Study of photometric and spectral variability of the roAp star HD~210684

Abstract

This paper studies photometric and spectropolarimetric variability of HD210684 in order to derive its magnetic properties, rotational period, evolutionary stage, and global stellar parameters. The Discrete Fourier Transform is used to measure frequencies and amplitudes of periodic signals present in light curves of HD210684. Evolution models are calculated with MESA, while roAp type pulsations are simulated with GYRE. The values of $T_{eff}$, log(g), $v\sin{i}$, and radial velocity (RV) are derived from the best fit of Balmer line profiles using FITSB2. The Least Square Deconvolution (LSD) method is applied to available Stokes I&V spectra to measure the mean longitudinal magnetic field <Bz> and RV. Detailed analysis of photometric variability reveals rotational modulation with period P=5.02188$\pm$0.00005d and splitting of high-overtone pulsations that corresponds to the same rotational period. Derived <Bz> measurements also show periodic variability with P=5.02188d, but this variability appears to be different from the one predicted by a centred magnetic dipole model. We have determined the inclination angle between the line of sight and the rotation axis to be $i = 31^{\circ} \pm 2^{\circ}$, and the angle between the rotation and magnetic dipole axes as $β= 77^{\circ} \pm 3^{\circ}$. Simulations of stellar pulsations constrain $\log T_{eff}$<3.85 and show that our best fitting model depends on whether the observed modes are $\ell = 1$ or $\ell =2$. Considering the derived value of $β$, we prefer the best fit model with $\ell =2$ mode, which predicts that HD210684 lies on the main sequence with an age of approximately 1.45Gyr. The best fit of Balmer line profiles has resulted in higher values of $T_{eff}$ and log(g) for spectra acquired at rotational phases $φ$= 0.14 - 0.39 suggesting visibility of an area with higher surface temperature.