Estimating the Bulk Velocity of Energetic Particle Populations Using IS⊙IS/EPI-Lo Measurements

We introduce a method to derive the bulk velocity of the solar energetic particle population, given intensity measurements for a set of apertures viewing half of the sky, as is the case for energetic particle measurements from IS⊙IS/EPI-Lo on the Parker Solar Probe spacecraft. In the comoving frame, intensity distribution is modeled as an isotropic power-law energy spectrum multiplied by an arbitrary pitch angle distribution. This distribution is shifted by an arbitrary bulk velocity vector, then converted to expectation values for the particle counts that would be observed by the instrument. By assuming that the observed particle counts are Poisson-distributed samples of the model, a maximum likelihood bulk velocity is found. To test the method, we used simulated measurements to explore the reliability of the method. We found that, even with half-sky measurements, the method can provide nearly unbiased estimates of the bulk velocity within the uncertainty as long as the pitch angle distribution is resolved. We also took advantage of a period during which the spacecraft was rolling for calibration purposes, effectively giving EPI-Lo full-sky viewing. By comparing the result obtained from different segments of the sky, we found that those obtained from different half-sky fields of view are generally compatible within the uncertainty, especially when the pitch angle distribution is resolved. We also compared the perpendicular part of the bulk energetic velocity to the perpendicular part of the bulk solar wind velocity, finding a strong correlation (∼0.78), as expected.