Turbulent Control of the Star Formation Efficiency

Supersonic turbulence plays a dual role in molecular clouds: On one hand, it contributes to the global support of the clouds, while on the other it promotes the formation of small-scale density fluctuations, identifiable with clumps and cores. Within these, the local Jeans length \Ljc is reduced, and collapse ensues if \Ljc becomes smaller than the clump size and the magnetic support is insufficient (i.e., the core is ``magnetically supercritical''); otherwise, the clumps do not collapse and are expected to re-expand and disperse on a few free-fall times. This case may correspond to a fraction of the observed starless cores. The star formation efficiency (SFE, the fraction of the cloud's mass that ends up in collapsed objects) is smaller than unity because the mass contained in collapsing clumps is smaller than the total cloud mass. However, in non-magnetic numerical simulations with realistic Mach numbers and turbulence driving scales, the SFE is still larger than observational estimates. The presence of a magnetic field, even if magnetically supercritical, appears to further reduce the SFE, but by reducing the probability of core formation rather than by delaying the collapse of individual cores, as was formerly thought. Precise quantification of these effects as a function of global cloud parameters is still needed.Comment: Invited review for the conference "IMF@50: the Initial Mass Function 50 Years Later", to be published by Kluwer Academic Publishers, eds. E. Corbelli, F. Palla, and H. Zinnecke

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

Galactic and Magellanic Evolution with the SKA

As we strive to understand how galaxies evolve it is crucial that we resolve physical processes and test emerging theories in nearby systems that we can observe in great detail. Our own Galaxy, the Milky Way, and the nearby Magellanic Clouds provide unique windows into the evolution of galaxies, each with its own metallicity and star formation rate. These laboratories allow us to study with more detail than anywhere else in the Universe how galaxies acquire fresh gas to fuel their continuing star formation, how they exchange gas with the surrounding intergalactic medium, and turn warm, diffuse gas into molecular clouds and ultimately stars. The $\lambda$21-cm line of atomic hydrogen (HI) is an excellent tracer of these physical processes. With the SKA we will finally have the combination of surface brightness sensitivity, point source sensitivity and angular resolution to transform our understanding of the evolution of gas in the Milky Way, all the way from the halo down to the formation of individual molecular clouds.Comment: 25 pages, from "Advancing Astrophysics with the Square Kilometre Array", to appear in Proceedings of Scienc

Analytical theory for the initial mass function: CO clumps and prestellar cores

We derive an analytical theory of the prestellar core initial mass function based on an extension of the Press-Schechter statistical formalism. With the same formalism, we also obtain the mass spectrum for the non self-gravitating clumps produced in supersonic flows. The mass spectrum of the self-gravitating cores reproduces very well the observed initial mass function and identifies the different mechanisms responsible for its behaviour. The theory predicts that the shape of the IMF results from two competing contributions, namely a power-law at large scales and an exponential cut-off (lognormal form) centered around the characteristic mass for gravitational collapse. The cut-off exists already in the case of pure thermal collapse, provided that the underlying density field has a lognormal distribution. Whereas pure thermal collapse produces a power-law tail steeper than the Salpeter value, dN/dlog M\propto M^{-x}, with x=1.35, this latter is recovered exactly for the (3D) value of the spectral index of the velocity power spectrum, n\simeq 3.8, found in observations and in numerical simulations of isothermal supersonic turbulence. Indeed, the theory predicts that x=(n+1)/(2n-4) for self-gravitating structures and x=2-n'/3 for non self-gravitating structures, where n' is the power spectrum index of log(rho). We show that, whereas supersonic turbulence promotes the formation of both massive stars and brown dwarfs, it has an overall negative impact on star formation, decreasing the star formation efficiency. This theory provides a novel theoretical foundation to understand the origin of the IMF and to infer its behaviour in different environments. It also provides a complementary approach and useful guidance to numerical simulations exploring star formation, while making testable predictions.Comment: To appear in Ap

One-Point Probability Distribution Functions of Supersonic Turbulent Flows in Self-Gravitating Media

Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability distribution functions (pdf's) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds. However, the interpretation of these data requires comparison with numerical simulations. To address this issue, SPH simulations of driven and decaying, supersonic, turbulent flows with and without self-gravity are presented. In addition, random Gaussian velocity fields are analyzed to estimate the influence of variance effects. To characterize the flow properties, the pdf's of the density, of the line-of-sight velocity centroids, and of the line centroid increments are studied. This is supplemented by a discussion of the dispersion and the kurtosis of the increment pdf's, as well as the spatial distribution of velocity increments for small spatial lags. From the comparison between different models of interstellar turbulence, it follows that the inclusion of self-gravity leads to better agreement with the observed pdf's in molecular clouds. The increment pdf's for small spatial lags become exponential for all considered velocities. However, all the processes considered here lead to non-Gaussian signatures, differences are only gradual, and the analyzed pdf's are in addition projection dependent. It appears therefore very difficult to distinguish between different physical processes on the basis of pdf's only, which limits their applicability for adequately characterizing interstellar turbulence.Comment: 38 pages (incl. 17 figures), accepted for publication in ApJ, also available with full resolution figures at http://www.strw.leidenuniv.nl/~klessen/Preprint

The Local Leo Cold Cloud and New Limits on a Local Hot Bubble

We present a multi-wavelength study of the local Leo cold cloud (LLCC), a very nearby, very cold cloud in the interstellar medium. Through stellar absorption studies we find that the LLCC is between 11.3 pc and 24.3 pc away, making it the closest known cold neutral medium cloud and well within the boundaries of the local cavity. Observations of the cloud in the 21-cm HI line reveal that the LLCC is very cold, with temperatures ranging from 15 K to 30 K, and is best fit with a model composed of two colliding components. The cloud has associated 100 micron thermal dust emission, pointing to a somewhat low dust-to-gas ratio of 48 x 10^-22 MJy sr^-1 cm^2. We find that the LLCC is too far away to be generated by the collision among the nearby complex of local interstellar clouds, but that the small relative velocities indicate that the LLCC is somehow related to these clouds. We use the LLCC to conduct a shadowing experiment in 1/4 keV X-rays, allowing us to differentiate between different possible origins for the observed soft X-ray background. We find that a local hot bubble model alone cannot account for the low-latitude soft X-ray background, but that isotropic emission from solar wind charge exchange does reproduce our data. In a combined local hot bubble and solar wind charge exchange scenario, we rule out emission from a local hot bubble with an 1/4 keV emissivity greater than 1.1 Snowdens / pc at 3 sigma, 4 times lower than previous estimates. This result dramatically changes our perspective on our local interstellar medium.Comment: 13 pages, 12 figures. Accepted for publication in the Astrophysical Journal. Vector figure version available at http://www.astro.columbia.edu/~jpeek

Does Turbulent Pressure Behave as a Logatrope?

We present numerical simulations of an isothermal turbulent gas undergoing gravitational collapse, aimed at testing for ``logatropic'' behavior of the form $P_t \sim \log \rho$, where $P_t$ is the ``turbulent pressure'' and $\rho$ is the density. To this end, we monitor the evolution of the turbulent velocity dispersion $\sigma$ as the density increases during the collapse. A logatropic behavior would require that $\sigma \propto \rho^{-1/2}$, a result which, however, is not verified in the simulations. Instead, the velocity dispersion increases with density, implying a polytropic behavior of $P_t$. This behavior is found both in purely hydrodynamic as well as hydromagnetic runs. For purely hydrodynamic and rapidly-collapsing magnetic cases, the velocity dispersion increases roughly as $\sigma \propto \rho^{1/2}$, implying $P_t\sim \rho^2$, where $P_t$ is the turbulent pressure. For slowly-collapsing magnetic cases the behavior is close to $\sigma \propto \rho^{1/4}$, which implies $P_t \sim \rho^{3/2}$. We thus suggest that the logatropic ``equation of state'' may represent only the statistically most probable state of an ensemble of clouds in equilibrium between self-gravity and kinetic support, but does not adequately represent the behavior of the ``turbulent pressure'' within a cloud undergoing a dynamic compression due to gravitational collapse. Finally, we discuss the importance of the underlying physical model for the clouds (in equilibrium vs. dynamic) on the results obtained.Comment: Accepted in ApJ. 10 pages, 3 postscript figure