Characterizing Magnetohydrodynamic Turbulence in the Small Magellanic Cloud

Abstract

We investigate the nature and spatial variations of turbulence in the Small Magellanic Cloud (SMC) by applying several statistical methods on the neutral hydrogen (HI) column density image of the SMC and a database of isothermal numerical simulations. By using the 3rd and 4th statistical moments we derive the spatial distribution of the sonic Mach number (M s ) across the SMC. We find that about 90% of the HI in the SMC is subsonic or transonic. However, edges of the SMC 'bar' have M s ∼ 4 and may be tracing shearing or turbulent flows. Using numerical simulations we also investigate how the slope of the spatial power spectrum depends on both sonic and Alfvén Mach numbers. This allows us to gauge the Alfvén Mach number of the SMC and conclude that its gas pressure dominates over the magnetic pressure. The super-Alfvénic nature of the HI gas in the SMC is also highlighted by the bispectrum, a three-point correlation function which characterizes the level of non-Gaussianity in wave modes. We find that the bispectrum of the SMC HI column density displays similar largescale correlations as numerical simulations, however it has localized enhancements of correlations. In addition, we find a break in correlations at a scale of ∼ 160 pc. This may be caused by numerous expanding shells of a similar size.

The Phase Coherence of Interstellar Density Fluctuations

“…Recently, several studies have promoted the study of phase information for ISM MHD turbulence. These include threepoint statistics, such as the bispectrum studied here and in Burkhart et al (2009Burkhart et al ( , 2010. Furthermore, it was recently shown in Correia et al (2016) that the principle component analysis (PCA; see Heyer & Schloerb 1997;Heyer et al 2008) is sensitive to the phase information.…”

“…This led to extensive studies of alternative measures of turbulence. Probability distribution functions of column densities, including different measures obtained with them, e.g., skewness and kurtosis (Burkhart et al 2009(Burkhart et al , 2010, Tsalis statistics (Esquivel & Lazarian 2010;Toffelmire, Burkhart & Lazarian 2011), and dispersion (Burkhart & Lazarian 2012), were considered as tools to obtain the properties of turbulence from observations. Together with the techniques for the anisotropy of turbulence studies Esquivel & Lazarian 2011;Heyer et al 2008;Burkhart et al 2014) and intermittency studies (Padoan et al 2004;Kowal et al 2007), they present an impressive toolbox for quantitative studies of interstellar turbulence.…”

“…In particular, Burkhart et al (2009) found that this result applied to both 3D density and observable 2D column density. Due to the bispectrum's sensitivity to the sonic Mach number and magnetic field when applied to column density, Burkhart et al (2010) performed a follow-up study on the HI column density map of the SMC in order to constrain the nonlinear interaction of turbulence in atomic hydrogen gas. Burkhart et al (2010) also compared the bispectrum to other statistical methods for obtaining turbulence parameters.…”

“…The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the power spectrum while the Fourier transform of the third-order cumulant is known as the bispectrum. The bispectrum contains information on both amplitude and phase and has been applied to both MHD simulations (Burkhart et al 2009;Cho & Lazarian 2009) and observations of neutral hydrogen (Burkhart et al 2010). These studies found that the bispectrum is a sensitive diagnostic for the sonic and Alfvénic Mach numbers and can describe the behavior of nonlinear mode correlation across spatial scales.…”

Galactic and Magellanic Evolution with the SKA

“…It will be particularly important to test whether the neutral medium has structure similar to the extreme scattering events (ESE) in the ionized gas (Fiedler et al 1987;Walker & Wardle 1998), and to match structures in the H I with scattering screens deduced from pulsar scintillation (Bhat & Gupta 2002). Additional statistical measures such as those proposed by Burkhart et al (2010) will probe deeper into the fluctuations of the ISM.…”