Using ZDI maps to determine magnetic forces and torques at the photospheres of early-type stars

We use the magnetic field components measured by Zeeman Doppler imaging (ZDI) to calculate the stellar surface force and torque due to magnetic stresses for the fast rotators σ Ori E, 36 Lyn, and CU Vir, and the slow rotator τ Sco. If we assume the stars have spherical photospheres, the estimated torques give spin-down time-scales no larger than 7 × 105 yr. For σ Ori E, the predicted spin-down time-scale, ≃ 6000 yr, is much less than the observationally measured time-scale of ≃ 106 yr. However, for CU Vir, we find that the spin-down time-scale from its ZDI map is 7 × 105 yr in good agreement with its average rate of spin-down from 1960 to 2010. With the exception of τ Sco, the net force due to magnetic stresses at the stellar surface are large compared to the surface-integrated pressure. We discuss possible reasons for the large values of the forces (and torques), and suggest that the likely explanation is that rotation and the magnetic stresses create significant departures from spherical symmetry.
This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: © 2024 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( licenses/ by/ 4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. The version of record is available at:
stars: early-type, stars: magnetic field, stars: rotation
James MacDonald, Tali Natan, Véronique Petit, Oleg Kochukhov, Matthew E Shultz, Using ZDI maps to determine magnetic forces and torques at the photospheres of early-type stars, Monthly Notices of the Royal Astronomical Society, Volume 530, Issue 3, May 2024, Pages 2840–2851,