The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-Dependent PCA Calibration

TL;DR

This study investigates how turbulence spectra in molecular clouds can be accurately derived from spectral maps by calibrating PCA, accounting for density effects, and applying the method to Galactic Ring Survey data.

Contribution

The paper develops a PCA calibration method that accounts for density effects and intermittency, improving turbulence spectrum measurements in molecular clouds.

Findings

PCA is insensitive to density spectral index and low density dispersion.

For high density dispersion, PCA slope increases with dispersion due to intermittency.

Calibrated PCA suggests turbulence velocity exponent ~1.9 in molecular clouds.

Abstract

Turbulence plays a major role in the formation and evolution of molecular clouds. The problem is that turbulent velocities are convolved with the density of an observed region. To correct for this convolution, we investigate the relation between the turbulence spectrum of model clouds, and the statistics of their synthetic observations obtained from Principal Component Analysis (PCA). We apply PCA to spectral maps generated from simulated density and velocity fields, obtained from hydrodynamic simulations of supersonic turbulence, and from fractional Brownian motion fields with varying velocity, density spectra, and density dispersion. We examine the dependence of the slope of the PCA structure function, alpha_PCA, on intermittency, on the turbulence velocity (beta_v) and density (beta_n) spectral indexes, and on density dispersion. We find that PCA is insensitive to beta_n and to the log-density dispersion sigma_s, provided sigma_s < 2. For sigma_s>2, alpha_PCA increases with sigma_s due to the intermittent sampling of the velocity field by the density field. The PCA calibration also depends on intermittency. We derive a PCA calibration based on fBms with sigma_s<2 and apply it to 367 CO spectral maps of molecular clouds in the Galactic Ring Survey. The average slope of the PCA structure function, <alpha_PCA>=0.62\pm0.2, is consistent with the hydrodynamic simulations and leads to a turbulence velocity exponent <beta_v>=2.06\pm0.6 for a non-intermittent, low density dispersion flow. Accounting for intermittency and density dispersion, the coincidence between the PCA slope of the GRS clouds and the hydrodynamic simulations suggests beta_v~1.9, consistent with both Burgers and compressible intermittent turbulence.