Velocities from Cross-Correlation: A Guide for Self-Improvement

TL;DR

This paper introduces a 'self-improvement' technique to enhance the accuracy of velocity measurements from spectra by ensuring consistency across multiple observations, significantly improving precision especially at low signal-to-noise ratios.

Contribution

It proposes a novel iterative method for refining velocity estimates by leveraging all pairwise spectral comparisons, improving accuracy in large spectroscopic surveys.

Findings

Refined relative velocities by over 50% at low S/N ratios.

Applicable to combining multiple observations into a single high-quality spectrum.

Demonstrated effectiveness with simulated G-type star survey data.

Abstract

The measurement of Doppler velocity shifts in spectra is a ubiquitous theme in astronomy, usually handled by computing the cross-correlation of the signals, and finding the location of its maximum. This paper addresses the problem of the determination of wavelength or velocity shifts among multiple spectra of the same, or very similar, objects. We implement the classical cross-correlation method and experiment with several simple models to determine the location of the maximum of the cross-correlation function. We propose a new technique, 'self-improvement', to refine the derived solutions by requiring that the relative velocity for any given pair of spectra is consistent with all others. By exploiting all available information, spectroscopic surveys involving large numbers of similar objects may improve their precision significantly. As an example, we simulate the analysis of a survey of G-type stars with the SDSS instrumentation. Applying 'self-improvement' refines relative radial velocities by more than 50% at low signal-to-noise ratio. The concept is equally applicable to the problem of combining a series of spectroscopic observations of the same object, each with a different Doppler velocity or instrument-related offset, into a single spectrum with an enhanced signal-to-noise ratio.