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

TL;DR

This paper investigates how debris discs are stirred by planetary perturbations, applying a mixed-stirring framework to HD 16743. Using $N$-body simulations across a grid of mass partitions between a interior giant planet and embedded dwarf planets, the authors generate synthetic ALMA observations to compare with the observed disc geometry. They find that a 50/50 mixture of giant-planet and dwarf-planet mass can reproduce the vertical and radial structure within $\sim80$ Myr, often matching or exceeding the efficacy of pure self-stirring while requiring roughly half the disc mass. The results imply that mixed-stirring can alleviate the disc-mass budget problem and provide constraints on possible inner planetary companions, including scenarios with a misaligned inner planet compatible with observational limits.

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.

Figures (8)

• Figure 1: Initial conditions of a representative simulation from the model grid: $M_{\rm tot} = 27~M_{\oplus}$, with 50% of the mass in DPs, and $\sigma = \mathrm{FWHM}/4$. Top: Distribution of instantaneous positions of test particles (TP; blue), dwarf planets (DP; purple), giant planet (GP; black), and the star (white) in $X$--$Y$ and $X$--$Z$ planes. For reference, the planet's orbit is denoted by the dashed line. Note the change in scale between the vertical axes of the top left and top right panels. Bottom: Distribution of eccentricities $e$ and inclinations $i$ as a function of semimajor axis $a$ for all bodies involved (TPs, DPs, and the GP). The vertical solid and dashed lines denote the peak and extent of the planetesimal belt ($\mu_{0}~\pm~3\sigma_{\rm disc}$, where $\sigma = \mathrm{FWHM}/4$). TPs and DPs located within 3 Hill radii of the planet were removed and their orbital elements redrawn from the distributions, leading to the truncation of the disc's inner edge.
• Figure 2: Evolution of RMS$_{e}$ (top) and RMS$_{i}$ (bottom) for the 27 M$_\oplus$ total mass model, with a disc standard deviation $\sigma = \mathrm{FWHM}/4$ (the central model in our grid, see Figures \ref{['fig:rms_e']} and \ref{['fig:rms_i']}). The light blue curves denote the 0% mass in DPs scenario, which barely stirs the disc. The remaining mass fractions are denoted by cyan (10%), blue (50%), and black (100%) lines. Solid lines denote the RMS values for DPs, and dashed lines denote the RMS values for TPs. The shaded regions (top panel) and grey dotted lines (both panels) denote a $t^{1/4}$ dependence increase for the RMS values, based on Krivov18.
• Figure 3: Evolution of RMS$_{e}$ as a function of time for mass fractions in DPs of 10% (left), 50% (middle), and 100% (right) and initial planetesimal belt widths of $\mathrm{FWHM}/2$ (top), $\mathrm{FWHM}/4$ (middle), and $\mathrm{FWHM}/8$ (bottom). Colours denote total disc mass of 18 (cyan), 27 (blue), and 36 (black) $M_{\oplus}$. Dashed lines denote RMS$_{e}$ of TPs, whilst solid lines denote RMS$_{e}$ for DPs. See the text (Section \ref{['subsec:grid_sims_3_4']}) for further details.
• Figure 4: Evolution of RMS$_{i}$, presented in the same manner as Figure \ref{['fig:rms_e']}. See the text (Section \ref{['subsec:grid_sims_3_4']}) for further details.
• Figure 5: Final ($t = 80~$Myr) RMS$_{e}$ (top) and RMS$_{i}$ (bottom) values as a function of the disc mass in DPs for models with total masses of 18 (cyan), 27 (blue), and 36 (black) $M_{\oplus}$ and fractions of 10%, 50%, and 100% in dwarf planets (DPs). The left, middle, and right panels show results for initial belt widths $\sigma$, factors of 2, 4, and 8 narrower than the width inferred from observations. See the text (Section \ref{['subsec:grid_sims_3_4']}) for further details.