David Chappell

On the Probability Density Function of Galactic Gas. I. Numerical Simulations and the Significance of the Polytropic Index

We investigate the form of the one-point probability density 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 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 at large densities with logarithmic slope between -1.7 and -2.3. This suggests that a power-law shape 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 one-dimensional 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 should probably occur at densities around 103 and is possible at larger densities, depending strongly on the role of gas-grain heating and cooling. Several applications are examined. First, we question a recent derivation of the initial mass function from the density pdf by Padoan, Nordlund, & Jones because (1) the pdf does not contain spatial information and (2) 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.

Clustering Properties of Stars in Simulations of Wind-driven Star Formation

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 that 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.

Wind-driven gas networks and star formation in galaxies: reaction–advection hydrodynamic simulations

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 non-linear 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 which have the overall appearance of 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 strongly resembles the model envisioned by Norman & Silk, and observations of gas in the Large Magellanic Cloud (LMC) and local molecular clouds. The dependence of the frequency distribution of present-to-past average global star formation rate on a number of parameters is investigated. Bursts of star formation only occur when the time-averaged star formation rate per unit area is low, or the system is small. Percolation does not play a role. The broad distribution observed in late-type galaxies can be understood as a result of either small size or small metallicity, resulting in larger shell column densities required for gravitational instability. The star formation rate increases with density, but dependences on gas velocity dispersion and average shell column density suggest that the dependence is multivariate. The distribution of gas velocities exhibits exponential tails over a broad range of parameter values and the velocity distribution for gas in filaments is nearly exponential. Decay simulations with no star formation suggest that the exponential tails are caused by multiple shell interactions, not individual stellar winds. The cloud mass spectra, estimated using a simplified version of the structure tree method, tend to be power laws at the higher-mass end, with an index that is nearly independent of the star formation activity or model parameters. Kinetic energy decay in simulations without star formation yields a t−1 dependence. We discuss how the simulations can be viewed in the context of various incomplete conceptual models, including collisional cloud coalescence, wind-driven turbulence, propagating star formation, forced mass-conserving Burgers turbulence, and granular fluids.