Time dependence of the evolution of test particles. The two left-most panels show the survival times of particles that get ejected (left-most) or are star-grazing (middle), as a function of the initial semi-major axis at which the particles are seeded. The percentage of all simulated particles that is removed from the simulation is indicated with the colourbar. The right-most panel shows particles that become classified as star-grazing after 10 million years. We call these ‘late star-grazers’ and investigate them in further detail in Sect. 3.2. Note: there seem to be two different sources of late star-grazers, in the inner and outer parts of the system, respectively. Orbital resonances with β Pic b are also indicated such as in Fig. 2, clearly showing that star-grazers are not expected to be produced from low-order resonances (e.g. 1:3 and 1:4) because these have been cleared earlier in the life of the system.