Measurements of microturbulence of Cepheids using the autocorrelation function

Abstract

The autocorrelation function (ACF) is a simple and useful tool that allows us to measure the average linewidth of spectra with great precision. Unlike the cross-correlation function, the ACF can be used without having to rely on weighted binary masks. It makes the ACF much easier to use. We analyse seven Cepheids and present a new method to obtain very precise turbulent velocity curves for six of them using the ACF. We compare our full width at half-maximum (FWHM) curves as a function of the pulsational phase to those of Nardetto et al., who used the Fe i 6056.005 Å line only. We note a significant improvement in the shape of the FWHM curves for all Cepheids on using the ACF. From the FWHM curves, we measure microturbulence curves for six Cepheids using a Gaussian approximation. Finally, we artificially degrade the resolution of the spectra and add noise to further assess and highlight the advantages of the ACF. The FWHM curves obtained with the ACF remain virtually unchanged up to degradation by a factor of 10. Degradation by a factor of 20 slightly affected the results but an average linewidth variation remains easily detectable.