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Register a new userProjected velocity statistics of interstellar turbulence
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Siyao Xu
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Velocity statistics is a direct probe of the dynamics of interstellar turbulence. Its observational measurements are very challenging due to the convolution between density and velocity and projection effects. We introduce the projected velocity structure function, which can be generally applied to statistical studies of both sub- and super-sonic turbulence in different interstellar phases. It recovers the turbulent velocity spectrum from the projected velocity field in different regimes, and when the thickness of a cloud is less than the driving scale of turbulence, it can also be used to determine the cloud thickness and the turbulence driving scale. By applying it to the existing core velocity dispersion measurements of the Taurus cloud, we find a transition from the Kolmogorov to the Burgers scaling of turbulent velocities with decreasing length scales, corresponding to the large-scale solenoidal motions and small-scale compressive motions, respectively. The latter occupy a small fraction of the volume and can be selectively sampled by clusters of cores with the typical cluster size indicated by the transition scale.
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We used magnetohydrodynamic (MHD) simulations of interstellar turbulence to study the probability distribution functions (PDFs) of increments of density, velocity, and magnetic field. We found that the PDFs are well described by a Tsallis distribution, following the same general trends found in solar wind and Electron MHD studies. We found that the PDFs of density are very different in subsonic and supersonic turbulence. In order to extend this work to ISM observations we studied maps of column density obtained from 3D MHD simulations. From the column density maps we found the parameters that fit to Tsallis distributions and demonstrated that these parameters vary with the sonic and Alfven Mach numbers of turbulence. This opens avenues for using Tsallis distributions to study the dynamical and perhaps magnetic states of interstellar gas.
I discuss the role of self-gravity and radiative heating and cooling in shaping the nature of the turbulence in the interstellar medium (ISM) of our galaxy. The heating and cooling cause it to be highly compressible, and, in some regimes of density and temperature, to become thermally unstable, tending to spontaneously segregate into warm/diffuse and cold/dense phases. On the other hand, turbulence is an inherently mixing process, tending to replenish the density and temperature ranges that would be forbidden under thermal processes alone. The turbulence in the ionized ISM appears to be transonic (i.e, with Mach numbers $Ms sim 1$), and thus to behave essentially incompressibly. However, in the neutral medium, thermal instability causes the sound speed of the gas to fluctuate by up to factors of $sim 30$, and thus the flow can be highly supersonic with respect to the dense/cold gas, although numerical simulations suggest that this behavior corresponds more to the ensemble of cold clumps than to the clumps internal velocity dispersion. Finally, coherent large-scale compressions in the warm neutral medium (induced by, say, the passage of spiral arms or by supernova shock waves) can produce large, dense molecular clouds that are subject to their own self-gravity, and begin to contract gravitationally. Because they are populated by nonlinear density fluctuations, whose local free-fall times are significantly smaller than that of the whole cloud, the fluctuations terminate their collapse earlier, giving rise to a regime of hierarchical gravitational fragmentation, with small-scale collapses occurring within larger-scale ones. Thus, the turbulence in molecular clouds may be dominated by a gravitationally contracting component at all scales.
Guided by the duality of turbulence (random versus coherent we seek coherent structures in the turbulent velocity field of molecular clouds, anticipating their importance in cloud evolution. We analyse a large map (40 by 20) obtained with the HERA multibeam receiver (IRAM-30m telescope) in a high latitude cloud of the Polaris Flare at an unprecedented spatial (11) and spectral (0.05 km/s) resolutions in the 12CO(2-1) line. We find that two parsec-scale components of velocities differing by ~2 km/s, share a narrow interface ($<0.15$ pc) that appears as an elongated structure of intense velocity-shear, ~15 to 30 km/s/pc. The locus of the extrema of line--centroid-velocity increments (E-CVI) in that field follows this intense-shear structure as well as that of the 12CO(2-1) high-velocity line wings. The tiny spatial overlap in projection of the two parsec-scale components implies that they are sheets of CO emission and that discontinuities in the gas properties (CO enrichment and/or increase of gas density) occur at the position of the intense velocity shear. These results disclose spatial and kinematic coherence between scales as small as 0.03 pc and parsec scales. They confirm that the departure from Gaussianity of the probability density functions of E-CVIs is a powerful statistical tracer of the intermittency of turbulence. They disclose a link between large scale turbulence, its intermittent dissipation rate and low-mass dense core formation.
By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid $^4$He are strongly non-Gaussian with $1/v^3$ power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.
Turbulence is ubiquitous in the insterstellar medium and plays a major role in several processes such as the formation of dense structures and stars, the stability of molecular clouds, the amplification of magnetic fields, and the re-acceleration and diffusion of cosmic rays. Despite its importance, interstellar turbulence, alike turbulence in general, is far from being fully understood. In this review we present the basics of turbulence physics, focusing on the statistics of its structure and energy cascade. We explore the physics of compressible and incompressible turbulent flows, as well as magnetized cases. The most relevant observational techniques that provide quantitative insights of interstellar turbulence are also presented. We also discuss the main difficulties in developing a three-dimensional view of interstellar turbulence from these observations. Finally, we briefly present what could be the the main sources of turbulence in the interstellar medium.
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