Velocity Dispersion of Solar Energetic Particles in the Turbulent Heliosphere

Abstract Solar energetic particles (SEPs) are a signature of solar eruptions, and to link them to acceleration mechanisms many studies investigate their injection time at the Sun, t Sun . We assess velocity dispersion analysis (VDA), an often-used method to derive t Sun . We use full-orbit simulations of 1–100 MeV SEP protons in our recent new model of the interplanetary magnetic turbulence superposed on a Parker spiral magnetic field. The turbulence is described analytically as dominant transverse fluctuations that are 2D with respect to the mean field, supplemented with a minor contribution of asymptotically slab turbulence modes. We determine simulated SEP intensities for four turbulence strengths and use VDA to obtain t Sun and the apparent path length s of the SEPs, employing an SEP onset threshold to mimic a realistic energetic proton background before the SEP event. We find that turbulence strongly affects t Sun and s . For weak to strong turbulence, VDA estimates of t Sun are 2–30 minutes after the actual solar injection time, and the path lengths are 0.2–5 au longer than the Parker spiral. For very strong turbulence, the path lengths are > 5 au, considerably longer than those typically obtained from SEP observations. We also investigate the effect of energy dependence of the pre-event proton background, and find that different background spectra result in 5–20 minutes difference in VDA injection times, depending on the heliolongitude. We conclude that in many cases VDA-derived injection times include a significant contribution from turbulence and/or the pre-event background and are not an accurate estimate of the acceleration time.