Spectral Properties of Interstellar Turbulence via Velocity Channel Analysis

In this presentation we review the link between the statistics of intensity fluctuations in spectral line data cubes with underlying statistical properties of turbulence in the interstellar medium. Both the formalism of Velocity Channel Analysis for optically thin lines and its extension to the lines with self-absorption is described. We demonstrate that by observing optically thin lines from cold gas in sufficiently narrow (thin) velocity channels one may recover the scaling of the stochastic velocities from turbulent cascade, in particular, Kolmogorov velocities give $K^{-2.7}$ contribution to the intensity power spectrum. Synthetically increasing the channel thickness separates out the underlying density inhomogeneities of the gas. Effects of self absorption, on the other hand, retain the velocity signature even for integrated lines. As a result, intensity fluctuations tend to show universal but featureless scaling of the power $\propto K^{-3}$ over the range of scales.Comment: 12 pages, 1 figure. To appear in: "Magnetic fields in the Universe", eds. E. M. de Gouveia Dal Pino, A. Lazarian & G. Lugones. Angra dos Reis, Brazil Nov. 23 - Dec 3, 200

Extending Velocity Channel Analysis for Studying Turbulence Anisotropies

We extend the velocity channel analysis (VCA), introduced by Lazarian & Pogosyan, of the intensity fluctuations in the velocity slices of position-position-velocity (PPV) spectroscopic data from Doppler broadened lines to study statistical anisotropy of the underlying velocity and density that arises in a turbulent medium from the presence of magnetic field. In particular, we study analytically how the anisotropy of the intensity correlation in the channel maps changes with the thickness of velocity channels. In agreement with the earlier VCA studies we find that the anisotropy in the thick channels reflects the anisotropy of the density field, while the relative contribution of density and velocity fluctuations to the thin velocity channels depends on the density spectral slope. We show that the anisotropies arising from Alfven, slow and fast magnetohydrodynamical modes are different, in particular, the anisotropy in PPV created by fast modes is opposite to that created by Alfven and slow modes, and this can be used to separate their contributions. We successfully compare our results with the recent numerical study of the PPV anisotropies measured with synthetic observations. We also extend our study to the medium with self-absorption as well as to the case of absorption lines. In addition, we demonstrate how the studies of anisotropy can be performed using interferometers.Comment: 36 pages, 16 figures, Accepted to MNRAS, minor changes to match the accepted versio

The invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D

The full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian is presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of extrema counts as functions of the excursion set threshold and the spectral parameter, as illustrated on model examples.Comment: 4 pages, 2 figures. Corrected expansion coefficients for orders n>=5. Relation between Gram-Charlier and Edgeworth expansions is clarified

Non Gaussian Minkowski functionals and extrema counts for 2D sky maps

In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post- Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on the flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.Comment: 6 pages, to appear as proceedings of the IAU Symposium No. 308, 2014 The Zeldovich Universe, Genesis and Growth of the Cosmic Web Rien van de Weygaert, Sergei Shandarin, Enn Saar and Jaan Einast

Magnetic field strength from turbulence theory (I): Using differential measure approach (DMA)

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis-Chandrasekhar-Fermi (DCF) technique. However, we identify the major problem of the DCF to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF, the new technique uses not the dispersion of the polarization angle and line of sight velocities, but increments of these quantities given by the structure functions. To address the variety of the astrophysical conditions for which our technique can be applied, we consider the turbulence in both media with magnetic pressure larger than the gas pressure corresponding e.g. to molecular and the gas pressure larger than the magnetic pressure corresponding to the warm neutral medium. We provide general expressions for arbitrary admixture of Alfv\'en, slow and fast modes in these media and consider in detail the particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our Differential Measure Approach (DMA), unlike the DCF, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data and is much more stable in the presence of large scale variations induces of non-turbulent nature. In parallel, our study uncover the deficiencies of the earlier DCF research.Comment: 53 pages, 32 figures, Accepted by ApJ for publications. Code: https://github.com/kyuen2/MHD_Mod