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

One 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 of extending 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 the 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 the Catania Astrophysical Observatory Spectropolarimeter (CAOS). We show that themulti-line slope method is a fast alternative to the least squares deconvolution 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 is an element of 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.