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.

Figures (3)

• Figure 1: The contour shows the simulated proton intensities as a function of inverse of velocity (in light-speed units) and time at $\Delta\phi=0^\circ$, for the moderate turbulence case. The yellow symbols the onset times determined with the local onset criterion, Equation (\ref{['eq:local']}), and the yellow curve the fit of the onset times to Equation (\ref{['eq:VDA']})/ The blue diamonds, connected with the dashed line, show the arrival time of scatter-free protons.
• Figure 2: The VDA apparent path length (a) and solar injection time relative to the simulation injection time $t_0$ (b) of SEPs as a function of the observer heliolongitude for strong (rouge circle), moderate (orange diamond) and weak (green square) turbulence and energy-dependent onset threshold fraction $f(E)$. The solid blue line shows the length of the nominal Parker Spiral. In panel (b), the solar injection times for $\Delta\phi=-80^\circ$, $40^\circ$ and $60^\circ$ for the high turbulence case are omitted for clarity, as they are at $t_{sun}<-100$ minutes. Note that the points from different turbulence sets are staggered by $1^\circ$ to avoid overlapping of error bars.
• Figure 3: The VDA apparent path length (a) and solar injection time (b) of SEPs as a function of the heliolongitude for energy-dependent (Equation (\ref{['eq:thresh_E']}), yellow cross) and constant (blue hexagon) threshold fraction $f(E)=0.01$, for moderate turbulence. In panel (a), the apparent path length $s=-0.05$ au for $\Delta\phi=-60^\circ$ is omitted for clarity.