Modelling shock-like injections of solar energetic particles with 3D test particle simulations

Context. Solar energetic particle (SEP) acceleration and injection into interplanetary space during gradual SEP events is thought to take place at coronal mass ejection (CME)-driven shocks. Various features of measured intensity profiles at 1 au have been attributed to properties of the radial, longitudinal, and latitudinal SEP injections at the shock. Focussed transport models are typically used to model acceleration at a CME-shock and subsequent propagation. Test particle simulations are an alternative approach but so far they have been carried out only with instantaneous injection near the Sun. Aims. We develop the first temporally extended shock-like injection for our 3D test particle code and investigate how the spatial features of injection at a shock affect SEP intensity and anisotropy profiles for observers at 0.3 and 1.0 au. Methods. We conducted simulations of a monoenergetic population of 5 MeV protons considering three different radial injection functions and two longitudinal and latitudinal injection functions. We considered a range of scattering conditions with scattering mean free path values ranging from λ = 0.1 - 1.0 au, and determined intensity and anisotropy profiles at six observers at different longitudinal locations. Results. We find that the radial, longitudinal, and latitudinal injection functions play a relatively minor role in shaping the SEP intensity profiles. The dependence of intensity profiles on the value of the scattering mean free path is also weak, unlike what is found from 1D focussed transport models. Spatial factors, such as the times of observer-shock connection and disconnection as well as the time of shock passage have a much stronger influence on SEP intensities and anisotropies. Persistent anisotropies, until shock passage, are seen in our simulations. Comparing instantaneous and shock-like injections, we find that the link between the duration of injection and the duration of the SEP event is very weak, unlike what is commonly assumed.