Random-error minimization during cross-correlation of early-type spectra

Astrophysics Research Group, University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

Send offprint request to: W. Verschueren

Received: 16 October 1998
Accepted: 18 February 1999

Abstract

Owing to the typical morphology of spectra of early-type stars, random errors play a much more important role in the derivation of their radial velocities than in the case of late-type spectra. We derive a generalised lower bound of the random error on a cross-correlation derived radial velocity shift in the presence of random noise on both object and template spectrum, and discuss its dependence on spectral parameters and noise. In order to limit in practice the random error to this lower bound for early-type spectra, we show that a number of specific cross-correlation peak centering techniques are required. The influence of rotational mismatch between object and template on the random error is examined. Finally, the widely used error estimate based on the so-called r-statistic is critically evaluated in the context of early-type spectra.