Numerical predictions for planets in the debris discs of HD 202628 and HD 207129

Resolved debris disc images can exhibit a range of radial and azimuthal structures, including gaps and rings, which can result from planetary companions shaping the disc by their gravitational influence. Currently there are no tools available to determine the architecture of potential companions from disc observations. Recent work by Rodigas et al. (2014) presents how one can estimate the maximum mass and minimum semi major axis of a hidden planet empirically from the width of the disc in scattered light. In this work, we use the predictions of Rodigas et al. applied to two debris discs HD 202628 and HD 207129. We aim to test if the predicted orbits of the planets can explain the features of their debris disc, such as eccentricity and sharp inner edge. We first run dynamical simulations using the predicted planetary parameters of Rodigas et al., and then numerically search for better parameters. Using a modified N-body code including radiation forces, we perform simulations over a broad range of planet parameters and compare synthetics images from our simulations to the observations. We find that the observational features of HD 202628 can be reproduced with a planet five times smaller than expected, located 30 AU beyond the predicted value, while the best match for HD 207129 is for a planet located 5-10 AU beyond the predicted location with a smaller eccentricity. We conclude that the predictions of Rodigas et al. provide a good starting point but should be complemented by numerical simulations.