The 19th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun Edited by G. A. Feiden Monitoring of the magnetic ﬁeld topology and activity of the core helium-burning giant β Ceti in the period 2010-2013 Svetla Tsvetkova1, Pascal Petit2,3, Renada Konstantinova-Antova1,3, Michel Aurière2,3, Gregg A. Wade4, Corinne Charbonnel5, Rumen Bogdanovski1, Ana Borisova1 1 Institute of Astronomy and NAO, Bulgarian Academy of Sciences, 72 Tsarigradsko shose, 1784 Soﬁa, Bulgaria stsvetkova@astro.bas.bg 2 CNRS, Institut de Recherche en Astrophysique et Planétologie, IRAP, 14 Avenue Edouard Belin, 31400 Toulouse, France 3 Université de Toulouse, UPS-OMP, IRAP, Toulouse, France 4 Department of Physics, Royal Military College of Canada, PO Box 17000, Station ‘Forces’, Kingston, Ontario, Canada K7K 4B4 5 Geneva Observatory, University of Geneva, 51, Chemin des Maillettes, 1290 Versoix, Switzerland Abstract β Ceti is a slowly rotating (v sin i = 3.5 km s−1) single giant. In our previous study (Tsvetkova et al. (2013)) we showed that it is in the core He-burning phase and we reconstructed two Zeeman Doppler imaging (ZDI) maps (using data from 2010 and 2011) revealing a simple large-scale magnetic ﬁeld structure. We concluded that the magnetic ﬁeld of β Ceti could have a fossil ﬁeld origin. In addition, the study of Aurière et al. (2015) about the properties and origin of the magnetism of late-type giants, where β Ceti was a member of that sample, revealed that this star did not follow the general trends for dynamo-generated magnetic ﬁelds. Now, we present a new ZDI map of β Ceti and compare the new results with our previous study. This monitoring for several years of the magnetic ﬁeld topology and line activity indicators variability supports our previous conclusion about the fossil ﬁeld origin of the magnetic ﬁeld of β Ceti. 1 Introduction β Ceti (HD 4128) is a star of spectral class K0 with V = 2.04 mag and B −V = 1.02 mag. It is a single giant with the highest X-ray luminosity log Lx = 30.2 erg s−1 (Maggio et al. (1998); Hünsch et al. (1996)) in the near solar neighborhood (d ≤30 pc). Magnetic events such as coronal loops (Eriksson et al. (1983)) and ﬂares (Ayres et al. (2001)) have been detected. It is a slowly rotating giant with v sin i = 3.5 km s−1. In the previous study of Tsvetkova et al. (2013), we showed that β Ceti is a 3.5 M⊙giant in the core helium- burning phase with a radius of 18 R⊙. The main se- quence progenitor of β Ceti was a late B-type star. We were able to reconstruct two magnetic maps of the sur- face magnetic ﬁeld topology of the star employing the ZDI technique. Both maps showed that the large-scale magnetic ﬁeld of β Ceti was dominated by the poloidal component. The behavior of the line activity indicators Hα, CaII K, CaII IR (854.2 nm), and the radial veloc- ity correlated rather well with the longitudinal magnetic ﬁeld Bl. Our main conclusion was that the magnetism of β Ceti might be (at least partly) of fossil origin and inherited from a main sequence Ap/Bp star. Here, we present a new dataset of β Ceti. We are able to reconstruct one more ZDI map and to compare the new results with the previous study. 2 Observations and data reduction 1 Observational data were obtained with two twin ﬁber-fed echelle spectropolarimeters – Narval (Aurière (2003)), which operates at the 2-m Bernard Lyot Téle- scope (TBL) at Pic du Midi Observatory, France, and ESPaDOnS (Donati et al. (2006a)), which operates at the 3.6-m Canada-France-Hawaii Telescope (CFHT) of Mauna Kea Observatory, Hawaii. In polarimetric mode, both have a spectral resolution of about 65 000 and a nearly continuous spectrum coverage from the near- ultraviolet (at about 370 nm) to the near-infrared domain (at 1050 nm) in a single exposure, with 40 orders aligned on the CCD frame by two cross-disperser prisms. Stokes I (unpolarized light) and Stokes V (circular polarization) parameters are simultaneously obtained by four subex- posures between which the retard