Using eigenmode-mixing to measure or constrain the Sun's interior B-field

Understanding the generation and distribution of the Sun's interior magnetic (B-) field is a longstanding challenge. Here we describe how measurements of the Sun's oscillation eigenfunctions might be used to measure the Sun's interior B-field. The B-field induces mode-mode couplings, causing the angular patterns of the eigenfunctions to differ from simple Y_{lm}'s We concentrate on the magnetic coupling between modes with the same (n,l) values and different but nearby $m$-values, since these non-axisymmetric couplings clearly cannot be due to the Sun's axisymmetric rotation and since for these cases, mode mixing is enhanced by the near-degeneracy of the mode frequencies. We analyze magnetically-induced mode mixing in two stages of increasing complexity: first neglecting mode damping, and then incorporating realistic damping rates. We introduce a novel detection statistic that tests for the presence of non-axisymmetric mode-mixing in Solar Doppler data. We show that our detection statistic is naturally robust against spatial aliasing. We estimate our statistic's signal-to-noise ratio (SNR) as a function of the mode-mixing amplitude. While B-induced mode-mixing is probably not detectable in a single mode pair, we argue that the phase of the B-induced mixing should be approximately the same across a wide range of modes. The total SNR then grows roughly as Np^{1/2}, where Np is the number of mode pairs. We conclude that B-induced mode-mixing should be detectable for a fairly wide range of B-field magnitudes and geometries.