The multi-line slope method for measuring the effective magnetic field of cool stars: an application to the solar-like cycle of ε Eri

Abstract

A method for the determination of integrated longitudinal stellar fields from low-resolution spectra is the so-called slope method, which is based on the regression of the Stokes V signal against the first derivative of Stokes I. Here we investigate the possibility to extend this technique to measure the magnetic fields of cool stars from high resolution spectra. For this purpose we developed a multi-line modification to the slope method, called multi-line slope method. We tested this technique by analysing synthetic spectra computed with the COSSAM code and real observations obtained with the high resolution spectropolarimeters Narval, HARPSpol and Catania Astrophysical Observatory Spectropolarimeter (CAOS). We show that the multi-line slope method is a fast alternative to the Least Squares Deconvolution (LSD) technique for the measurement of the effective magnetic fields of cool stars. Using a Fourier transform on the effective magnetic field variations of the star $\epsilon$ Eri, we find that the long term periodicity of the field corresponds to the 2.95 yr period of the stellar dynamo, revealed by the variation of the activity index.