Refining the Stellar Parameters of $\tau$ Ceti: a Pole-on Solar Analog

To accurately characterize the planets a star may be hosting, stellar parameters must first be well-determined. $\tau$ Ceti is a nearby solar analog and often a target for exoplanet searches. Uncertainties in the observed rotational velocities have made constraining $\tau$ Ceti's inclination difficult. For planet candidates from radial velocity (RV) observations, this leads to substantial uncertainties in the planetary masses, as only the minimum mass ($m \sin i$) can be constrained with RV. In this paper, we used new long-baseline optical interferometric data from the CHARA Array with the MIRC-X beam combiner and extreme precision spectroscopic data from the Lowell Discovery Telescope with EXPRES to improve constraints on the stellar parameters of $\tau$ Ceti. Additional archival data were obtained from a Tennessee State University Automatic Photometric Telescope and the Mount Wilson Observatory HK project. These new and archival data sets led to improved stellar parameter determinations, including a limb-darkened angular diameter of $2.019 \pm 0.012$ mas and rotation period of $46 \pm 4$ days. By combining parameters from our data sets, we obtained an estimate for the stellar inclination of $7\pm7^\circ$. This nearly-pole-on orientation has implications for the previously-reported exoplanets. An analysis of the system dynamics suggests that the planetary architecture described by Feng et al. (2017) may not retain long-term stability for low orbital inclinations. Additionally, the inclination of $\tau$ Ceti reveals a misalignment between the inclinations of the stellar rotation axis and the previously-measured debris disk rotation axis ($i_\mathrm{disk} = 35 \pm 10^\circ$).