Determination of Electromagnetic Source Direction as an Eigenvalue Problem

Low-frequency solar and interplanetary radio bursts are generated at frequencies below the ionospheric plasma cutoff and must therefore be measured in space, with deployable antenna systems. The problem of measuring both the general direction and polarization of an electromagnetic source is commonly solved by iterative fitting methods such as linear regression that deal simultaneously with both directional and polarization parameters. We have developed a scheme that separates the problem of deriving the source direction from that of determining the polarization, avoiding iteration in a multi-dimensional manifold. The crux of the method is to first determine the source direction independently of concerns as to its polarization. Once the source direction is known, its direct characterization in terms of Stokes vectors in a single iteration if desired, is relatively simple. This study applies the source-direction determination to radio signatures of flares received by STEREO. We studied two previously analyzed radio type III bursts and found that the results of the eigenvalue decomposition technique are consistent with those obtained previously by Reiner et al. (Solar Phys. 259, 255, 2009). For the type III burst observed on 7 December 2007, the difference in travel times from the derived source location to STEREO A and B is the same as the difference in the onset times of the burst profiles measured by the two spacecraft. This is consistent with emission originating from a single, relatively compact source. For the second event of 29 January 2008, the relative timing does not agree, suggesting emission from two sources separated by 0.1 AU, or perhaps from an elongated region encompassing the apparent source locations.