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A large fraction of white dwarfs (WDs) have metal-polluted atmospheres, which are produced by accreting material from remnant planetary systems. The composition of the accreted debris broadly resembles that of rocky Solar system objects. Volatile-enriched debris with compositions similar to long-period comets (LPCs) is rarely observed. We attempt to reconcile this dearth of volatiles with the premise that exo-Oort clouds (XOCs) occur around a large fraction of planet-hosting stars. We estimate the comet accretion rate from an XOC analytically, adapting the ‘loss cone’ theory of LPC delivery in the Solar system. We investigate the dynamical evolution of an XOC during late stellar evolution. Using numerical simulations, we show that 1–30 per cent of XOC objects remain bound after anisotropic stellar mass-loss imparting a WD natal kick of ${\sim}1 \, {\rm km \, s^{-1}}$. We also characterize the surviving comets’ distribution function. Surviving planets orbiting a WD can prevent the accretion of XOC comets by the star. A planet’s ‘dynamical barrier’ is effective at preventing comet accretion if the energy kick imparted by the planet exceeds the comet’s orbital binding energy. By modifying the loss cone theory, we calculate the amount by which a planet reduces the WD’s accretion rate. We suggest that the scarcity of volatile-enriched debris in polluted WDs is caused by an unseen population of 10–$100 \, \mathrm{au}$ scale giant planets acting as barriers to incoming LPCs. Finally, we constrain the amount of volatiles delivered to a planet in the habitable zone of an old, cool WD.

About ten percent of Sun-like (1–2M_⊙) stars will engulf a 1–10M_Jplanet as they expand during the red giant branch (RGB) or asymptotic giant branch (AGB) phase of their evolution. Once engulfed, these planets experience a strong drag force in the star’s convective envelope and spiral inward, depositing energy and angular momentum. For these mass ratios, the inspiral takes ∼10–10²yr (∼10²–10³orbits); the planet undergoes tidal disruption at a radius of ∼1R_⊙. We use the Modules for Experiments in Stellar Astrophysics (MESA) software instrument to track the stellar response to the energy deposition while simultaneously evolving the planetary orbit. For RGB stars, as well as AGB stars withM_p≲ 5M_Jplanets, the star responds quasi-statically but still brightens measurably on a timescale of years. In addition, asteroseismic indicators, such as the frequency spacing or rotational splitting, differ before and after engulfment. For AGB stars, engulfment of anM_p≳ 5M_Jplanet drives supersonic expansion of the envelope, causing a bright, red, dusty eruption similar to a “luminous red nova.” Based on the peak luminosity, color, duration, and expected rate of these events, we suggest that engulfment events on the AGB could be a significant fraction of low-luminosity red novae in the Galaxy. We do not find conditions where the envelope is ejected prior to the planet’s tidal disruption, complicating the interpretation of short-period giant planets orbiting white dwarfs as survivors of common envelope evolution.

Secular oscillations in multiplanet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This ‘secular chaos’ readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets’ properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-scales spanning several orders of magnitude in a given system. We apply our results to the evolution of planetary systems around white dwarfs (WDs), specifically the tidal disruption and high-eccentricity migration of planetesimals and planets. We find that secular chaos in a planetesimal belt driven by large (≳10 M⊕), distant ($\gtrsim 10 \, \mathrm{au}$) planets can sustain metal accretion on to a WD over Gyr time-scales. We constrain the total mass of planetesimals initially present within the chaotic zone by requiring that the predicted mass delivery rate to the Roche limit be consistent with the observed metal accretion rates of WDs with atmospheric pollution throughout the cooling sequence. Based on the occurrence of long-period exoplanets and exo-asteroid belts, we conclude that secular chaos can be a significant (perhaps dominant) channel for polluting solitary WDs. Secular chaos can also produce short-period planets and planetesimals around WDs in concert with various circularization mechanisms. We discuss prospects for detecting exoplanets driving secular chaos around WDs using direct imaging and microlensing.