Estimating the azimuthal mode structure of ULF waves based on multiple GOES satellite observations

Characterizing the azimuthal mode number, m, of ultralow-frequency (ULF) waves is necessary for calculating radial diffusion of radiation belt electrons. A cross-spectral technique is applied to the compressional Pc5 ULF waves observed by multiple pairs of GOES satellites to estimate the azimuthal mode structure during the 28-31 May 2010 storm. We find that allowing for both positive and negative m is important to achieve a more realistic distribution of mode numbers and to resolve wave propagation direction. During the storm commencement when the solar wind dynamic pressure is high, ULF wave power is found to dominate at low-mode numbers. An interesting change of sign in m occurred around noon, which is consistent with the driving of ULF waves by solar wind buffeting around noon, creating antisunward wave propagation. The low-mode ULF waves are also found to have a less global coverage in magnetic local time than previously assumed. In contrast, during the storm main phase and early recovery phase when the solar wind dynamic pressure is low and the auroral electrojet index is high, wave power is shown to be distributed over all modes from low to high. The high-mode waves are found to cover a wider range of magnetic local time than what was previously assumed. Furthermore, to reduce the 2n pi ambiguity in resolving m, a cross-pair analysis is performed on satellite field measurements for the first time, which is demonstrated to be effective in generating more reliable mode structure of ULF waves during high auroral electrojet periods.