Magnetic field of the roAp star KIC 10685175: Observations versus theory

Context. KIC 10685175 is a roAp star whose polar magnetic field is predicted to be 6 kG through a nonadiabatic axisymmetric pulsation theoretical model.Aims. 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.Methods. Two high-resolution unpolarized spectra have been analyzed to ascertain the presence of magnetically split lines and derive the iron abundance of this star through equivalent width measurements of 10 Fe lines. One polarized spectrum has been used to measure the mean longitudinal magnetic field with the least-squares deconvolution technique. Further, to examine the presence of chemical spots on the stellar surface, we have measured the mean longitudinal magnetic fields using different lines belonging to different elements.Results. From the study of two high-resolution unpolarized spectra, we obtained the spectroscopic atmospheric parameters including the effective temperature (T_{eff), surface gravity (log 𝑔), iron abundance ([Fe/H]), abundance ratio of alpha elements to iron ([α/Fe]), and micro-turbulent velocity (Vmic). The final result is [Teff, log g, [Fe/H], [α/Fe], Vmic)]=[8250 ± 200 K, 4.4 ± 0.1, −0.4 ± 0.2, 0.16 ± 0.1, 1.73 ± 0.2 km s^{−1]. Although the Fe absorption lines appear relatively weak in comparison to typical Ap stars with similar Teff, the lines belonging to rare earth elements (Eu and Nd) are stronger than those in chemically normal stars, indicating the peculiar nature of KIC 10685175. The mean longitudinal magnetic field, 〈Bℓ〉 = −226 ± 39 G, was measured in the polarized spectrum, but magnetically split lines were not detected. No significant line profile variability is evident in our spectra. Also, the longitudinal magnetic field strengths measured using line masks constructed for different elements are rather similar. Due to the poor rotation phase coverage of our data, additional spectroscopic and polarimetric observations are needed to allow us to come to any conclusions about the inhomogeneous element distribution over the stellar surface.Conclusions. The estimated polar magnetic field is 4.8 ± 0.8 kG, which is consistent with the predicted polar magnetic field strength of about 6kG within 3σ. This work therefore provides support for the pulsation theoretical model.}}