Magnetic field of the roAp star KIC~10685175: observations versus theory

KIC 10685175 is a roAp star whose polar magnetic field is predicted to be 6 kG through a non-adiabatic axisymmetric pulsation theoretical model. In this work, we aim to measure the magnetic field strength of KIC 10685175 using high-resolution spectropolarimetric observations, and compare it with the one predicted by the theoretical model. From the study of two high-resolution unpolarized spectra, we obtained [$T_{\rm eff}$, $\log g$, [Fe/H], [$\alpha$/Fe], $V_{mic}$]=[8250 $\pm$ 200\,K, 4.4 $\pm$ 0.1, -0.4 $\pm$ 0.2, 0.16 $\pm$ 0.1, 1.73 $\pm$ 0.2\,km~s$^{-1}$]. Although the Fe absorption lines appear relatively weak in comparison to typical Ap stars with similar $T_{\rm eff}$, the lines belonging to rare earth elements (Eu and Nd) are stronger than that in chemically normal stars, indicating the peculiar nature of KIC~10685175. The mean longitudinal magnetic field $\langle B_\ell \rangle=-226\pm39$\,G has been measured in the polarized spectrum, but magnetically split lines were not detected. No significant line profile variability was evident in our spectra. Also the longitudinal magnetic field strengths measured using line masks constructed for different elements have been rather similar. Due to a poor rotation phase coverage of our data, additional spectroscopic and polarimetric observations are needed to allow us to conclude on the inhomogeneous element distribution over the stellar surface. The estimated polar magnetic field is $4.8 \pm 0.8$\,kG, which is consistent with the predicted polar magnetic field strength of about 6\,kG within 3$\sigma$. This work therefore provides support for the pulsation theoretical model.