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Register a new userTsallis statistics as a tool for studying interstellar turbulence
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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.
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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.
The characteristic outer scale of turbulence and the ratio of the random to ordered components of the magnetic field are key parameters to characterise magnetic turbulence in the interstellar gas, which affects the propagation of cosmic rays within the Galaxy. We provide new constraints to those two parameters. We use the LOw Frequency ARray (LOFAR) to image the diffuse continuum emission in the Fan region at (l,b) (137.0,+7.0) at 80x70 resolution in the range [146,174] MHz. We detect multi-scale fluctuations in the Galactic synchrotron emission and compute their power spectrum. Applying theoretical estimates and derivations from the literature for the first time, we derive the outer scale of turbulence and the ratio of random to ordered magnetic field from the characteristics of these fluctuations . We obtain the deepest image of the Fan region to date and find diffuse continuum emission within the primary beam. The power spectrum of the foreground synchrotron fluctuations displays a power law behaviour for scales between 100 and 8 arcmin with a slope of (-1.84+/-0.19). We find an upper limit of about 20 pc for the outer scale of the magnetic interstellar turbulence toward the Fan region. We also find a variation of the ratio of random to ordered field as a function of Galactic coordinates, supporting different turbulent regimes. We use power spectra fluctuations from LOFAR as well as earlier GMRT and WSRT observations to constrain the outer scale of turbulence of the Galactic synchrotron foreground, finding a range of plausible values of 10-20 pc. Then, we use this information to deduce lower limits of the ratio of ordered to random magnetic field strength. These are found to be 0.3, 0.3, and 0.5 for the LOFAR, WSRT and GMRT fields considered respectively. Both these constraints are in agreement with previous estimates.
The detection of solar-like oscillations in G and K giants with the CoRoT and Kepler space-based satellites allows robust constraints to be set on the mass and radius of such stars. The availability of these constraints for thousands of giants sampling different regions of the Galaxy promises to enrich our understanding on the Milky Ways constituents. In this contribution we briefly recall which are the relevant constraints that red-giant seismology can currently provide to the study of stellar populations. We then present, for a few nearby stars, the comparison between radius and mass determined using seismic scaling relations and those obtained by other methods.
We explore the utility of narrow band X-ray surface photometry as a tool for making fully Bayesian, hydrostatic mass measurements of clusters of galaxies, groups and early-type galaxies. We demonstrate that it is sufficient to measure the surface photometry with the Chandra X-ray observatory in only three (rest frame) bands (0.5--0.9 keV, 0.9--2.0 keV and 2.0--7.0 keV) in order to constrain the temperature, density and abundance of the hot interstellar medium (ISM). Adopting parametrized models for the mass distribution and radial entropy profile and assuming spherical symmetry, we show that the constraints on the mass and thermodynamic properties of the ISM that are obtained by fitting data from all three bands simultaneously are comparable to those obtained by fitting similar models to the temperature and density profiles derived from spatially resolved spectroscopy, as is typically done. We demonstrate that the constraints can be significantly tightened when exploiting a recently derived, empirical relationship between the gas fraction and the entropy profile at large scales, eliminating arbitrary extrapolations at large radii. This Scaled Adiabatic Model (ScAM) is well suited to modest signal-to-noise data, and we show that accurate, precise measurements of the global system properties are inferred when employing it to fit data from even very shallow, snapshot X-ray observations. The well-defined asymptotic behaviour of the model also makes it ideally suited for use in Sunyaev-Zeldovich studies of galaxy clusters.
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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