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

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

Spin fluctuations in the stacked-triangular antiferromagnet YMnO3

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO3 was studied above the Neel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above TN, a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line-width that increases with q like Dq^z and the dynamical exponent z=2.3. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable q-dependence at small wave-vectors.Comment: JETP LETTERS, in pres

Weak differentiability of product measures

In this paper, we study cost functions over a finite collection of random variables. For these types of models, a calculus of differentiation is developed that allows us to obtain a closed-form expression for derivatives where "differentiation" has to be understood in the weak sense. The technique for proving the results is new and establishes an interesting link between functional analysis and gradient estimation. The key contribution of this paper is a product rule of weak differentiation. In addition, a product rule of weak analyticity is presented that allows for Taylor series approximations of finite products measures. In particular, from characteristics of the individual probability measures, a lower bound (i.e., domain of convergence) can be established for the set of parameter values for which the Taylor series converges to the true value. Applications of our theory to the ruin problem from insurance mathematics and to stochastic activity networks arising in project evaluation review techniques are provided. © 2010 INFORMS

Spin-Glass State in CuGa2O4\rm CuGa_2O_4

Magnetic susceptibility, magnetization, specific heat and positive muon spin relaxation (\musr) measurements have been used to characterize the magnetic ground-state of the spinel compound $\rm CuGa_2O_4$. We observe a spin-glass transition of the S=1/2 $\rm Cu^{2+}$ spins below $\rm T_f=2.5K$ characterized by a cusp in the susceptibility curve which suppressed when a magnetic field is applied. We show that the magnetization of $\rm CuGa_2O_4$ depends on the magnetic histo Well below $\rm T_f$, the muon signal resembles the dynamical Kubo-Toyabe expression reflecting that the spin freezing process in $\rm CuGa_2O_4$ results Gaussian distribution of the magnetic moments. By means of Monte-Carlo simulati we obtain the relevant exchange integrals between the $\rm Cu^{2+}$ spins in this compound.Comment: 6 pages, 16 figure

The <i>Herschel</i> view of the massive star-forming region NGC 6334

Aims: Fundamental to any theory of high-mass star formation are gravity and turbulence. Their relative importance, which probably changes during cloud evolution, is not known. By investigating the spatial and density structure of the high-mass star-forming complex NGC 6334 we aim to disentangle the contributions of turbulence and gravity. Methods: We used Herschel PACS and SPIRE imaging observations from the HOBYS key programme at wavelengths of 160, 250, 350, and 500 μm to construct dust temperature and column density maps. Using probability distribution functions (PDFs) of the column density determined for the whole complex and for four distinct sub-regions (distinguished on the basis of differences in the column density, temperature, and radiation field), we characterize the density structure of the complex. We investigate the spatial structure using the Δ-variance, which probes the relative amount of structure on different size scales and traces possible energy injection mechanisms into the molecular cloud. Results: The Δ-variance analysis suggests that the significant scales of a few parsec that were found are caused by energy injection due to expanding HII regions, which are numerous, and by the lengths of filaments seen everywhere in the complex. The column density PDFs have a lognormal shape at low densities and a clearly defined power law at high densities for all sub-regions whose slope is linked to the exponent α of an equivalent spherical density distribution. In particular with α = 2.37, the central sub-region is largly dominated by gravity, caused by individual collapsing dense cores and global collapse of a larger region. The collapse is faster than free-fall (which would lead only to α = 2) and thus requires a more dynamic scenario (external compression, flows). The column density PDFs suggest that the different sub-regions are at different evolutionary stages, especially the central sub-region, which seems to be in a more evolved stage

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We present numerical studies of compressible, decaying turbulence, with and without magnetic fields, with initial rms Alfven and Mach numbers ranging up to five, and apply the results to the question of the support of star-forming interstellar clouds of molecular gas. We find that, in 1D, magnetized turbulence actually decays faster than unmagnetized turbulence. In all the regimes that we have studied 3D turbulence-super-Alfvenic, supersonic, sub-Alfvenic, and subsonic-the kinetic energy decays as (t-t0)^(-x), with 0.85 < x < 1.2. We compared results from two entirely different algorithms in the unmagnetized case, and have performed extensive resolution studies in all cases, reaching resolutions of 256^3 zones or 350,000 particles. We conclude that the observed long lifetimes and supersonic motions in molecular clouds must be due to external driving, as undriven turbulence decays far too fast to explain the observations.Comment: Submitted to Phys. Rev. Letters, 29 Nov. 1997. 10 pages, 2 figures, also available from http://www.mpia-hd.mpg.de/theory/preprints.html#maclo

Submillimeter Studies of Prestellar Cores and Protostars: Probing the Initial Conditions for Protostellar Collapse

Improving our understanding of the initial conditions and earliest stages of protostellar collapse is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. Observationally, there are two complementary approaches to this problem: (1) studying the structure and kinematics of prestellar cores observed prior to protostar formation, and (2) studying the structure of young (e.g. Class 0) accreting protostars observed soon after point mass formation. We discuss recent advances made in this area thanks to (sub)millimeter mapping observations with large single-dish telescopes and interferometers. In particular, we argue that the beginning of protostellar collapse is much more violent in cluster-forming clouds than in regions of distributed star formation. Major breakthroughs are expected in this field from future large submillimeter instruments such as Herschel and ALMA.Comment: 12 pages, 9 figures, to appear in the proceedings of the conference "Chemistry as a Diagnostic of Star Formation" (C.L. Curry & M. Fich eds.