The rotational and magnetic properties of Polaris from long-term spectropolarimetric monitoring

Abstract

Polaris is a highly unusual Cepheid with observed properties that are difficult to reconcile with stellar evolutionary models. Since the initial detection of Polaris' magnetic field in 2020, we have conducted a magnetic monitoring campaign with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. We compute Stokes $V$ least-squares deconvolution profiles and measure the associated mean longitudinal magnetic field strengths $\langle B_{z}\rangle$. The surface magnetic field has remained remarkably stable over five years of observations, with $\langle B_{z}\rangle$ varying between approximately $-3$ G and $+0.6$ G. From the periodic modulation of $\langle B_{z}\rangle$ we infer a stellar rotation period of $P_{\mathrm{rot}}=100.29\pm0.19$ days. This is the first direct measurement of $P_{\mathrm{rot}}$ for a classical Cepheid. Previous interferometric radius measurements and $P_{\mathrm{rot}}$ imply an equatorial rotation velocity of $v_{\mathrm{eq}}=23.3\pm0.2$ km s$^{-1}$. We set a conservative upper bound on the projected equatorial rotational velocity of $v_{\mathrm{eq}}\sin i_{\star} < 13.5$ km s$^{-1}$ and constrain the stellar inclination angle to be $i_{\star}<37^{\circ}$. Using the previously determined orbital solution, we find a high likelihood of a strong spin-orbit misalignment. We determine the lower bound on the obliquity angle between the stellar rotation and orbital axes to be $β>18.7^{\circ}$ at 99% confidence. We discuss the challenges in interpreting the origin and properties of the surface magnetic field in the context of Polaris' uncertain evolutionary history and the merger hypothesis.

Figures (17)

• Figure 1: Offset corrected $\mathrm{RV}_{\mathrm{cog}}$ measurements (black markers) shown in relation to the best fit orbital RV curve (solid blue line) given by Evans_2024. The scatter in $\mathrm{RV}_{\mathrm{cog}}$ is due to pulsation.
• Figure 2: Top: Orbit and offset corrected RV measurements shown over two pulsation cycles. The grey lines show 100 random samples drawn from the MCMC joint posterior distribution. Bottom: Variation in radius inferred from the best fit pulsation model. The black dotted lines correspond to $R_{\mathrm{min}}$ and the dashed coloured lines correspond to the LSD profiles shown in Fig. \ref{['fig:LSD_StokesIV_pulsation']}.
• Figure 3: From top to bottom: GLS periodogram of $\langle B_{z}\rangle$ measurements, GLS periodogram of $\langle B_{z}\rangle$ residuals after subtraction of best fitting model, GLS periodogram of model $\langle B_{z}\rangle$ curve and window power spectrum. The solid and dashed grey lines denote the $0.01$ and $0.001$ FAP levels respectively. The blue 'X' denotes $P_{\mathrm{rot}}$ and red triangles denote long period aliases. Grey shaded regions indicate allowed rotation periods above $P_{\mathrm{rot}}^{\mathrm{min}}$.
• Figure 4: Polaris $\langle B_{z} \rangle$ measurements plotted as a function of HJD (left) and $\phi_{\mathrm{rot}}$ (right). The marker shapes and colours denote $N_{\mathrm{rot}}$. The grey lines show 100 random samples drawn from the MCMC joint posterior distribution.
• Figure 5: Continuum normalized and $\mathrm{RV}_{\mathrm{cog}}$ corrected LSD profiles of Polaris plotted as a function of $\phi_{\mathrm{rot}}$. From left to right, LSD Stokes $I$ (black), LSD Stokes $V$ (red) and LSD $N$ (blue). The vertical dashed gray lines mark the integration bounds in the FAP and $\langle B_{z}\rangle$ analysis.