The entry geometry and velocity of planetary debris into the Roche sphere of a white dwarf

Our knowledge of white dwarf planetary systems predominately arises from the region within a few Solar radii of the white dwarfs, where minor planets breakup, form rings and discs, and accrete on to the star. The entry location, angle, and speed into this Roche sphere has rarely been explored but crucially determines the initial geometry of the debris, accretion rates on to the photosphere, and ultimately the composition of the minor planet. Here, we evolve a total of over 10(5) asteroids with single-planet N-body simulations across the giant branch and white dwarf stellar evolution phases to quantify the geometry of asteroid injection into the white dwarf Roche sphere as a function of planetary mass and eccentricity. We find that lower planetary masses increase the extent of anisotropic injection and decrease the probability of head-on (normal to the Roche sphere) encounters. Our results suggest that one can use dynamical activity within the Roche sphere to make inferences about the hidden architectures of these planetary systems.