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Debris Disks: Dynamics and Structure

Main-sequence stars are commonly surrounded by debris disks, analogous to the Kuiper belt in the Solar system. High-resolution observations of debris disks over the last decades have revealed a rich variety of morphologies such as gaps, spirals, and warps. Most existing models for explaining such morphologies often focus on the role of point-mass perturbers, i.e. planets and/or stellar companions, ignoring the gravitational effects of the disk itself. That is, debris disks are usually treated as a collection of massless particles subject only to the gravity of planets. However, this treatment may not always be justified, especially in view of observations suggesting that debris disks could contain tens if not hundreds of Earth masses in large planetesimals.

In Sefilian et al. (2021), we investigated the secular interaction between an eccentric planet and a massive, external debris disk. We demonstrated that even when the disk is less massive than the planet, the system may feature secular resonances at two locations within the disk (contrary to what may be naively expected), where planetesimals eccentricities get significantly excited. Based on this we proposed that gaps (i.e. depleted regions) in debris disks, akin to those observed in HD 107146 and HD 92945, could be the result of secular resonances with a yet-undetected planet interior to the disk (rather than within the gap itself as may otherwise be expected).

Our results may be used to infer the presence of a yet-undetected planet based on the observed gap features (as we do for HD 107146 and HD 92945). Additionally - and more importantly - if a companion is already known (or discovered later), our results may be used to indirectly measure the total mass of the debris disk based on the gap features. We demonstrated this for HD 206893, for which we infer a total disk mass of approximately 170 Earth masses based on the properties of the known brown dwarf companion in that system.

An animation showing the secular interaction between a 0.6 Jupiter mass planet and a 20 Earth mass debris disk. Note the formation of a crescent-shaped gap centred at around 70 AU, where the combined gravity of the disk and the planet establish a secular resonance.(For more animations, see the "ancillary files" section in here}

Solar System Dynamics

Observational campaigns over the last decades have revealed that a subset of icy bodies orbiting the Sun beyond Neptune exhibit an unexpected orbital architecture. Namely, such small bodies – known as trans-Neptunian objects (TNOs) – orbit the Sun on highly-elongated paths which appear to be spatially clustered. Such a configuration can not be explained by the current eight-planet solar system architecture, challenging our understanding of the solar system. This has led to the so-called "Planet Nine" hypothesis which suggests the existence of an as-yet undiscovered super-Earth planet in the distant reaches of the solar system as an explanation for the puzzling orbits of TNOs.

In Sefilian & Touma (2019), we presented an alternative to the "Planet Nine" hypothesis. We demonstrated that a (relatively) massive disc of trans-Neptunian objects, lying in the same plane as the giant planets, could be responsible for the observed clustering of trans-Neptunian orbits. In particular, we showed that the gravitational effects of such a disc can effectively counteract the differential precession driven by the giant planets, and in the process shepherd members of its population onto highly elliptical orbits with roughly fixed orbital orientations. In short, this shepherding disc hypothesis faithfully reproduces key orbital properties of the puzzling TNO population, and could obviate the need for Plane Nine altogether.

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Astrophysical Disks

Astrophysical discs orbiting a central mass are ubiquitous in a variety of contexts – galactic, stellar, and planetary. Generally, the masses of such disks are much less than that of the central body. Nevertheless, gravity of such disks can still play an important dynamical role in the orbital evolution of their constituent particles as well as the dynamics of external objects. It is thus important to characterize the secular (long-term) dynamical effects of disk gravity. This is often done by using softened forms of gravity (i.e. by spatially smoothing the Newtonian point-mass potential) in order to circumvent singularities inherent in the classical Laplace-Lagrange secular theory (when applied to disks).

In Sefilian & Rafikov (2019), we analysed the performance of several softening prescriptions found in the literature in reproducing the expected - unsoftened - eccentricity dynamics driven by razor-thin disks. We identified softening prescriptions that, in the limit of vanishing softening, yield results converging to the expected behaviour exactly, approximately or not converging at all. We further developed a general analytic framework for computing the orbit-averaged disc potential given an arbitrary softening prescription. This framework accurately reproduces the expected secular dynamical behaviour for a wide class of softened gravity models. Theory aside, our results suggest that caution must be exercised in numerical treatments of disks which involve modelling the disk as a collection of massive, nested rings. In particular, disks should be modelled by relatively large number of rings to ensure that the correct secular behaviour is properly captured. We also show that this constraint is further aggravated for disks with sharp edges, such as planetary rings.