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Register a new userOn the structure of molecular clouds
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Added by
Javier Ballesteros-Paredes
Publication date
2012
fields
Physics
and research's language is
English
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We show that the inter-cloud Larson scaling relation between mean volume density and size $rhopropto R^{-1}$, which in turn implies that mass $Mpropto R^2$, or that the column density $N$ is constant, is an artifact of the observational methods used. Specifically, setting the column density threshold near or above the peak of the column density probability distribution function Npdf ($Nsim 10^{21}$ cmalamenos 2) produces the Larson scaling as long as the Npdf decreases rapidly at higher column densities. We argue that the physical reasons behind local clouds to have this behavior are that (1) this peak column density is near the value required to shield CO from photodissociation in the solar neighborhood, and (2) gas at higher column densities is rare because it is susceptible to gravitational collapse into much smaller structures in specific small regions of the cloud. Similarly, we also use previous results to show that if instead a threshold is set for the volume density, the density will appear to be constant, implying thus that $M propto R^3$. Thus, the Larson scaling relation does not provide much information on the structure of molecular clouds, and does not imply either that clouds are in Virial equilibrium, or have a universal structure. We also show that the slope of the $M-R$ curve for a single cloud, which transitions from near-to-flat values for large radii to $alpha=2$ as a limiting case for small radii, depends on the properties of the Npdf.
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The energy cascade rate of turbulence can be measured with the structure function. In practice, the 3D velocity of the gas in molecular cloud is hard to measure, which makes the measurement of structure function difficult. In the case of thin molecular clouds perpendicular to the line of sight, the structure function $S^2_{ tt}$ can be measured with core velocity dispersion (CVD), ${rm CVD}^2=frac{1}{2}S^2_{ tt}$. This method was extended to the case when the thin molecular cloud is not perpendicular to the line of sight, with intersection angle $theta$, ${rm CVD}^2=frac{1}{2}S^2_{ tt}left(1-frac{1}{8}cos^2thetaright)R^{2/3}$, where $R$ can be expressed with elliptic integrals of the second kind $E(k,varphi)$ as $R=frac{2}{pi}E(costheta,frac{pi}{2})$.
The structure of molecular clouds (MCs) holds important clues on the physical processes that lead to their formation and subsequent evolution. While it is well established that turbulence imprints a self-similar structure to the clouds, other processes, such as gravity and stellar feedback, can break their scale-free nature. The break of self-similarity can manifest itself in the existence of characteristic scales that stand out from the underlying structure generated by turbulent motions. We investigate the structure of the Cygnus-X North and the Polaris MCs which represent two extremes in terms of their star formation activity. We characterize the structure of the clouds using the delta-variance ($Delta$-variance) spectrum. In Polaris, the structure of the cloud is self-similar over more than one order of magnitude in spatial scales. In contrast, the $Delta$-variance spectrum of Cygnus-X exhibits an excess and a plateau on physical scales of ~0.5-1.2 pc. In order to explain the observations for Cygnus-X, we use synthetic maps in which we overlay populations of discrete structures on top of a fractal Brownian motion (fBm) image. The properties of these structures such as their major axis sizes, aspect ratios, and column density contrasts are randomly drawn from parameterized distribution functions. We show that it is possible to reproduce a $Delta$-variance spectrum that resembles the one of the Cygnus-X cloud. We also use a reverse engineering approach in which we extract the compact structures in the Cygnus-X cloud and re-inject them on an fBm map. The calculated $Delta$-variance using this approach deviates from the observations and is an indication that the range of characteristic scales observed in Cygnus-X is not only due to the existence of compact sources, but is a signature of the whole population of structures, including more extended and elongated structures
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