Characterizing Scale of Surface B Field with Spherical Harmonic Decomposition of ZDI Maps

Angular momentum loss in massive main sequence stars is due, in part, to the strength and structure of surface magnetic fields. The torque created by a surface magnetic field can be calculated through integration of a Zeeman Doppler Imaging (ZDI) map. ZDI maps are generated by inverting the time series Stokes V profiles to output a vector magnetic field that best fits observational results. This is decomposed into radial, meridional, and azimuthal magnetic field maps. This is a novel way of looking at spindown that does not need to consider mass loss or magnetic braking. To characterize how the scale of magnetic structures affect the spindown of the star, the ZDI maps are decomposed into spherical harmonics. From these, we can calculate the torque associated with different truncations of the harmonic series. We looked at three massive fast rotators, CU Vir (HD124224), 36 Lyn (HD79158), and σ Ori E (HD37479), as well as the slowly rotating early B-type star, τ Sco (HD149438). For the fast rotators, we saw that the loss of angular momentum in massive stars is primarily due to large structures in the surface magnetic field but for τ Sco, large and mediums scale structures are equally important. This result agrees with the consensus that the surface magnetic fields of massive stars are dominated by simple geometry for fast rotators.