Revising the cross correlation technique at high spectral resolution

TL;DR

This paper revises the cross-correlation technique for high spectral resolution data, adapting it for better accuracy with modern spectrographs and analyzing its assumptions and errors.

Contribution

It develops an adapted cross-correlation method for very high spectral resolution data and compares its performance on different spectrograph datasets.

Findings

The Gaussian assumption of the cross-correlation function breaks down at high resolutions.

Masking nebular lines introduces significant errors in velocity dispersion measurements.

Proposes a new method to calculate broadening functions using galaxy-galaxy and star-galaxy correlations.

Abstract

Cross-correlation techniques have been used since 1974 for measuring velocity shifts and velocity dispersions from stellar and nebular spectra and, since 1979, the analysis based on the Fourier Method has been applied. However, we are currently obtaining data with spectral resolutions higher than those for which this technique was developed, hence some revision seems timely. The principal aim of this work is adapting Tonry and Davis' method and implementing it for the treatment of very high spectral resolution data. We have applied this technique to two different sets of spectroscopic data of moderate and high resolutions obtained with the MUSE and MEGARA spectrographs respectively. Using stellar spectra obtained with these two instruments (i) we have optimised the input parameters; (ii) we have analysed the method assumptions; and (iii) we have compared the results for the two sets of data. For MEGARA data, we have found that the cross-correlation function lost its Gaussian behavior at higher resolutions. Thus, we have developed an equivalent mathematical method that can be used for this kind of data. Additionally, the velocity dispersion error analysis suggests that the greatest error introduced in this method is due to the subtraction or masking of the nebular lines. For the application of cross-correlation techniques to high spectral resolution data, we propose to calculate the galaxy-galaxy and star-galaxy correlations, with widths $\mu_{gg}$ and $\mu_{gt}$ respectively. Then, the width of the broadening function can be calculated as $\sigma = \sqrt{\mu_{gg}^2 - \mu_{gt}^2}$.