Turbulence Spectra from Doppler-broadened Spectral Lines: Tests of the Velocity Channel Analysis and Velocity Coordinate Spectrum Techniques

TL;DR

This paper numerically tests two key spectral analysis techniques, VCA and VCS, for studying turbulence through Doppler-broadened spectral lines, highlighting resolution requirements and effective sampling strategies.

Contribution

It provides a detailed numerical validation of VCA and VCS methods, including shot noise analysis and resolution dependence, for turbulence spectrum recovery.

Findings

Shot noise expression derived and tested.

Resolution depends on velocity spectral index.

Sampling along a dozen directions suffices for absorption lines.

Abstract

Turbulent motions induce Doppler shifts of observable emission and absorption lines motivating studies of turbulence using precision spectroscopy. We provide the numerical testing of the two most promising techniques, Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS). We obtain an expression for the shot noise that the discretization of the numerical data entails and successfully test it. We show that the numerical resolution required for recovering the underlying turbulent spectrum from observations depend on the spectral index of velocity fluctuations, which makes low resolution testing misleading. We demonstrate numerically that, dealing with absorption lines, sampling of turbulence along just a dozen directions provides a high quality spectrum with the VCS technique.