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Peaks and lulls in the star formation rate (SFR) over the history of the Galaxy produce plateaux and declines in the present day mass function (PDMF) where the main-sequence lifetime overlaps the age and duration of the SFR variation. These PDMF features can be misinterpreted as the form of the intrinsic stellar initial mass function (IMF) if the star formation rate is assumed to be constant or slowly varying with time. This effect applies to all regions that have formed stars for longer than the age of the most massive stars, including OB associations, star complexes, and especially galactic field stars. Related problems may apply to embedded clusters. Evidence is summarized for temporal SFR variations from parsec scales to entire galaxies, all of which should contribute to inferred IMF distortions. We give examples of various star formation histories to demonstrate the types of false IMF structures that might be seen. These include short-duration bursts, stochastic histories with log-normal amplitude distributions, and oscillating histories with various periods and phases. The inferred IMF should appear steeper than the intrinsic IMF over mass ranges where the stellar lifetimes correspond to times of decreasing SFRs; shallow portions of the inferred IMF correspond to times of increasing SFRs. If field regions are populated by dispersed clusters and defined by their low current SFRs, then they should have steeper inferred IMFs than the clusters. The SFRs required to give the steep field IMFs in the LMC and SMC are determined. Structure observed in several determinations of the Milky Way field star IMF can be accounted for by a stochastic and bursty star formation history.

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)

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

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 self-gravitating supersonic MHD and hydrodynamic turbulence, and of decaying Burgers turbulence, produce in all cases filamentary density structures and 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 $\gamma=1$ (or nearly lognormal for $\gamma\not=1$ if the Mach number is sufficiently small), while power laws develop at high densities if $\gamma

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau_p1 and tau_p2, of two particles of arbitrary sizes. The friction time of particles included in the simulation ranges from 0.1 tau_eta to 54T_L, with tau_eta and T_L the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau_p1, the PDF is the fattest for equal-size particles (tau_p2~tau_p1), and becomes thinner at both tau_p2tau_p1. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in 1/2>T_L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanerary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem., Comment: 25 pages, 19 figures, accepted by ApJ

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

A new method of image analysis is described, in which images partitioned into 'clouds' are represented by simplified skeleton images, called structure trees, that preserve the spatial relations of the component clouds while disregarding information concerning their sizes and shapes. The method can be used to discriminate between images of projected hierarchical (multiply nested) and random three-dimensional simulated collections of clouds constructed on the basis of observed interstellar properties, and even intermediate systems formed by combining random and hierarchical simulations. For a given structure type, the method can distinguish between different subclasses of models with different parameters and reliably estimate their hierarchical parameters: average number of children per parent, scale reduction factor per level of hierarchy, density contrast, and number of resolved levels. An application to a column density image of the Taurus complex constructed from IRAS data is given. Moderately strong evidence for a hierarchical structural component is found, and parameters of the hierarchy, as well as the average volume filling factor and mass efficiency of fragmentation per level of hierarchy, are estimated. The existence of nested structure contradicts models in which large molecular clouds are supposed to fragment, in a single stage, into roughly stellar-mass cores.

Consideration is given to the use of the white dwarf luminosity function (WDLF) to study the history of the star formation rate in the Galaxy. It is shown that the WDLF is much more sensitive to the star formation rate than to variations in the initial mass function. A marginal feature in the WDLF at log(L/solar L) = -2 is found to represent the burst of star formation which occurred 300 million yrs ago, as proposed by Barry (1988) and Scalo (1987, 1988). Observations are used to limit the ratio of recent to past average star formation rates for smoothly decreasing and increasing star formation rates. The star formation rate histories derived from the results of Twarog (1980) and Barry (1988) are compared. 34 refs.

We discuss nonequilibrium chemistry in isotropic models of expanding circumstellar shells surrounding oxygen-rich red giant stars, using time-scale arguments and chemical kinetic calculations. We predict that most observable molecules should attain significant abundances only beyond a critical radius, approx.3 x 10/sup 14/ cm for low-density shells; beyond that limit H/sub 2/O is efficiently photo-dissociated by interstellar ultraviolet radiation. We show that observation of SiS should give an unambiguous limit to the fraction of circumstellar silicon tied up in grains if chromospheric radiation is unimportant, while SiO is unsuitable for this purpose. Photodissociation of H/sub 2/O by chromospheric radiation may be important in the inner part of the shell, and it is suggested that observations of molecular column densities of H/sub 2/O and other molecules in shells may be used to constrain chromospheric models for red giants.

An attempt is made to estimate the true average space density of gas-rich dwarf galaxies by comparing the luminosity and size distributions of visible dwarf irregulars with a set of simulated observations of a bursting population of galaxies on which selection effects corresponding to the real observations have been imposed. The true size distribution is assumed to be a power law f(r) proportional to r exp y. A value of y = - 4.2 + or - 0.2 gives good agreement with the observed frequency distributions of luminosity, optical radius, and angular size. The same model accounts for the observed luminosity function in the Virgo cluster. The implications of this result for the true shape of the Galaxy luminosity function and the contribution to the cosmological density are discussed. 48 references.