then be interpreted in terms of the well-known power spectrum of a system of shocks. The induced vortical energy should quickly be converted to compressible and MHD modes, and so would be difficult to observe directly, even though it would still be the power source for the other modes. The shockpump thus produces density structure without the necessity of any sort of instability. We argue that the shockpump should lead to nested shock-induced structures, providing a cascade mechanism for supersonic "turbulence" and a physical explanation for the fractal-like structure of the cool interstellar medium., Comment: 46 pages (LaTeX), 4 figures (eps), The Astrophysical Journal - in press. This version of the paper represents a significant (years in the making) revision at the request of the referee and the discretion of the authors

The relation between the star formation rate and the kinetic energy increase in a region containing a large number of stellar sources is investigated as a possible prescription for star formation feedback in larger scale galaxy evolution simulations, and in connection with observed scaling relations for molecular clouds, extragalactic giant H II regions, and starburst galaxies. The kinetic energy increase is not simply proportional to the source input rate, but depends on the competition between stellar power input and dissipation due to interactions between structures formed and driven by the star formation. A simple one-zone model is used to show that, in a steady-state, the energy increase should be proportional to the two-thirds power of the stellar energy injection rate, with additional factors depending on the mean density of the region and mean column density of fragments. The scaling relation is tested using two-dimensional pressureless hydrodynamic simulations of wind-driven star formation, in which star formation occurs according to a threshold condition on the column density through a shell, and a large number of shells are present at any one time. The morphology of the simulations resembles an irregular network or web of dynamically-interacting filaments. A set of 16 simulations in which different parameters were varied agree remarkably with the simple analytical prescription for the scaling relation. Converting from wind power of massive stars to Lyman continuum luminosity shows that the cluster wind model for giant H II regions may still be viable., 8 pp, LaTeX, 2 ps figs, mnras.sty, submitted to MNRAS, Revisions and clarifications made in response to referee's comments

We examine the effects of turbulent intermittency on the deflagration to detonation transition (DDT) in Type Ia supernovae. The Zel'dovich mechanism for DDT requires the formation of a nearly isothermal region of mixed ash and fuel that is larger than a critical size. We primarily consider the hypothesis by Khokhlov et al. and Niemeyer and Woosley that the nearly isothermal, mixed region is produced when the flame makes the transition to the distributed regime. We use two models for the distribution of the turbulent velocity fluctuations to estimate the probability as a function of the density in the exploding white dwarf that a given region of critical size is in the distributed regime due to strong local turbulent stretching of the flame structure. We also estimate lower limits on the number of such regions as a function of density. We find that the distributed regime, and hence perhaps DDT, occurs in a local region of critical size at a density at least a factor of 2-3 larger than predicted for mean conditions that neglect intermittency. This factor brings the transition density to be much larger than the empirical value from observations in most situations. We also consider the intermittency effect on the more stringent conditions for DDT by Lisewski et al. and Woosley. We find that a turbulent velocity of $10^8$ cm/s in a region of size $10^6$ cm, required by Lisewski et al., is rare. We expect that intermittency gives a weaker effect on the Woosley model with stronger criterion. The predicted transition density from this criterion remains below $10^7$ g/cm$^3$ after accounting for intermittency using our intermittency models., Comment: 31 pages, accepted for publication in ApJ

Smaller terrestrial planets (< 0.3 Earth masses) are less likely to retain the substantial atmospheres and ongoing tectonic activity probably required to support life. A key element in determining if sufficiently massive "sustainably habitable" planets can form is the availability of solid planet-forming material. We use dynamical simulations of terrestrial planet formation from planetary embryos and simple scaling arguments to explore the implications of correlations between terrestrial planet mass, disk mass, and the mass of the parent star. We assume that the protoplanetary disk mass scales with stellar mass as Mdisk ~ f Mstar^h, where f measures the relative disk mass, and 1/2 < h < 2, so that disk mass decreases with decreasing stellar mass. We consider systems without Jovian planets, based on current models and observations for M stars. We assume the mass of a planet formed in some annulus of a disk with given parameters is proportional to the disk mass in that annulus, and show with a suite of simulations of late-stage accretion that the adopted prescription is surprisingly accurate. Our results suggest that the fraction of systems with sufficient disk mass to form > 0.3 Earth mass habitable planets decreases for low-mass stars for every realistic combination of parameters. This "habitable fraction" is small for stellar masses below a mass in the interval 0.5 to 0.8 Solar masses, depending on disk parameters, an interval that excludes most M stars. Radial mixing and therefore water delivery are inefficient in lower-mass disks commonly found around low-mass stars, such that terrestrial planets in the habitable zones of most low-mass stars are likely to be small and dry., Accepted to ApJ. 11 pages, 6 figures

Putative organisms on the Martian surface would be exposed to potentially high doses of ionizing radiation during strong solar X-ray flares. We extrapolate the observed flare frequency-energy release scaling relation to releases much larger than seen so far for the sun, an assumption supported by observations of flares on other solar- and subsolar-mass main sequence stars. We calculate the surficial reprocessed X-ray spectra using a Monte Carlo code we have developed. Biological doses from indirect genome damage are calculated for each parameterized flare spectrum by integration over the X-ray opacity of water. We estimate the mean waiting time for solar flares producing a given biological dose of ionizing radiation on Mars and compare with lethal dose data for a wide range of terrestrial organisms. These timescales range from decades for significant human health risk to 0.5 Myr for D. radiodurans lethality. Such doses require total flare energies of 10^33--10^38 erg, the lower range of which has been observed for other stars. Flares are intermittent bursts, so acute lethality will only occur on the sunward hemisphere during a sufficiently energetic flare, unlike low-dose-rate, extended damage by cosmic rays. We estimate the soil and CO_2 ice columns required to provide 1/e shielding as 4--9 g cm^-2, depending on flare mean energy and atmospheric column density. Topographic altitude variations give a factor of two variation in dose for a given flare. Life in ice layers that may exist ~ 100 g cm^-2 below the surface would be well protected., To be published in Planetary and Space Science; 33 pages, 3 figures

Stable, hydrogen-burning, M dwarf stars comprise about 75% of all stars in the Galaxy. They are extremely long-lived and because they are much smaller in mass than the Sun (between 0.5 and 0.08 MSun), their temperature and stellar luminosity are low and peaked in the red. We have re-examined what is known at present about the potential for a terrestrial planet forming within, or migrating into, the classic liquid-surface-water habitable zone close to an M dwarf star. Observations of protoplanetary disks suggest that planet-building materials are common around M dwarfs, but N-body simulations differ in their estimations of the likelihood of potentially-habitable, wet planets residing within their habitable zones, which are only ~ 1/5 to 1/50 of the width of that for a G star. Particularly in light of the claimed detection of the planets with masses as small as 5.5 and 7.5 MEarth orbiting M stars, there seems no reason to exclude the possibility of terrestrial planets. Tidally locked synchronous rotation within the narrow habitable zone doesn't necessarily lead to atmospheric collapse, and active stellar flaring may not be as much of an evolutionarily disadvantageous factor as has previously been supposed. We conclude that M dwarf stars may indeed be viable hosts for planets on which the origin and evolution of life can occur. A number of planetary processes such as cessation of geothermal activity, or thermal and non-thermal atmospheric loss processes may limit the duration of planetary habitability to periods far shorter than the extreme lifetime of the M dwarf star. Nevertheless, it makes sense to include M dwarf stars in programs that seek to find habitable worlds and evidence of life., Comment: To be published in Astrobiology. approx. 34 pages

Motivated by an interpretation of $z \sim 3$ objects by Jimenez and Haiman (2006), we examine processes that control the fraction of primordial ($Z = 0$) gas, and so primordial stars, in high-SFR Lyman break galaxies. A primordial fraction different from 1 or 0 requires microscopic diffusion catalyzed by a velocity field with timescale comparable to the duration of star formation. The only process we found that satisfies this requirement for LBGs without fine-tuning is turbulence-enhanced mixing induced by exponential stretching and compressing of metal-rich ejecta. The time-dependence of the primordial fraction for this model is calculated. We show that conclusions for all the models discussed here are virtually independent of the IMF, including extremely top-heavy IMFs., Comment: 5 pages, 1 figure. Accepted for publication in ApJ Letters

Coupled one-dimensional photochemical-climate calculations have been performed for hypothetical Earth-like planets around M dwarfs. Visible, near-infrared and thermal-infrared synthetic spectra of these planets were generated to determine which biosignature gases might be observed by a future, space-based telescope. Our star sample included two observed active M dwarfs, AD Leo and GJ 643, and three quiescent model stars. The spectral distribution of these stars in the ultraviolet generates a different photochemistry on these planets. As a result, the biogenic gases CH4, N2O, and CH3Cl have substantially longer lifetimes and higher mixing ratios than on Earth, making them potentially observable by space-based telescopes. On the active M-star planets, an ozone layer similar to Earth's was developed that resulted in a spectroscopic signature comparable to the terrestrial one. The simultaneous detection of O2 (or O3) and a reduced gas in a planet's atmosphere has been suggested as strong evidence for life. Planets circling M stars may be good locations to search for such evidence., Comment: 34 pages, 10 figures, Astrobiology, in press

In this paper, we investigate some chemokinematical properties of the Milky Way disk, by using a sample composed by 424 late-type dwarfs. We show that the velocity dispersion of a stellar group correlates with the age of this group, according to a law proportional to t^0.26, where t is the age of the stellar group. The temporal evolution of the vertex deviation is considered in detail. It is shown that the vertex deviation does not seem to depend strongly on the age of the stellar group. Previous studies in the literature seem to not have found it due to the use of statistical ages for stellar groups, rather than individual ages. The possibility to use the orbital parameters of a star to derive information about its birthplace is investigated, and we show that the mean galactocentric radius is likely to be the most reliable stellar birthplace indicator. However, this information cannot be presently used to derive radial evolutionary constraints, due to an intrinsic bias present in all samples constructed from nearby stars. An extensive discussion of the secular and stochastic heating mechanisms commonly invoked to explain the age-velocity dispersion relation is presented. We suggest that the age-velocity dispersion relation could reflect the gradual decrease in the turbulent velocity dispersion from which disk stars form, a suggestion originally made by Tinsley and Larson (1978) and supported by several more recent disk evolution calculations. A test to distinguish between the two types of models using high-redshift galaxies is proposed., 20 pages, 10 encapsulated postscript figures, LaTeX, uses Astronomy and Astrophysics macro aa.cls, graphicx package, to be published in Astronomy and Astrophysics (2004), Also available at: http://www.astro.iag.usp.br/~maciel

Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small scale turbulence in the ionized medium, giving information about the power spectrum and amplitude of fluctuations. The theory of diffraction and refraction is reviewed, as are the main observations and scintillation regions., 46 pages, 2 figures, submitted to Annual Reviews of Astronomy and Astrophysics

This two-part review summarizes interstellar turbulence and its implications. The first part begins with diagnostics and energy sources. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments, energy transfer and cascade, velocity probability distributions, and turbulent pressure. Theories of magnetohydrodynamic turbulence, including collisionless MHD turbulence, are discussed, emphasizing various proposals for energy spectra. A large variety of numerical simulations of interstellar turbulence are reviewed. Models have reproduced many of the basic features of the observed scaling relations, predicted fast decay rates for supersonic MHD turbulence, and derived probability distribution functions for density. Thermal instabilities and thermal phases have a new interpretation in a turbulent medium. Large-scale models with various combinations of self-gravity, magnetic fields, supernovae, and star formation are beginning to resemble the observed interstellar medium in morphology and statistical properties. The role of self-gravity in turbulent gas is clarified, leading to new paradigms for the formation of star clusters, the stellar mass function, the origin of stellar rotation and binary stars, and the effects of magnetic fields., 71 pages, 5 figures, submitted to Annual Reviews of Astronomy and Astrophysics

(Abridged) The propagation of ionizing radiation through model atmospheres of terrestrial-like exoplanets is studied for a large range of column densities and incident photon energies using a Monte Carlo code we have developed to treat Compton scattering and photoabsorption. Incident spectra from parent star flares, supernovae, and gamma-ray bursts are modeled and compared to energetic particles in importance. We find that terrestrial-like exoplanets with atmospheres thinner than about 100 g cm^-2 transmit and reprocess a significant fraction of incident gamma-rays, producing a characteristic, flat surficial spectrum. Thick atmospheres (>~ 100 g cm^-2) efficiently block even gamma-rays, but nearly all incident energy is redistributed into diffuse UV and visible aurora-like emission, increasing the effective atmospheric transmission by many orders of magnitude. Depending on the presence of molecular UV absorbers and atmospheric thickness, up to 10% of the incident energy can reach the surface as UV reemission. For the Earth, between 2 x 10^-3 and 4 x 10^-2 of the incident flux reaches the ground in the biologically effective 200--320 nm range, depending on O_2/O_3 shielding. Finally, we suggest that transient atmospheric ionization layers can be frequently created at low altitudes. We conclude that these events can produce frequent fluctuations in atmospheric ionization levels and surficial UV fluxes on terrestrial-like planets., 59 pages, 15 figures; in press in Icarus; minor edits, no results changed

(Abridged) We show that sizeable fractions of incident ionizing radiation from stochastic astrophysical sources can be redistributed to biologically and chemically important UV wavelengths, a significant fraction of which can reach the surface. This redistribution is mediated by secondary electrons, resulting from Compton scattering and X-ray photoabsorption, with energies low enough to excite atmospheric molecules and atoms, resulting in a rich aurora-like spectrum. We calculate the fraction of energy redistributed into biologically and chemically important wavelength regions for spectra characteristic of stellar flares and supernovae using a Monte-Carlo transport code written for this problem and then estimate the fraction of this energy that is transmitted from the atmospheric altitudes of redistribution to the surface for a few illustrative cases. Redistributed fractions are found to be of order 1%, even in the presence of an ozone shield. This result implies that planetary organisms will be subject to mutationally significant, if intermittent, fluences of UV-B and harder radiation even in the presence of a narrow-band UV shield like ozone. We also calculate the surficial transmitted fraction of ionizing radiation and redistributed ultraviolet radiation for two illustrative evolving Mars atmospheres whose initial surface pressures were 1 bar. Our results suggest that coding organisms on planets orbiting low-mass stars (and on the early Earth) may evolve very differently than on contemporary Earth, with diversity and evolutionary rate controlled by a stochastically varying mutation rate and frequent hypermutation episodes., 21 pages, 2 figures, accepted for publication in Origins of Life and Evolution of the Biosphere

According to recent models, gamma-ray bursts apparently explode in a wide variety of ambient densities ranging from ~ 10^{-3} to 30 cm^{-3}. The lowest density environments seem, at first sight, to be incompatible with bursts in or near molecular clouds or with dense stellar winds and hence with the association of gamma-ray bursts with massive stars. We argue that low ambient density regions naturally exist in areas of active star formation as the interiors of superbubbles. The evolution of the interior bubble density as a function of time for different assumptions about the evaporative or hydrodynamical mass loading of the bubble interior is discussed. We present a number of reasons why there should exist a large range of inferred afterglow ambient densities whether gamma-ray bursts arise in massive stars or some version of compact star coalescence. We predict that many gamma-ray bursts will be identified with X-ray bright regions of galaxies, corresponding to superbubbles, rather than with blue localized regions of star formation. Massive star progenitors are expected to have their own circumstellar winds. The lack of evidence for individual stellar winds associated with the progenitor stars for the cases with afterglows in especially low density environments may imply low wind densities and hence low mass loss rates combined with high velocities. If gamma-ray bursts are associated with massive stars, this combination might be expected for compact progenitors with atmospheres dominated by carbon, oxygen or heavier elements, that is, progenitors resembling Type Ic supernovae., Comment: 14 pages, no figures, submitted to The Astrophysical Journal

Combining results for the local cosmic rate and mean peak luminosity of GRBs with the cosmic history of the star formation rate, we provide estimates for the local GRB rate per unit blue luminosity in galaxies. We find a typical GRB rate per unit B luminosity of 2.4x10^-17 h_{70}^2/Lsun/yr. The corresponding mean rate in the Milky Way is 5.5x10^-7 h_{70}^2/yr. We conclude: 1) the ratio of supernova rate to isotropic equivalent GRB rate is large: more than 6000 SNIbc per GRB or 30,000 SNII per GRB. GRBs could arise in a large fraction of black hole-forming events only with collimation in the range 0.01 - 0.001 and a steep enough slope of the IMF; 2) GRBs cannot account for the majority of large HI holes observed in galaxies; 3) the probability that the solar system was exposed to a fluence large enough to melt the chondrules during the first 10^7 yr of solar system history is negligibly small; 4) Even for very opaque atmospheres, a significant fraction of the GRB energy is transmitted as UV lines due to excitation by secondary electrons. For eukaryotic-like organisms in thin atmospheres (e.g. contemporary Mars), or for UV line exposure in thick atmospheres (e.g. Earth), biologically significant events occur at a rate of about 100--500 /Gyr. The direct contribution of these "jolts" to mutational evolution may, however, be negligible because of the short duration of the GRBs. Evolutionary effects due to partial sterilizations and to longer-lived disruptions of atmospheric chemistry should be more important. (Abridged), 36 pages, no figures Accepted by Astrophysical Journal Oct. 2001. First submitted December,1999. Substantially rewritten discussion of burst source count distributions and of biological implications

The star formation rate history of the Milky Way is derived using the chromospheric age distribution for 552 stars in the solar neighborhood. The stars sample birthsites distributed over a very large range of distances because of orbital diffusion, and so give an estimate of the global star formation rate history. The derivation incorporates the metallicity dependence of chromospheric emission at a given age, and corrections to account for incompleteness, scale height-age correlations, and stellar evolutionary effects. The results show that the Milky Way has undergone fluctuations in the global star formation rate with amplitudes greater than a factor of 2-3 on timescales less than 0.2-1 Gyr. The actual history is likely to be more bursty than found here because of the smearing effect of age uncertainties. There is some evidence for a slow secular increase in the star formation rate, perhaps a record of the accumulation history of our galaxy. A smooth nearly-constant star formation rate history is strongly ruled out, confirming the result first discovered by Barry (1988) using a smaller sample and a different age calibration. This result suggests that galaxies can fluctuate coherently on large scales., Minor revision reflecting comments by referee. 16 pages (LaTeX), 2 Postscript figures, accepted for publication in The Astrophysical Journal (Letters)

The effects of wind-driven star formation feedback on the spatio-temporal organization of stars and gas in galaxies is studied using two-dimensional intermediate-representational quasi-hydrodynamical simulations. The model retains only a reduced subset of the physics, including mass and momentum conservation, fully nonlinear fluid advection, inelastic macroscopic interactions, threshold star formation, and momentum forcing by winds from young star clusters on the surrounding gas. Expanding shells of swept-up gas evolve through the action of fluid advection to form a ``turbulent'' network of interacting shell fragments whose overall appearance is a web of filaments (in two dimensions). A new star cluster is formed whenever the column density through a filament exceeds a critical threshold based on the gravitational instability criterion for an expanding shell, which then generates a new expanding shell after some time delay. A filament- finding algorithm is developed to locate the potential sites of new star formation. The major result is the dominance of multiple interactions between advectively-distorted shells in controlling the gas and star morphology, gas velocity distribution and mass spectrum of high mass density peaks, and the global star formation history. The gas morphology observations of gas in the LMC and in local molecular clouds. The frequency distribution of present-to-past average global star formation rate, the distribution of gas velocities in filaments (found to be exponential), and the cloud mass spectra (estimated using a structure tree method), are discussed in detail., Comment: 40 pp, 15 eps figs, mnras style, accepted for publication in MNRAS, abstract abridged, revisions in response to referee's comments

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., 10 pages, LaTeX, 2 figures, submitted to Astrophysical Journal. Additions made in response to referee report; typos and references corrected

The probability density functions (pdfs) of molecular line centroid velocity fluctuations and fluctuation differences at different spatial lags are estimated for several nearby molecular clouds with active internal star formation. The data consist of over 75,000 $^{13}$CO line profiles divided among twelve spatially and/or kinematically distinct regions. Although three regions (all in Mon R2) appear nearly Gaussian, the others show strong evidence for non-Gaussian, often nearly exponential, centroid velocity pdfs, possibly with power law contributions in the far tails. Evidence for nearly exponential centroid pdfs in the neutral HI component of the ISM is also presented, based on older optical and radio observations. These results are in contrast to pdfs found in isotropic incompressible turbulence experiments and simulations. Furthermore, no evidence is found for the scaling of difference pdf kurtosis with Reynolds number which is seen in incompressible turbulence, and the spatial distribution of high-amplitude velocity differences shows little indication of the filamentary appearance predicted by decay simulations dominated by vortical interactions. The variation with lag of the difference pdf moments is presented as a constraint on future simulations., Comment: LaTeX, 23 pages, with 15 Figures included separately as gif image files. Refereed/revised version accepted to the Astrophysical Journal. A complete (but much larger) postscript version is available from http://ktaadn.gsfc.nasa.gov/~miesch

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 and justified in an appendix, 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: strong point-like concentrations, line- like filaments or fronts, and 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. (Abstract truncated), 27 pages, (LaTeX), 13 figures, 1 table, submitted to Astrophysical Journal

Probability density functions (pdfs) of $^{13}CO$ emission line centroid (line-of-sight, intensity-weighted average) velocities are presented for several densely sampled molecular clouds as quantitative descriptors of their underlying dynamics. Although some are approximately Gaussian in form, most of the pdfs exhibit relatively broader, often nearly exponential, tails, similar to the pdfs of velocity {\em differences} and {\em derivatives} (but not the velocity field itself) found in experiments and numerical simulations of incompressible turbulence. The broad pdf tails found in the present work are also similar to those found in decades-old measurements of interstellar velocity pdfs using atomic line centroids, and to the excess wing emission recently found in individual molecular line profiles. Some possible interpretations of the observed deviations are briefly discussed, although none of these account for the nearly exponential tails., Comment: 13 pages, one figure, LaTeX format. There was an error in the initial submission that was simply an invalid name for the postscript file (it should have been called pdf_paper.ps rather than fig1_pp.ps). Correcting this reference in the tex file was the only change

The frequency distributions of sizes of ``clouds" and ``clumps" within clouds are significantly flatter for extinction surveys than for CO spectral line surveys, even for comparable size ranges. A possible explanation is the blocking of extinction clouds by larger foreground clouds (occlusion), which should not affect spectral line surveys much because clouds are resolved in velocity space along a given line of sight. We present a simple derivation of the relation between the true and occluded size distributions, assuming clouds are uniformly distributed in space or the distance to a cloud comples is much greater than the size of the complex. Because the occlusion is dominated by the largest clouds, we find that occlusion does not affect the measured size distribution except for sizes comparable to the largest size, implying that occlusion is not responsible for the discrepancy if the range in sizes of the samples is large. However, we find that the range in sizes for many of the published observed samples is actually quite small, which suggests that occlusion does affect the extinction sample and/or that the discrepancy could arise from the different operational definitions and selection effects involved in the two samples. Size and mass spectra from an IRAS survey (Wood \etal\ 1994) suggest that selection effects play a major role in all the surveys. We conclude that a reliable determination of the ``true" size and mass spectra of clouds will require spectral line surveys with very high signal-to-noise and sufficient resolution and sampling to cover a larger range of linear sizes, as well as careful attention to selection effects., Comment: 13 pages, LATEX, aas style, Submitted to ApJ