Formation of Gaps in Self-Gravitating Debris Disks by Secular Resonance in a Single-planet System I: A Simplified Model

Abstract

Spatially resolved images of debris disks frequently reveal complex morphologies such as gaps, spirals, and warps. Most existing models for explaining such morphologies focus on the role of massive perturbers (i.e. planets, stellar companions), ignoring the gravitational effects of the disk itself. Here we investigate the secular interaction between an eccentric planet and a massive, external debris disk using a simple analytical model. Our framework accounts for both the gravitational coupling between the disk and the planet, as well as the disk self-gravity -- with the limitation that it ignores the non-axisymmetric component of the disk (self-)gravity. We find generally that even when the disk is less massive than the planet, the system may feature secular resonances within the disk (contrary to what may be naively expected), where planetesimal eccentricities get significantly excited. Given this outcome we propose that double-ringed debris disks, such as those around HD 107146 and HD 92945, could be the result of secular resonances with a yet-undetected planet interior to the disk. We characterize the dependence of the properties of the secular resonances (i.e. locations, timescales, and widths) on the planet and disk parameters, finding that the mechanism is robust provided the disk is massive enough. As an example, we apply our results to HD 107146 and find that this mechanism readily produces $\sim 20$ au wide non-axisymmetric gaps. Our results may be used to set constraints on the total mass of double-ringed debris disks. We demonstrate this for HD 206893, for which we infer a disk mass of $\approx 170$ Earth masses by considering perturbations from the known brown dwarf companion.

Accepted for publication in ApJ: 25 Pages, 13 Figures, 1 Table, 3 Animations (see Ancillary files)

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• Planet formation in stellar binaries: Global simulations of planetesimal growth
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• Giant Impacts and Debris Disk Morphology
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• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) I: Motivation, sample, data reduction, and results overview
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• Self-gravity of debris discs can strongly change the outcomes of interactions with inclined planets
• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS): VI. Asymmetries and offsets
• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) V: Comparison between scattered light and thermal emission
• Radial Profiles of Surface Density in Debris Discs
• Millimeter Dust Emission and Planetary Dynamics in the HD 106906 System
• Formation of the warped debris disc around $\beta$ Pictoris
• ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk
• Non-linear Electrodynamics in Blandford-Znajeck Energy Extraction
• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS). X. Interpreting the peculiar dust rings around HD 131835
• Rotating Einstein-Maxwell-Dilaton Black Hole as a Particle Accelerator
• Steeper Scattered Disks Buckle Faster
• Testing the Impact of Planet-stirring, Self-stirring, and Mixed-stirring on Debris Disc Architecture: A Case Study of HD 16743