Zeeman Doppler Imaging of $\tau$Ceti: The Weakest Magnetic Field Detected in a Sun-like Star

Abstract

For nearly a decade, observations have shown that many older Sun-like stars spin faster than predicted, a phenomenon known as weakened magnetic braking (WMB). The leading hypothesis for WMB is a weakening of the large-scale dipole field, which leads to a less efficient angular momentum loss. To test this hypothesis on a star known to be in the WMB regime, we present the first Zeeman Doppler Imaging (ZDI) map of the Sun-like star $\tau$Ceti, reconstructed using spectropolarimetric data from the Canada-France-Hawai'i Telescope (CFHT). Our ZDI analysis reveals a remarkably simple, stable and weak ($\langle B\rangle =0.17 \mathrm{G}$) magnetic field, characterized by a predominantly dipolar ($\sim92\%$ magnetic energy contained in $l=1$ modes), and highly axisymmetric ($\sim88\%$ magnetic energy contained in $m<l/2$ modes) morphology. We infer a dipole field strength of $B_{\mathrm{dip}}=0.31 \mathrm{G}$, nearly an order of magnitude weaker than standard braking model predictions, providing direct confirmation of the weakened large-scale dipole predicted by the WMB hypothesis. This work establishes a new benchmark for ZDI, demonstrating that even extremely quiet stars in the WMB regime are accessible to this technique.