Velocity dispersion of Solar Energetic Particles in 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 a novel 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 three 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 and moderate turbulence, VDA estimates of $t_{sun}$ are 2-16 minutes after the actual solar injection time, and the path lengths are 0.2-0.3 au longer than the Parker spiral. For 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-minute 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.