tokens: distribution ranging from 0° to 10°. Asteroids which were initialized at the beginning of the simulation with two different eccentricity distributions depending on the simulation. The first is circular asteroids, and the second are asteroids with eccentricities chosen between 0.3 and 0.7. We emphasize that we are not attempting to reproduce realistic exo-debris discs in these systems (which would require a more detailed Yarkovsky model), but rather are placing bounds and observing trends. The evolution of most initially eccentric asteroids that we simulated are not shown, unless they provide a revealing physical trait. Asteroids which were initialized at the beginning of the simulation with orbital angles chosen from a random uniform distribution across their entire ranges. Yarkovsky prescriptions according to the following values of : Our choices for Models A–C arise from our intention to place bounds on the motion by considering only extreme cases. We approximate these extreme cases by focusing on and from the analytic limits in equation ( 25 ). In terms of semimajor axis, Model A pushes asteroids outwards, Model B pushes asteroids inwards, and Model C does not push them outwards or inwards. Alternatively, Models A and B have only a minor effect on asteroid inclination evolution, whereas Model C has a relatively large effect. We actually ran additional simulations with other combinations of entries, but found that they represent intermediate cases to Models A–C, supporting the analytics and our choices. 4 SIMULATION RESULTS The asteroids in our simulations are accelerated by three major effects: (i) mass-loss from the star, (ii) perturbations from the planet, and the (iii) radiation-driven Yarkovsky effect. 4 Mass-loss always pushes the asteroids away from the star (the orbital pericentre is always increasing, even in non-adiabatic motion; Veras et al. 2011 ), whereas the planet and the Yarkovsky effect may perturb the asteroids in either direction. Although both mass-loss and planets can increase e ast to unity (causing escape; e.g. Veras et al. 2011 ; Adams, Anderson Bloch 2013 ), Yarkovsky acceleration cannot. Veras et al. ( 2015 ) investigated the relative magnitudes of stellar mass-loss and the Yarkovsky effect, but did not include a planet nor run numerical simulations. The Yarkovsky drift varies in a complex manner, and is a function of all orbital elements, even in our simple approximation where the matrix elements of remain constant over time. However, equations ( 25 )–( 26 ) reveal that for small inclinations, the key parameters are and . Although the Yarkovsky acceleration drops roughly as , the acceleration increases linearly as a function of L ⋆ ( t ). The time dependence of L ⋆ ( t ) is, in turn, non-linear, and dominates changes in the Yarkovsky acceleration. Mass-loss is largely adiabatic within about 10 3 au (Veras et al. 2011 ), meaning that within this region it feeds back into the Yarkovsky acceleration only through an
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