The polar debris disc around 99 Herculis: A potential signpost for polar circumbinary planets

TL;DR

The study tackles why the 99 Herculis polar debris disc forms a narrow ring by testing whether unseen polar circumbinary planets sculpt it. It combines analytic dynamical constraints (chaotic-zone width $Δa = c\,μ^{2/7}a_p$ with $c=1.3$, Hill-radius clearing, diffusion timescales, and polar-alignment timescales) with $N$-body simulations to compare architectures where planets are interior, exterior, or bracketing the disc. The results show that a two-planet configuration bracketing the disc best reproduces the observed narrow polar ring near $r\sim120$ au and preserves near-polar disc orientation, whereas single-planet models fail to truncate both edges. This supports a testable model in which two polar circumbinary planets shepherd the debris, highlighting how planetary bodies can sculpt debris discs in binary systems and guiding future observational efforts to detect such planets.

Abstract

The nearby binary star system 99 Herculis (99 Her) is host to the only known polar-aligned circumbinary debris disc. We investigate the hypothesis that the narrow structure of this circumbinary disc is sculpted by the gravitational influence of one or more unseen polar circumbinary planets. We first establish the theoretically viable parameter space for a sculpting planet by considering dynamical stability and clearing mechanisms, including the chaotic zone, Hill radius, diffusion, and polar alignment timescales. We then use $N$-body simulations to test three specific architectures: a single planet interior to the disc, a single planet exterior, and a two-planet system bracketing the disc. Our simulations demonstrate that single-planet models are insufficient to reproduce the observed morphology, as they can only truncate one edge of the disc while leaving the other dynamically extended. In contrast, the two-planet shepherding model successfully carves both the inner and outer edges, confining the debris into a narrow, stable polar ring consistent with observations. We conclude that the structure of the 99 Her debris disc is most plausibly explained by the presence of two shepherding, polar circumbinary planets. We present a specific, testable model for this unique system, which elucidates the pivotal role of planetary bodies in sculpting the architecture of debris discs.

Figures (5)

• Figure 1: Dynamical constraints on the semi-major axis ($a_{\rm p}$) and mass ($M_{\rm p}$) of a hypothetical polar circumbinary planet in the 99 Her system for eccentricity $e = e_{\rm p} = 0$. The observed location of the debris disc is marked by the vertical red band at $120\pm 10\, \rm au$. The purple line denotes the dynamically unstable region due to perturbations from the central binary ($a_{\rm p} \lesssim 27\, {\rm au}\, (1.5a_{\rm p})$). The lines represent constraints from the chaotic zone (black; Eq. \ref{['eq::M_chaos']}), Hill radius sculpting (blue; Eq. \ref{['eq::hill_rad']}), and diffusion timescale (red; Eq. \ref{['eq::diff_time']}). The unshaded (white) region indicates the viable parameter space for a planet capable of sculpting the inner and/or outer edge of the observed polar debris disc. Star symbols ($\star$) mark the parameters chosen for the $N$-body simulations presented in Section \ref{['sec::nbody']}.
• Figure 2: Same as Fig. \ref{['fig::a_M']} but for eccentricities $e = e_{\rm p} = e_{\rm crit}$ (Eq. (\ref{['eq::e_crit']}); top panel) and $e = e_{\rm p} = e_{\rm max}$ (Eq. (\ref{['eq::e_max']}); bottom panel). The lines represent constraints from the eccentric chaotic zone (black; Eq. (\ref{['eq::M_chaos_ecc']})), eccentric Hill radius sculpting (blue; Eq. (\ref{['eq::hill_rad']})), and diffusion timescale (red; Eq. (\ref{['eq::diff_time']})). The unshaded (white) region indicates the viable parameter space for a planet capable of sculpting the observed polar debris disc.
• Figure 3: The polar alignment time-scale, $\tau_{\rm polar}$, as a function of outer disc radius, $r_{\rm out}$, around 99 Her for different viscosities: $\alpha = 10^{-4}$ (solid), $10^{-3}$ (dashed), and $10^{-2}$ (dotted). The orange line denotes the upper limit of the protoplanetary disc lifetime, $\sim 10^7\, \rm yr$. We find that even for low viscosity discs with $\alpha=10^{-4}$, planets inwards of $\approx 250$ au would have remained coupled to the disk during its polar alignment, lending credence to the hypothesis that planets around 99 Her are in a polar configuration.
• Figure 4: The left-hand panels show the eccentricity $e$ versus semi-major axis $a$, while the right-hand panels show inclination $i$ versus $a$. All panels illustrate the final state of the debris disc after a 100 Myr integration. The three panels display different planetary configurations: a two-planet system (top), an inner-planet-only system (middle), and an outer-planet-only system (bottom). The initial distribution of test particles is shown in gray, while the surviving particles are shown using black circles. The vertical dashed blue and green lines mark the initial locations of the inner and outer planets, respectively, while the corresponding dots show their final semi-major axes and eccentricities or inclinations after 100 Myr. Shaded regions indicate the locations of mean-motion resonances associated with the inner (blue) and outer (green) planets, with several prominent resonances labeled. Although we only show the widths for first and second-order resonances, the third-order 5:2 MMR visibly excites eccentricities near 160 au in the middle panel.
• Figure 5: The structure of a polar-aligned debris ring (black dots) as it is dynamically sculpted by two circumbinary planets (orbits in blue and green). The red vector denotes the binary’s eccentricity vector, while the black vector represents the net angular momentum of the particles, which is nearly aligned with the binary eccentricity vector, confirming a polar configuration. A small population of transient particles ($< 20$ per cent), which have been perturbed by the planets but not yet ejected, are excluded from the calculation of the disc's angular momentum.