Blakesley Burkhart

DENSITY STUDIES OF MHD INTERSTELLAR TURBULENCE: STATISTICAL MOMENTS, CORRELATIONS AND BISPECTRUM

We present a number of statistical tools that show promise for obtaining information on turbulence in molecular clouds (MCs) and diffuse interstellar medium (ISM). For our tests we make use of three-dimensional 5123 compressible MHD isothermal simulations performed for different sonic, i.e., , where VL is the injection velocity, Vs is the sound velocity, and Alfvenic , where VA is the Alfven velocity, Mach numbers. We introduce the bispectrum, a new tool for statistical studies of the interstellar medium which, unlike an ordinary power spectrum of turbulence, preserves the phase information of the stochastic field. We show that the bispectra of the three-dimensional stochastic density field and of column densities, available from observations, are similar. This opens good prospects for studies of MCs and diffuse media with the new tool. We use the bispectrum technique to define the role of nonlinear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. As expected, a strong correlation is obtained for wave modes k 1 = k 2 for all models. Larger values of result in increased correlations for modes with k 1 ≠ k 2. This effect becomes more evident with increasing magnetic field intensity. We believe that the different MHD wave modes, e.g., Alfven and magneto-acoustic, which arise in strongly magnetized turbulence, may be responsible for the increased correlations compared to purely hydrodynamical perturbations. In addition to the bispectrum, we calculated the third and fourth statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with . In particular, as increases, so does the Gaussian asymmetry of the density distribution. We also studied the correlations of two-dimensional column density with dispersion of velocities and magnetic field, as well as the correlations of three-dimensional density with magnetic and kinetic energy and for comparison. Our results show that column density is linearly correlated with magnetic field for high . This trend is independent of the turbulent kinetic energy and can be used to characterize inhomogeneities of physical properties in low density clumps in the ISM.

INTERSTELLAR SONIC AND ALFVÉNIC MACH NUMBERS AND THE TSALLIS DISTRIBUTION

In an effort to characterize the Mach numbers of interstellar medium (ISM) magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of spatial increments of density, velocity, and magnetic field for 14 ideal isothermal MHD simulations at a resolution of 5123. In particular, we fit the PDFs using the Tsallis function and study the dependency of the fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfv?n Mach numbers. For three-dimensional density, column density, and Position-Position-Velocity data, we find that the amplitude and width of the PDFs show a dependency on the sonic Mach number. We also find that the width of the PDF is sensitive to the global Alfv?nic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize the sonic and Alfv?nic Mach numbers of simulated ISM turbulence points to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.

THE TURBULENCE POWER SPECTRUM IN OPTICALLY THICK INTERSTELLAR CLOUDS

The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic (MHD) turbulence in the interstellar medium. Lazarian & Pogosyan predicted that the spectral slope should saturate to –3 for an optically thick medium and many observations exist in support of their prediction. However, there have not been any numerical studies to date for testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfvenic Mach numbers, which include radiative transfer effects of the 13CO transition. We numerically confirm the predictions of Lazarian & Pogosyan that the spectral slope of line intensity maps of an optically thick medium saturates to –3. Furthermore, for very optically thin supersonic CO gas, where the density or CO abundance values are too low to excite emission in all but the densest shock compressed gas, we find that the spectral slope is shallower than expected from the column density. Finally, we find that mixed optically thin/thick CO gas, which has average optical depths on the order of unity, shows mixed behavior: for super-Alfvenic turbulence, the integrated intensity power spectral slopes generally follow the same trend with sonic Mach number as the true column density power spectrum slopes. However, for sub-Alfvenic turbulence the spectral slopes are steeper with values near –3 which are similar to the very optically thick regime.

The Turbulence Velocity Power Spectrum of Neutral Hydrogen in the Small Magellanic Cloud

We present the results of the Velocity Coordinate Spectrum (VCS) technique to calculate the velocity power spectrum of turbulence in the Small Magellanic Cloud (SMC) in 21cm emission. We have obtained a velocity spectral index of -3.85 and an injection scale of 2.3 kpc. The spectral index is steeper than the Kolmogorov index which is expected for shock-dominated turbulence which is in agreement with past works on the SMC gas dynamics. The injection scale of 2.3 kpc suggests that tidal interactions with the Large Magellanic Cloud are the dominate driver of turbulence in this dwarf galaxy. This implies turbulence maybe driven by multiple mechanisms in galaxies in addition to supernova injection and that galaxy-galaxy interactions may play an important role.

Measuring the Alfvénic nature of the interstellar medium: Velocity anisotropy revisited

The dynamics of the interstellar medium (ISM) are strongly affected by turbulence, which shows increased anisotropy in the presence of a magnetic field. We expand upon the Esquivel & Lazarian method to estimate the Alfven Mach number using the structure function anisotropy in velocity centroid data from position-position-velocity maps. We utilize 3D magnetohydrodynamic (MHD) simulations of fully developed turbulence, with a large range of sonic and Alfvenic Mach numbers, to produce synthetic observations of velocity centroids with observational characteristics such as thermal broadening, cloud boundaries, noise, and radiative transfer effects of carbon monoxide. In addition, we investigate how the resulting anisotropy-Alfven Mach number dependency found in Esquivel & Lazarian (2011) might change when taking the second moment of the position-position-velocity cube or when using different expressions to calculate the velocity centroids. We find that the degree of anisotropy is related primarily to the magnetic field strength (i.e. Alfven Mach number) and the line-of-sight orientation, with a secondary effect on sonic Mach number. If the line-of-sight is parallel to up to ~45 deg off of the mean field direction, the velocity centroid anisotropy is not prominent enough to distinguish different Alfvenic regimes. The observed anisotropy is not strongly affected by including radiative transfer, although future studies should include additional tests for opacity effects. These results open up the possibility of studying the magnetic nature of the ISM using statistical methods in addition to existing observational techniques.

Galactic interstellar turbulence across the southern sky seen through spatial gradients of the polarization vector

Radio synchrotron polarization maps of the Galaxy can be used to infer the properties of interstellar turbulence in the diffuse warm ionized medium (WIM). In this paper, we investigate the spatial gradient of linearly polarized synchrotron emission (

Hierarchical Structure of Magnetohydrodynamic Turbulence in Position-Position-Velocity Space

|\nabla\textbf{P}|/|\textbf{P}|

The Effects of Radiative Transfer on the Probability Distribution Functions of Molecular Magnetohydrodynamic Turbulence

) as a tracer of turbulence, the relationship of the gradient to the sonic Mach number of the WIM, and changes in morphology of the gradient as a function of Galactic position in the southern sky. We use data from the S-band Polarization All Sky Survey (S-PASS) to image the spatial gradient of the linearly polarized synchrotron emission (

The Interaction of Relativistic Spacecrafts with the Interstellar Medium

|\nabla \textbf{P}|/|\textbf{P}|

The H i-to-H2 Transition in a Turbulent Medium

) of the entire southern sky at