An observationally based wind model contemporaneous with the radio detections in $\tau$ Bo\"otis

TL;DR

This study combines spectropolarimetric observations and 3D stellar wind modeling to interpret radio signals from the $ au$ Bo"otis system, highlighting the role of stellar magnetic activity in star-planet interactions.

Contribution

First to derive a contemporaneous magnetic map of $ au$ Bo"otis A and model its stellar wind to assess its impact on radio emissions from its exoplanet.

Findings

Predicted radio flux densities are much lower than observed, suggesting stronger stellar magnetic fields are needed.

Stellar wind variations due to magnetic cycle may explain inconsistent radio detections.

Contemporaneous magnetic and radio observations are crucial for understanding star-planet interactions.

Abstract

Recent low-frequency array (LOFAR) radio signal detections bearing from the $\tau$ Bo\"otis system have been cautiously attributed to auroral emissions from the hot Jupiter $\tau$ Bo\"otis 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 $\tau$ Bo\"otis A from the same epoch as the LOFAR detections. We derive a contemporaneous large-scale magnetic map of $\tau$ Bo\"otis 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 $\tau$ Bo\"otis Ab. To compute the wind power dissipated in $\tau$ Bo\"otis 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 $\tau$ Bo\"otis 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.