Extending velocity channel analysis for studying turbulence anisotropies

Abstract

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 Alfvén, slow and fast magnetohydrodynamical modes are different, in particular, the anisotropy in PPV created by fast modes is opposite to that created by Alfvén 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.

Velocity Gradients as a Tracer for Magnetic Fields

“…These intrinsic properties of the eddies imprinted by the Alfvénic turbulence imply not only the condition of a preferential direction along the local magnetic field, but also that the eddy velocity depends the size of the eddy. The effects of the anisotropy of the velocity fluctuations on the turbulent medium have been described by analyzing intensity anisotropies of spectral line cube velocity channels Burkhart et al 2014;Esquivel et al 2015;Kandel et al 2016b), correlations of velocity centroids (Esquivel & Lazarian 2005;Federrath et al 2010;Kandel et al 2016a), the bispectrum (Burkhart et al 2009), and higher order statistical moments (Kowal et al 2007), as well as using Principal Component Analysis (PCA) (Heyer et al 2008). All these techniques, however, require that the statistical samples that limit their ability to trace magnetic fields over sufficiently small patches of the sky.…”

“…Velocity centroids were also suggested as a means of measuring anisotropy of turbulence using velocity correlations (Esquivel & Lazarian 2005Burkhart et al 2014). A theoretical elaboration of the latter technique using the analytical description of PPV (Lazarian & Pogosyan 2000, 2008 was obtained in Kandel et al (2016a). In the VGT we do not use correlations of centroids, but their gradients.…”

“…The velocity centroids can be calculated using raw interferometric data (see Kandel et al 2016b). Therefore gradients can be obtained with this data and used to trace magnetic fields in distant objects, in other galaxies.…”

Anisotropies in the HI gas distribution toward 3C 196

“…We can draw here our first conclusion about the nature of the observed MHD turbulence. According to Kandel et al (2016) Alfvén and slow modes cause the eddies to be elongated in direction parallel to the sky-projected mean magnetic field, while for fast modes the elongation is perpendicular. We find elongation parallel to the magnetic field, hence no evidence for fast modes.…”

Effects of the magnetic field direction on the Tsallis statistic

“…These calculations have been done on scintillation fluctuations (Narayan & Goodman 1989), density fluctua-E-mail: casanova@astro.wisc.edu † E-mail: lazarian@astro.wisc.edu tions via column density (Falgarone et al 1994;Lis et al 1998;Miesch et al 1999) and radio spectroscopy (Lithwick & Goldreich 2001;Cho & Lazarian 2003). The power index can also be estimated from position-position-velocity (PPV) data via Velocity Channel Analysis (VCA Lazarian & Pogosyan 2000;Padoan et al 2003;Kandel et al 2016), Spectral Correlation Function (Rosolowsky et al 1999;Padoan et al 2001), and Velocity Coordinate Spectrum (VCS Lazarian & Pogosyan 2006, 2008Padoan et al 2009), among others.…”