A simple bound for the variation at closest approach of a small body and star due to general relativity

As a comet, asteroid or planet approaches its parent star, the orbit changes shape due to the curvature of spacetime. For comets in particular, the deviation at the pericentre may noticeably change their ephemerides and affect the dynamics of outgassing, tidal disruption or other processes which act on orbital timescales and are assumed to follow Newtonian gravity. By obtaining and analysing the unaveraged equations of motion in orbital elements due to the dominant post-Newtonian contribution (1PN), I derive a simple analytic expression for the maximum deviation in terms of only the stellar mass and eccentricity of the orbit. This relation can be used to assess the potential importance of including short-period relativistic terms in models containing comets, asteroids or planets, and help determine the level of precision needed in numerical integrations. The magnitude of the deviation in systems with Solar-like stars is typically comparable to the size of comet nuclei, and the direction of the deviation is determined by the eccentricity. I show that for eccentricities above a critical value of approximately 0.359, the direction is away from the star.Comment: Accepted for publication in MNRAS Letter

The fates of Solar system analogues with one additional distant planet

The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that would incite future instability in systems with a Sun-like star and giant planets with masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I find that this boundary is diffuse and strongly dependent on each of the distant planet's orbital parameters. Nevertheless, I claim that instability occurs more often than not when the planet is as massive as Jupiter and harbours a semimajor axis exceeding about 300 au, or has a mass of a super-Earth and a semimajor axis exceeding about 3000 au. These results hold for orbital pericentres ranging from 100 to at least 400 au. This instability scenario might represent a common occurrence, as potentially evidenced by the ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.Comment: Accepted for publication in MNRA

A wide binary trigger for white dwarf pollution

Metal pollution in white dwarf atmospheres is likely to be a signature of remnant planetary systems. Most explanations for this pollution predict a sharp decrease in the number of polluted systems with white dwarf cooling age. Observations do not confirm this trend, and metal pollution in old (1-5 Gyr) white dwarfs is difficult to explain. We propose an alternative, time-independent mechanism to produce the white dwarf pollution. The orbit of a wide binary companion can be perturbed by Galactic tides, approaching close to the primary star for the first time after billions of years of evolution on the white dwarf branch. We show that such a close approach perturbs a planetary system orbiting the white dwarf, scattering planetesimals onto star-grazing orbits, in a manner that could pollute the white dwarf's atmosphere. Our estimates find that this mechanism is likely to contribute to metal pollution, alongside other mechanisms, in up to a few percent of an observed sample of white dwarfs with wide binary companions, independent of white dwarf age. This age independence is the key difference between this wide binary mechanism and others mechanisms suggested in the literature to explain white dwarf pollution. Current observational samples are not large enough to assess whether this mechanism makes a significant contribution to the population of polluted white dwarfs, for which better constraints on the wide binary population are required, such as those that will be obtained in the near future with Gaia.Comment: MNRAS accepted 10 page

The dynamical history of the evaporating or disrupted ice giant planet around white dwarf WD J0914+1914

Robust evidence of an ice giant planet shedding its atmosphere around the white dwarf WD J0914+1914 represents a milestone in exoplanetary science, allowing us to finally supplement our knowledge of white dwarf metal pollution, debris discs and minor planets with the presence of a major planet. Here, we discuss the possible dynamical origins of this planet, WD J0914+1914 b. The very young cooling age of the host white dwarf (13 Myr) combined with the currently estimated planet-star separation of about 0.07 au imposes particularly intriguing and restrictive coupled constraints on its current orbit and its tidal dissipation characteristics. The planet must have been scattered from a distance of at least a few au to its current location, requiring the current or former presence of at least one more major planet in the system in the absence of a hidden binary companion. We show that WD J0914+1914 b could not have subsequently shrunk its orbit through chaotic f-mode tidal excitation (characteristic of such highly eccentric orbits) unless the planet was or is highly inflated and possibly had partially thermally self-disrupted from mode-based energy release. We also demonstrate that if the planet is currently assumed to reside on a near-circular orbit at 0.07 au, then non-chaotic equilibrium tides impose unrealistic values for the planet’s tidal quality factor. We conclude that WD J0914+1914 b either (i) actually resides interior to 0.07 au, (ii) resembles a disrupted “Super-Puff” whose remains reside on a circular orbit, or (iii) resembles a larger or denser ice giant on a currently eccentric orbit. Distinguishing these three possibilities strongly motivates follow-up observations

Generating metal-polluting debris in white dwarf planetary systems from small-impact crater ejecta

Metal pollution in white dwarf photospheres originates from the accretion of some combination of planets, moons, asteroids, comets, boulders, pebbles and dust. When large bodies reside in dynamically stagnant locations – unable themselves to pollute nor even closely approach the white dwarf – then smaller reservoirs of impact debris may become a complementary or the primary source of metal pollutants. Here, we take a first step towards exploring this possibility by computing limits on the recoil mass that escapes the gravitational pull of the target object following a single impact onto an atmosphere-less surface. By considering vertical impacts only with the full-chain analytical prescription from Kurosawa & Takada (2019), we provide lower bounds for the ejected mass for basalt, granite, iron and water-rich target objects across the radii range 100 − 3 km. Our use of the full-chain prescription as opposed to physical experiments or hydrocode simulations allows us to quickly sample a wide range of parameter space appropriate to white dwarf planetary systems. Our numerical results could be used in future studies to constrain freshly-generated small debris reservoirs around white dwarfs given a particular planetary system architecture, bombardment history, and impact geometries

Post-main-sequence debris from rotation-induced YORP break-up of small bodies II : multiple fissions, internal strengths and binary production

Over one quarter of white dwarfs contain observable metallic debris from the breakup of exo-asteroids. Understanding the physical and orbital history of this debris would enable us to self-consistently link planetary system formation and fate. One major debris reservoir is generated by YORP-induced rotational fission during the giant branch phases of stellar evolution, where the stellar luminosity can exceed the Sun’s by four orders of magnitude. Here, we determine the efficacy of the giant branch YORP effect for asteroids with nonzero internal strength, and model post-fission evolution by imposing simple analytic fragmentation prescriptions. We find that even the highest realistic internal strengths cannot prevent the widespread fragmentation of asteroids and the production of a debris field over 100 au in size. We compute the number of successive fission events as they occur in progressively smaller time intervals as the star ascends the giant branches, providing a way to generate size distributions of asteroid fragments. The results are highly insensitive to progenitor stellar mass. We also conclude that the ease with which giant branch YORP breakup can generate binary asteroid subsystems is strongly dependent on internal strength. Formed binary subsystems in turn could be short-lived due to the resulting luminosity-enhanced BYORP effect