Principal Component Analysis studies of turbulence in optically thick gas

TL;DR

This study explores how Principal Component Analysis (PCA) can detect turbulence characteristics in high-opacity interstellar gas, revealing its sensitivity to phase information and potential as a turbulence diagnostic tool.

Contribution

It demonstrates PCA's sensitivity to phase information in PPV cubes and its ability to detect velocity and density spectra changes at high opacities, unlike traditional spectral analysis methods.

Findings

PCA is sensitive to phase information in PPV data.

PCA can detect changes in velocity and density spectra at high opacities.

PCA results vary irregularly with high sonic Mach numbers.

Abstract

In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes of fractional Brownian motion (fBm) and magnetohydrodynamics (MHD) simulations, post processed to include radiative transfer effects from CO. We find that PCA analysis is very different from the tools based on the traditional power spectrum of PPV data cubes. Our major finding is that PCA is also sensitive to the phase information of PPV cubes and this allows PCA to detect the changes of the underlying velocity and density spectra at high opacities, where the spectral analysis of the maps provides the universal -3 spectrum in accordance with the predictions of Lazarian \& Pogosyan (2004) theory. This makes PCA potentially a valuable tool for studies of turbulence at high opacities provided that the proper gauging of the PCA index is made. The later, however, we found to be not easy, as the PCA results change in an irregular way for data with high sonic Mach numbers. This is in contrast to synthetic Brownian noise data used for velocity and density fields that show monotonic PCA behavior. We attribute this difference to the PCA's sensitivity to Fourier phase information.