A purely statistical origin of hierarchical density structure in pressureless and nearly pressureless turbulent flows without self-gravity is proposed. It is argued that hydrodynamic (Navier-Stokes) flows with rms Mach numbers M_rms ≫ 1, like the cold interstellar medium or some cosmological flows, have a nearly pressureless behavior, except perhaps in a small fraction of the volume. Assuming that in these flows the density field can be considered as a random variable in time with an associated probability distribution function (pdf), a condition on the pdf for the spontaneous development of hierarchical structure is proposed. The condition is essentially a requirement that the joint probability of a succession of n constructively interfering relative density fluctuations of amplitude a be larger than the probability of a single, large fluctuation of the same final amplitude a . An analytic form for this condition is derived, under the assumption that the density pdf is scale- invariant, and three important functional forms of the pdf (a power-law, a lognormal, and an exponential distribution) are tested according to this criterion. It is found that development of hierarchical structure should always be expected for the lognormal and exponential distributions at large values of n and/or a, but is parameter-dependent in the case of the power law. The assumption of a scale-invariant density pdf is motivated (but not rigorously proved) by the scale invariance of the pressureless hydrodynamic equations with negligible self-gravity, and a numerical simulation of a compressible turbulent flow in two dimensions in a transonic regime (M ̃ 1) is used to test this and other secondary assumptions. The density field developed by the simulation clearly exhibits at least three levels of hierarchical nesting. The density statistics, albeit obscured by the limited resolution, which limits the feasible density contrasts, are shown to be consistent with the hypotheses. A discussion on the degree to which the dynamics of two- and three-dimensional flows may differ from one another in the compressible case is given. Finally, a remark is made that the hierarchical structure produced by this mechanism in turbulent compressible flows is transient although statistically stationary. This should be the case of all non-self-gravitating clouds in the cold interstellar medium and of small-scale structures in cosmological flows.

We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a hierarchical manner, we assume that density fluctuations follow a random multiplicative process. When the polytropic exponent $\gamma$ is equal to unity, the local Mach number is independent of the density, and our assumption leads us to expect that the probability density function (PDF) of the density field is a log-normal. This isothermal case is found to be special, with a dispersion ${\sigma }_s^2$ scaling as the square turbulent Mach number $M^2,$ where $s\equiv \ln \rho$ and $\rho$ is the fluid density. Density fluctuations are stronger than expected on the sole basis of shock jumps. Extrapolating the model to the case $\gamma \ne 1,$ we find that as the Mach number becomes large, the density PDF is expected to asymptotically approach a power-law regime at high densities when $\gamma <1,$ and at low densities when $\gamma >1.\mathrm{}$ This effect can be traced back to the fact that the pressure term in the momentum equation varies exponentially with $s,$ thus opposing the growth of fluctuations on one side of the PDF, while being negligible on the other side. This also causes the dispersion ${\sigma }_s^2$ to grow more slowly than $M^2$ when $\gamma \ne 1.$ In view of these results, we suggest that Burgers flow is a singular case not approached by the high-$\tilde{M}$ limit, with a PDF that develops power laws on both sides.

We study the formation of giant dense cloud complexes and of stars within them using SPH numerical simulations of the collision of gas streams (``inflows'') in the WNM at moderately supersonic velocities. The collisions cause compression, cooling, and turbulence generation in the gas, forming a cloud that then becomes self-gravitating and begins to collapse globally. Simultaneously, the turbulent, nonlinear density fluctuations induce fast, local collapse events. The simulations show that (1) The clouds are not in a state of equilibrium. Instead, they undergo secular evolution. During its early stages, the cloud's mass and gravitational energy |E<sub>g</sub>| increase steadily, while the turbulent energy E<sub>k</sub> reaches a plateau. (2) When |E<sub>g</sub>| becomes comparable to E<sub>k</sub>, global collapse begins, causing a simultaneous increase in |E<sub>g</sub>| and E<sub>k</sub> that maintains a near-equipartition condition |E<sub>g</sub>| ~ 2E<sub>k</sub>. (3) Longer inflow durations delay the onset of global and local collapse by maintaining a higher turbulent velocity dispersion in the cloud over longer times. (4) The star formation rate is large from the beginning, without any period of slow and accelerating star formation. (5) The column densities of the local star-forming clumps closely resemble reported values of the column density required for molecule formation, suggesting that locally molecular gas and star formation occur nearly simultaneously. The MC formation mechanism discussed here naturally explains the apparent ``virialized'' state of MCs and the ubiquity of H I halos around them. Also, within their assumptions, our simulations support the scenario of rapid star formation after MCs are formed, although long (15 Myr) accumulation periods do occur during which the clouds build up their gravitational energy, and which are expected to be spent in the atomic phase.

We discuss the nature of the velocity dispersion versus size relation for molecular clouds. In particular, we add to previous observational results s

We suggest that molecular clouds can be formed on short time scales by compressions from large scale streams in the interstellar medium (ISM). In particular, we argue that the Taurus-Auriga complex, with filaments of 10-20 pc $\times$ 2-5 pc, most have been formed by H I flows in $\lesssim 3$Myr, explaining the absence of post-T Tauri stars in the region with ages $\gtrsim 3$ Myr. Observations in the 21 cm line of the H I `halos' around the Taurus molecular gas show many features (broad asymmetric profiles, velocity shifts of H I relative to $^{12}$CO) predicted by our MHD numerical simulations, in which large-scale H I streams collide to produce dense filamentary structures. This rapid evolution is possible because the H I flows producing and disrupting the cloud have much higher velocities (5-10 kms) than present in the molecular gas resulting from the colliding flows. The simulations suggest that such flows can occur from the global ISM turbulence without requiring a single triggering event such as a SN explosion.

We discuss molecular cloud formation by large-scale supersonic compressions in the diffuse warm neutral medium (WNM). Initially, a shocked layer forms, and within it, a thin cold layer. An analytical model and high-resolution one-dimensional simulations predict the thermodynamic conditions in the cold layer. After similar to 1 Myr of evolution, the layer has column density similar to 2.5 x 10(19) cm(-2), thickness similar to 0.03 pc, temperature similar to 25 K, and pressure similar to 6650 K cm(-3). These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the one-dimensional simulations, the inflows into the sheets produce line profiles with a central line of width similar to 0.5 km s(-1) and broad wings of width similar to 1 km s(-1). Three-dimensional numerical simulations show that the cold layer develops turbulent motions and increases its thickness until it becomes a fully three-dimensional turbulent cloud. Fully developed turbulence arises on times ranging from similar to 7.5 Myr for inflow Mach number M(1,r) = 2.4 to > 80Myr for M(1,r) = 1.03. These numbers should be considered upper limits. The highest density turbulent gas (HDG, n > 100 cm(-3)) is always overpressured with respect to the mean WNM pressure by factors of 1.5 - 4, even though we do not include self-gravity. The intermediate-density gas (IDG, 10 < n/cm(-3) < 100) has a significant pressure scatter that increases with M(1,r), so that at M1; r 2: 4 a significant fraction of the IDG is at a higher pressure than the HDG. Our results suggest that the turbulence and at least part of the excess pressure in molecular clouds can be generated by the compressive process that forms the clouds themselves and that thin CNM sheets may be formed transiently by this mechanism, when the compressions are only weakly supersonicopen14713