An observationally based wind model contemporaneous with the radio detections in $τ$ Boötis

Abstract

Recent low-frequency array (LOFAR) radio signal detections bearing from the $τ$ Boötis system have been cautiously attributed to auroral emissions from the hot Jupiter $τ$ Boötis Ab. The auroral emissions are believed to be excited by interaction between the exoplanet and the winds of its host star. Since stellar winds respond to stellar surface magnetism, three-dimensional stellar wind modelling, able to account for the star's contemporaneous magnetic field geometry, can aid the interpretation of radio detections. For the first time, we present spectropolarimetric observations of $τ$ Boötis A from the same epoch as the LOFAR detections. We derive a contemporaneous large-scale magnetic map of $τ$ Boötis A, which shows a poloidally dominated field with mean strength 1.6 G. From our magnetic map, we create a three-dimensional numerical wind model and characterise the wind properties around $τ$ Boötis Ab. To compute the wind power dissipated in $τ$ Boötis Ab's magnetosphere, we apply two approaches: A) the solar system-based empirical relation called Bode's law; and B) a resolved numerical model of the planetary magnetosphere. When consistently applying best-case assumptions, we redict radio flux densities around 50 mJy and 0.68 mJy respectively. Our values are much too small to be consistent with the reported observation of $890_{-500}^{+690}$ mJy; a stellar surface magnetic field scaling $\gtrsim 10$ is required to reproduce the observed signal strength. As $τ$ Boötis A has a rapid magnetic cycle, we speculate that wind variations cased by variation in stellar magnetism may explain the lack of detections from follow-up observations. Our work emphasises the importance of contemporaneous observations of stellar magnetism and observational signatures of star-planet interaction.