Scattering of solar energetic electrons in interplanetary space

Context. Solar energetic electrons are observed to arrive between 10 and 30 min later at 1 AU compared to the expectation based on their production in a solar flare and the travel time along the Parker spiral. Both a delayed release of electrons from the Sun and scattering of the electrons along their path are discussed as possible underlying mechanisms. Aims. We investigate to what extent scattering of energetic electrons in interplanetary space influences the arrival times of electrons at a solar distance of 1 AU, as a function of electron energy and for different scattering models. Methods. A kinetic model for electrons in interplanetary space is used to study the propagation of solar-flare electrons injected into the corona. The electrons are scattered by resonant interaction with a whistler-wave spectrum that is based on observed magnetic field fluctuation spectra in the solar wind. The arrival times of the electrons at 1 AU is determined by the electron flux exceeding a given threshold value. Results. The simulation results show a significant influence of the scattering on electron arrival times. Electrons with energies in the range of several tens of keV are delayed by up to about one minute for a pure pitch-angle scattering model. It is demonstrated that this simplification is not applicable, and the full quasi-linear diffusion equation needs to be considered. This reduces the delays to values below 30 s. Conclusions. It follows from these numerical studies that scattering of electrons in interplanetary space due to resonant interaction with whistler waves cannot explain the observed delays of 600 s, unless an unrealistic wave spectrum is assumed in interplanetary space.