Bringing the cross-correlation method up to date

Abstract

The cross-correlation (XC) method of Tonry & Davis (1979, AJ, 84, 1511) is generalized to arbitrary parametrized line profiles. In the new algorithm the correlation function itself, rather than the observed galaxy spectrum, is fitted by the model line profile: this removes much of the complication in the error analysis caused by template mismatch. Like the Fourier correlation quotient (FCQ) method of Bender (1990, A&A, 229, 441), the inferred line profiles are, up to a normalization constant, independent of template mismatch as long as there are no blended lines. The standard reduced chi(exp 2) is a good measure of the fit of the inferred velocity distribution, largely decoupled from the fit of the spectral template. The updated XC method performs as well as other recently developed methods, with the added virtue of conceptual simplicity.