Magnetic field topology of the cool, active, short-period binary system $σ^2$ Coronae Borealis
The goal of this work is to study the cool, active binary star $σ^2$ CrB, focussing on its magnetic field. We used Stokes $IV$ data from the twin spectropolarimeters Narval at the TBL and ESPaDOnS at the CFHT. The least-squares deconvolution multi-line technique was used to increase the signal-to-noise ratio of the data. We then applied a new binary Zeeman-Doppler imaging code to reconstruct simultaneously the magnetic topology and brightness distribution of both components. This analysis was carried out for two observational epochs in 2014 and 2017. A previously unconfirmed magnetic field of the primary star has been securely detected. The polarisation signatures of the secondary appear to have a systematically larger amplitude than that of the primary. This corresponds to a stronger magnetic field, for which the magnetic energy of the secondary exceeds that of the primary by a factor of 3.3-5.7. While the magnetic energy is similar for the secondary star in the two epochs, the magnetic energy is about twice as high in 2017 for the primary. The magnetic field topology of the two stars in the earlier epoch (2014) is very different. In the earlier epoch, the magnetic field at the visible pole appears to be of opposite polarity for the primary and secondary, suggesting linked magnetospheres. The apparent rotational periods of both $σ^2$ CrB components are longer than the orbital period, which we interpret as an evidence of a solar-like differential rotation. Despite their nearly identical fundamental parameters, the components of $σ^2$ CrB system exhibit different magnetic field properties. This indicates that the magnetic dynamo process is a very sensitive function of stellar parameters.