Testing the Impact of Planet-stirring, Self-stirring, and Mixed-stirring on Debris Disc Architecture: A Case Study of HD 16743

Abstract

Dynamical interactions between planets and debris discs can excite the orbits of embedded planetesimals to such a degree that a collisional cascade is triggered, generating detectable amounts of dust. Millimetre wavelength observations are sensitive to emission from large and cold dust grains, which are unperturbed by radiation forces and act as a proxy for the location of the planetesimals. The influence of unseen planetary companions on debris discs can be inferred with high-resolution imaging observations at millimetre wavelengths, tracing the radial and vertical structure of these belts. Here we present a set of $N$-body simulations modelling ALMA observations of the HD~16743 debris disc. We consider a range of relative contributions from either a single planetary companion and/or a set of embedded massive planetesimals to reproduce the disc's observed radial and vertical structure. We compare our dynamical results for the limiting cases of planet-stirring and self-stirring, finding them to be consistent with theoretical expectations for each scenario. For the case of HD~16743, we find that a set of massive planetesimals on mildly eccentric orbits, confined to a relatively narrow range of semimajor axes (compared to the observed belt width), offers the best results to reproduce the vertical and radial extent of the observed emission. Our findings constrain the total planet-disk system mass. A combined giant and dwarf planet mass of $\geq~27~M_{\oplus}$ can reproduce the observed architecture, with the equipartition scenario requiring only half the disc mass of the self-stirring scenario.