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Register a new userDo Lognormal Column-Density Distributions in Molecular Clouds Imply Supersonic Turbulence?
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Added by
Konstantinos Tassis
Publication date
2010
fields
Physics
and research's language is
English
Authors
K. Tassis
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Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed clouds. We calculate and present the column-density distributions of three clouds, modeled with very different techniques, none of which is dominated by supersonic turbulence. The first star-forming cloud is simulated using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only by thermal-pressure forces, drives the evolution. The second cloud is magnetically subcritical with subsonic turbulence, simulated using nonideal MHD; in this case the evolution is due to gravitationally-driven ambipolar diffusion. The third cloud is isothermal, self-gravitating, and has a smooth density distribution analytically approximated with a uniform inner region and an r^-2 profile at larger radii. We show that in all three cases the column-density distributions are lognormal. Power-law tails develop only at late times (or, in the case of the smooth analytic profile, for strongly centrally concentrated configurations), when gravity dominates all opposing forces. It therefore follows that lognormal column-density distributions are generic features of diverse model clouds, and should not be interpreted as being a consequence of supersonic turbulence.
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The formation of stars is inextricably linked to the structure of their parental molecular clouds. Here we take a number of nearby giant molecular clouds (GMCs) and analyse their column density and mass distributions. This investigation is based on four new all-sky median colour excess extinction maps determined from 2MASS. The four maps span a range of spatial resolution of a factor of eight. This allows us to determine cloud properties at a common spatial scale of 0.1pc, as well as to study the scale dependence of the cloud properties. We find that the low column density and turbulence dominated part of the clouds can be well fit by a log-normal distribution. However, above a universal extinction threshold of 6.0 pm 1.5mag A_V there is excess material compared to the log-normal distribution in all investigated clouds. This material represents the part of the cloud that is currently involved in star formation, and thus dominated by gravity. Its contribution to the total mass of the clouds ranges over two orders of magnitude from 0.1 to 10%. This implies that our clouds sample various stages in the evolution of GMCs. Furthermore, we find that the column density and mass distributions are extremely similar between clouds if we analyse only the high extinction material. On the other hand, there are significant differences between the distributions if only the low extinction, turbulence dominated regions are considered. This shows that the turbulent properties differ between clouds depending on their environment. However, no significant influence on the predominant mode of star formation (clustered or isolated) could be found. Furthermore, the fraction of the cloud actively involved in star formation is only governed by gravity, with the column density and mass distributions not significantly altered by local feedback processes.
We introduce a theory for the development of a transitional column density $Sigma_{rm TP}$ between the lognormal and the power-law forms of the probability distribution function (PDF) in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of $Sigma_{rm TP}$ increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for $Sigma_{rm TP}$ based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value $Sigma_{rm TP}$ scales with $mathcal{M}^2_{rm 0}$, the square of the initial sonic Mach number, and $beta_{0}$, the initial ratio of gas pressure to magnetic pressure. We fit the variation of $Sigma_{rm TP}$ among different model clouds as a function of $mathcal{M}^2_{rm 0} beta_{0}$, or equivalently the square of the initial Alfvenic Mach number $mathcal{M}^2_{rm A0}$. This implies that the transition value $Sigma_{rm TP}$ is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of $Sigma_{rm TP}$ denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.
Jets and outflows from young stellar objects are proposed candidates to drive supersonic turbulence in molecular clouds. Here, we present the results from multi-dimensional jet simulations where we investigate in detail the energy and momentum deposition from jets into their surrounding environment and quantify the character of the excited turbulence with velocity probability density functions. Our study include jet--clump interaction, transient jets, and magnetised jets. We find that collimated supersonic jets do not excite supersonic motions far from the vicinity of the jet. Supersonic fluctuations are damped quickly and do not spread into the parent cloud. Instead subsonic, non-compressional modes occupy most of the excited volume. This is a generic feature which can not be fully circumvented by overdense jets or magnetic fields. Nevertheless, jets are able to leave strong imprints in their cloud structure and can disrupt dense clumps. Our results question the ability of collimated jets to sustain supersonic turbulence in molecular clouds.
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $mathcal{M}$, up to $mathcal{M}sim30$. The PDF width, $sigma_{s}$, follows the relation $sigma_{s}^2 = ln (1+b^2 {mathcal M}^2)$, with $bapprox0.38$. However, the PDF exhibits a negative skewness that increases with increasing $mathcal{M}$, so much of the growth of $sigma_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $mathcal{M}$, which may have a significant impact on theoretical models of star formation.
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our experiments cover a wide range of turbulent Mach number and virial parameter, allowing us for the first time to determine how the PDF responds as these parameters vary, and we introduce a new diagnostic, the dimensionless star formation efficiency versus density ($epsilon_{rm ff}(s)$) curve, which provides a sensitive diagnostic of the PDF shape and dynamics. We show that the PDF follows a universal functional form consisting of a log-normal at low density with two distinct power law tails at higher density; the first of these represents the onset of self-gravitation, and the second reflects the onset of rotational support. Once the star formation efficiency reaches a few percent, the PDF becomes statistically steady, with no evidence for secular time-evolution at star formation efficiencies from about five to 20 percent. We show that both the Mach number and the virial parameter influence the characteristic densities at which the log-normal gives way to the first power-law, and the first to the second, and we extend (for the former) and develop (for the latter) simple theoretical models for the relationship between these density thresholds and the global properties of the turbulent medium.
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