Post-main-sequence planetary system evolution

Dimitri Veras

Source-linked AI summary

Post-main-sequence planetary system evolution

Dimitri Veras

arXiv:1601.05419v1Jan 20, 2016astro-ph.EPastro-ph.SR

TL;DR

Post-main-sequence observations raise the need to understand how planetary systems evolve after their stars leave the main sequence. This review synthesizes the diverse dynamical processes affecting planets and smaller bodies through giant-branch, white-dwarf, and neutron-star evolution, concluding that these systems provide distinctive constraints on planetary remnants and evolution.

Problem
Observations of post-main-sequence systems are increasing, but interpreting their planetary remnants requires broader theoretical treatment of their diverse dynamical processes.
Method
The paper reviews theoretical and dynamical processes affecting planets, asteroids, comets, and pebbles as host stars evolve through giant-branch, white-dwarf, and neutron-star phases.
Results
Post-main-sequence systems provide access to substellar-body chemistry, formation–fate links, constraints on tidal, mass-losing, and radiative processes, and environments for detecting extreme bodies.
Takeaways & Limitations
The review provides a foundation for interpreting and modelling currently known post-main-sequence planetary systems and upcoming discoveries.
Takeaways & Limitations
Lithium overabundance after substellar-body ingestion remains degenerate with dredge-up, tidal mixing, and thermohaline or magneto-thermohaline processes.

Abstract

from arXiv · show

The fates of planetary systems provide unassailable insights into their formation and represent rich cross-disciplinary dynamical laboratories. Mounting observations of post-main-sequence planetary systems necessitate a complementary level of theoretical scrutiny. Here, I review the diverse dynamical processes which affect planets, asteroids, comets and pebbles as their parent stars evolve into giant branch, white dwarf and neutron stars. This reference provides a foundation for the interpretation and modelling of currently known systems and upcoming discoveries.

1. Introduction

Post-main-sequence planetary systems offer distinctive observational and dynamical insights into planetary remnants, while motivating theory beyond main-sequence studies. This review frames those systems and develops a broad treatment of their post-main-sequence dynamics.

Observational motivation: About 90% of known exoplanets orbit main-sequence stars that will eventually become white dwarfs, making post-main-sequence evolution relevant to most currently known systems.
Observational motivation: White-dwarf systems are especially important because their planetary remnants can be studied through atmospheric pollution and associated debris discs.The review notes that planetary signatures are common around white dwarfs and that nearly forty white dwarfs host observed debris discs.
Motivation: Post-main-sequence systems provide access to substellar-body chemistry, links between formation and fate, constraints on stellar and planetary processes, and opportunities to detect extreme bodies.The review identifies giant-branch, white-dwarf, and neutron-star systems as the main sources of these insights.
Review scope: The article focuses on dynamical processes after the host star leaves the main sequence, particularly during giant-branch and white-dwarf evolution.Introductory stellar-evolution and observational material supplies background, while the central sections treat dynamical aspects in greater detail.
Scope and nomenclature: The review includes planets, brown dwarfs, moons, asteroids, comets, and pebbles under the abbreviation “substellar body” (SB).It uses this broader category because restricting relations to planets, asteroids, comets, or pebbles alone would be too narrow.

2. Stellar evolution key points

Stellar evolution changes the mass, radius, and luminosity of planetary-system hosts, thereby reshaping the environments experienced by substellar bodies. The review summarizes these stages and the prescriptions and uncertainties relevant to modelling them.

Main sequence: Main-sequence evolution supplies the historical context and initial conditions for post-main-sequence studies, with stellar lifetime decreasing from about 10 Gyr to 0.1 Gyr as initial mass rises from 1M⊙ to 6M⊙.Main-sequence stars burn hydrogen in their cores and lose mass through winds.
Giant branches: During the RGB and AGB, stars can lose up to 80% of their mass, reach radii of about 10 au, and vary in luminosity by many tens of thousands of times the main-sequence value.These changes may completely transform planetary systems, while the dominant isotropic and anisotropic mass-loss mechanisms remain difficult to identify.
Mass-loss prescriptions: RGB mass loss is traditionally parameterized with the Reimers formula, whereas AGB evolution generally uses a different prescription because applying Reimers’ formula can produce significantly erroneous results.AGB pulses can change mass loss by a few orders of magnitude, with peak loss typically occurring during the terminal AGB superwind.
Giant-branch interactions: Ingesting a large substellar body during giant-branch evolution may enhance photospheric lithium and spin up the star, but lithium overabundance has several degenerate explanations.Alternative mechanisms include dredge-up, tidal mixing, and thermohaline or magneto-thermohaline processes.
White dwarfs: After the giant-branch envelope is completely lost, stars with initial masses ≲8M⊙ become white dwarfs, whose cores are usually composed primarily of carbon and oxygen.About 95% of Milky Way stars are expected to become white dwarfs.

3. Observational motivation

Post-main-sequence systems expose planetary properties and dynamical processes that are difficult to access around main-sequence stars. Observations of polluted white dwarfs, debris discs, disintegrating bodies, and unusual planets motivate theoretical study of post-main-sequence evolution.

WD atmospheric pollution: 18 metals heavier than carbon have been detected in white dwarfs with cooling ages of 30 Myr to 500 Myr.The detections span rock-forming elements, refractory lithophiles, volatile elements, and siderophiles.
WD atmospheric pollution: 25%–50% of white dwarfs are polluted, supporting the interpretation that their atmospheric metals commonly originate from remnant planetary material.The evidence includes debris discs, disintegrating bodies, Earth-like abundances, meteorite-like diversity, and the short sinking times of metals.
WD debris discs: Nearly 40 polluted white dwarfs host detected debris discs, whereas no confidently reported disc is known around a single unpolluted white dwarf.Discs are difficult to detect for cooling ages above 0.5 Gyr, despite pollution being observable to about 5 Gyr.
WD debris discs: For white dwarfs older than a few Myr, debris discs lie within the Roche radius, approximately 0.6–1.2 R⊙ from the star.This location indicates that the discs neither extend to the photosphere nor formed during the main-sequence or giant-branch phases.
Disintegrating bodies: WD 1145+017 contains at least six nearly coplanar disintegrating bodies with orbital periods of approximately 4.4930 hours.The same system shows circumstellar gas streams and 11 metals in the white-dwarf atmosphere.
Unusual post-main-sequence planets: Post-main-sequence systems include extreme planetary configurations, from the 7 MJup planet at about 2500 au around WD 0806-661 to the circumbinary planet PSR B1620-26AB b.The latter orbits a white dwarf and millisecond pulsar, with constrained parameters including MSB ∼2.5MJup and a ∼23 au.

4. Stellar mass ejecta

Stellar mass loss is presented as a central post-main-sequence force because it changes substellar-body orbits across the system. The resulting mass-variable two-body problem is dynamically rich and requires distinctions among several physical assumptions.

Stellar mass loss non-negligibly affects the orbits of all substellar bodies at all distances.
The mass-variable two-body problem is dynamically rich and not energy conserving.
Analysis must distinguish how many bodies lose mass, whether loss is isotropic or instantaneous, whether kicks occur, whether bodies are point masses, and whether ejecta causes drag.

(a) The mass-variable point-mass two-body problem

The point-mass treatment organizes post-main-sequence orbital evolution around equations for time-dependent stellar mass, with distinct isotropic, anisotropic, and solution-regime behaviors. These relations describe orbital expansion, escape, and the limits of interpreting osculating elements.

Formulation: For fixed-mass substellar bodies, the relevant equations distinguish anisotropic and isotropic stellar mass loss, while variable substellar-body mass requires different cases.
Formulation: Isolating the mass-loss term expresses the classic static two-body problem as a perturbation and yields equations for planetary orbital elements.
Isotropic mass loss: Isotropic mass loss always increases the semimajor axis and orbital pericentre.
Interpretation: Oscillations in eccentricity can mask a smooth spiral, so all orbital elements must be considered together when interpreting non-Keplerian evolution.
Anisotropic mass loss: Anisotropic mass loss changes inclination and ascending-node longitude, but requires asymmetry about the stellar equator; isotropy is usually adequate within a few hundred au.
Solution regimes: The equations lack a complete analytical solution but have two well-defined regimes separated by a difficult transition regime.

(b) The mass-variable solid body two-body problem

Treating a substellar body as a solid introduces accretion from stellar ejecta and therefore more complex, anisotropic orbital dynamics. The consequences range from atmospheric alteration to potentially substantial mass growth.

Solid-body treatment: Lifting the point-mass assumption is motivated by physical changes to substellar bodies during stellar evolution.
Accretion: Accretion by a solid body makes the orbital equations more complex because captured ejecta introduces anisotropic mass loss.
Accretion consequences: Small bodies such as pebbles may gain enough mass to become boulders or be destroyed, while planetary atmospheres may be permanently altered.
Accretion-rate models: Accretion-rate estimates depend on assumptions including gravitational focusing, orbital circularity, and wind speed relative to orbital speed.
Accretion-rate models: Integrating accretion over time is complicated because stellar mass-loss rate varies nonmonotonically with time, initial mass, and metallicity.
Accretion consequences: Brown dwarfs and large planets could accrete mass equal to multiple times their main-sequence atmospheric masses.

(c) Stellar wind/gas/atmospheric drag

Interactions with stellar winds, gas, and atmospheres can alter surviving bodies through gravitational and frictional drag, while sufficiently small bodies may be disrupted. The relevant force and survival regime depends strongly on the surrounding medium and body size.

Physical setting: The treatment considers stellar winds, gas, and stellar atmospheres because interactions with these media may significantly affect smaller bodies.
Disruption: Sufficiently small substellar bodies can catastrophically disrupt under ram pressure, with stability depending on surface gravity and surrounding wind density.
Survival regimes: Approximate conditions suggest giant planets and brown dwarfs survive stellar atmospheres, while asteroids, comets, planets, and brown dwarfs readily survive stellar winds.
Survival regimes: Boulders and pebbles remain uncertain because proposed criteria differ between destruction by encountering their own mass in wind and entrainment when drag exceeds stellar gravity.
Drag categories: The review separates drag into gravitational drag from a wake and frictional drag from motion through the medium.
Gravitational drag: Gravitational drag is negligible outside stellar atmospheres, so atmospheric applications require distinguishing it from wind-mediated frictional drag.

5. Star-planet tides

Post-main-sequence tidal evolution depends on which bodies raise tides and which dissipation mechanism dominates. For giant-branch systems, stellar tides generally control the evolution of sufficiently large substellar bodies, producing engulfment, orbital retardation, or survival depending on stellar and orbital properties.

Tidal theory: Tidal modeling must determine which body raises each bulge and which dissipation mechanism dominates.The answers depend on both stellar and substellar-body properties, and some classical theories require caution.
Tidal theory: For giant-branch systems, planets or brown dwarfs within a few au generally raise stellar tides, whereas giant-branch stars are unlikely to raise tides in large substellar bodies.Asteroids and comets are too small to induce significant orbital changes through stellar tides.
Tidal theory: Turbulent viscous dissipation in the giant-branch envelope drives orbital retardation, changing a substellar body's semimajor axis and eccentricity.The process is also described as retardation of the equilibrium tide by convective motions.
Tidal theory: The tidal quality factor compresses uncertain dissipation physics into one parameter, but its time and frequency dependence is unknown and its constant-time-lag model is inconsistent for solid-bearing bodies.For giant-branch stars, the formalism from is described as better constrained.
Tidal theory: Analytical engulfment distances require assumptions about tidal effects and stellar mass-loss prescriptions, so their accuracy depends on the intended application.Numerical simulations inform some derived scalings.
Simulation results: Jupiter-mass planets can be engulfed, tidally affected without engulfment, or survive largely unaffected during RGB evolution.Surviving planets stalled by tides end closer to the white dwarf than predicted by adiabatic mass-loss expansion alone.
Simulation results: Surviving the RGB phase does not ensure survival through the AGB phase, where Jovian-mass and Earth-mass planets experience different tidal outcomes.Jovian planets must begin at least 20 percent farther out than the maximum stellar radius, while some Earth-mass planets can start within it and survive.
Simulation results: The predicted planet-free region within about 0.5 au around RGB stars is too wide to result from tidal effects alone.If retired A stars have smaller masses, the origin of the void becomes an even larger mystery.

6. Stellar radiation

Post-main-sequence stellar radiation alters the orbits, spins, atmospheres, and volatile content of smaller bodies across planetary systems. The review combines radiation-force treatments with results on thermal evaporation, sublimation, and debris evolution to characterize these effects around giant-branch stars, white dwarfs, and pulsars.

Stellar radiation: Giant-branch luminosities can exceed the Sun's by several orders of magnitude, extending snowlines to hundreds of au and affecting pebbles, asteroids, and comets.Asteroids and comets can undergo complex orbital changes and may self-destruct through overspinning.
Stellar radiation: The radiation-force equation combines acceleration from absorbed radiation, immediately reflected radiation, and delayed thermal re-emission.The delayed re-emission term is the Yarkovsky effect.
Stellar radiation: The Yarkovsky effect requires a body larger than a critical size between 1 cm and 10 m across realistic thermal and spin parameters.Radiation negligibly affects planet-sized bodies because acceleration decreases with increasing radius.
Stellar radiation: The Yarkovsky and combined Poynting-Robertson-drag/radiation-pressure expressions differ by four orders of magnitude in their coefficients.Averaging removes 1/c terms from the latter expressions but not from the Yarkovsky effect.
Stellar radiation: Nearly every Solar-system-belt asteroid with radius 100m-10km could break apart after the Sun leaves the main sequence if it reaches the critical spin period of 2.33 hours.The resulting debris field could extend to thousands of au.
Effect on planetary atmospheres: Thermal-evaporation escape-rate expressions apply under the atmospheric-structure condition Γ ≳20, but fuller treatments require feedback, stripping, photodissociation, hot-bubble immersion, and atmospheric-structure solutions.Pebble and boulder accretion can also alter the atmosphere's composition and structure.
White dwarf radiation: For nearly parabolic orbits with e ≳0.998, sublimative forces robustly preserve pericentre, so comets outside the white-dwarf disruption sphere do not enter it without other agents.Other orbital parameters may change more readily.
Pulsar radiation: Pulsar radiation can prevent metals from forming unless particles are shielded, while magnetospheric Yarkovsky forces may allow only bodies with R_SB ≳5 km to avoid infall from nascent discs with a ≳1 au.These effects bear on both second-generation formation and the evolution of already formed substellar bodies.

7. Multi-body interactions

Post-main-sequence mass loss reshapes multi-body planetary systems, triggering delayed instabilities, scattering, resonant delivery of smaller bodies, and destructive moon liberation. Outcomes remain intrinsically sensitive to chaotic initial conditions and modelling assumptions.

A single N-body integration of a chaotic system is not a deterministic prediction, with tiny initial-condition changes producing radically different long-term outcomes.Mercury’s maximum eccentricity over 5 Gyr varied by nearly unity after changing its initial semimajor axis by 0.38 mm.
Smaller-body dynamics: Mass-loss-driven stability changes can scatter part of a belt inward, while subsequent interactions with interior planets can produce white-dwarf-grazing orbits.Collisional evolution can also deplete debris discs and erase memory of their initial mass as collisional lifetimes shorten near the central star.
An asteroid belt with a Jupiter: Resonant interactions can capture smaller bodies during mass loss and increase their eccentricities until they potentially enter the white-dwarf disruption distance.About 2% of test particles followed this path, with one asteroid per simulation disrupting after 200 Myr; matching white-dwarf observations would require belts 4 × 10^0–6 × 10^5 times as massive as the Solar System asteroid belt.
Post-main-sequence mass loss can trigger instability during or long after the giant-branch phase by effectively resetting the system’s dynamical architecture.The resulting instability can eject planets and place survivors on moderately to highly eccentric orbits with pericentres of only a few au.
GB and WD planet simulations: Closely packed terrestrial planets can remain stable through the giant-branch phase and several gigayears of white-dwarf evolution before late unpacking and orbital meandering.After scattering instability, a planet may approach the white dwarf closely enough to enter its disruption radius.
GB and WD planet simulations: Planet-planet scattering on the white-dwarf phase can liberate moons, which may later perturb or be perturbed into the white dwarf or affect smaller bodies, fragments, and dust.In three-planet systems, instability can occur across multiple generations; about 1% of cases lost all three planets, while white-dwarf-phase ejection was most common.

8. Formation from stellar fallback

The review examines possible second-generation substellar-body formation from stellar fallback, common-envelope remnants, supernova-related discs, and disrupted companions. These pathways remain viable in specific early cooling-age or unusual-system contexts, but depend strongly on disc properties and stellar evolution.

8. Formation from stellar fallback: Fallback material may form second-generation substellar bodies, but observations typically sample cooling ages far exceeding the less-than-10-Myr formation timescale.The chemical composition of white-dwarf pollution is also inconsistent with stellar mass ejecta.
8. Formation from stellar fallback: Second-generation formation could open previously forbidden formation regions and permit interactions between newly formed and pre-existing planets, including possible third-generation systems.These possibilities arise when both components of a binary undergo post-main-sequence evolution.
(a) Post-common envelope formation around white dwarfs: Post-common-envelope disc mass is only a fraction of the material remaining bound after envelope ejection, while photoheating, photoionization, radiation pressure, and metallicity can alter formation.Angular-momentum efficiency determines both the mass deposited into planets and the envelope fraction entering the disc.
(b) Post-supernova formation around neutron stars: Circumpulsar discs can arise through binary mass transfer, donor ejecta, supernova-related disruption, or direct collision scenarios.The review presents these as multiple possible post-supernova formation channels.
(b) Post-supernova formation around neutron stars: Accretion luminosity may evaporate a planet or disperse a remnant disc too quickly for post-supernova second-generation formation.These restrictions were argued from stellar-evolution considerations.
(b) Post-supernova formation around neutron stars: Second-generation asteroids, but not planets, could readily form observable signatures in systems like B1931+24 under a compact, low-mass, metal-rich fallback-disc scenario.The scenario additionally requires sufficient magnetospheric mass inflow and disc survival for at least 10 Myr.
(b) Post-supernova formation around neutron stars: PSR B1257+12 discs modeled with viscous and layered accretion contain material to 1-2 au and enough mass to produce its planets, while gas dissipates in under 0.1 Myr.The short gas lifetime makes gas-giant formation unlikely.
(c) Formation from tidal disruption of companions: Disrupted stellar companions provide an alternative to fallback discs, with disruption discs potentially carrying three orders of magnitude more angular momentum than fallback discs.For PSR B1937+21, a tenuous disrupted-companion disc could halt growth after forming asteroids rather than planets.

9. White dwarf disc formation from first-generation substellar bodies

Observed compact white-dwarf debris discs are generally attributed to tidal disruption of first-generation substellar bodies, especially asteroids. Tidal disruption establishes eccentric rings whose later evolution is shaped by radiation, particle size, and additional dynamical effects.

9. White dwarf disc formation from first-generation substellar bodies: Compact discs at rd ≲ 1.2R⊙ around isolated white dwarfs cannot have formed during the main-sequence or giant-branch phases.Their progenitors are therefore associated with later disruption processes.
9. White dwarf disc formation from first-generation substellar bodies: The canonical explanation is disruption of first-generation substellar bodies, particularly asteroids on highly eccentric orbits with e ≳ 0.998.Their semimajor axes must be at least a few au to avoid engulfment, vaporization, or rotational fission.
9. White dwarf disc formation from first-generation substellar bodies: The tidal disruption radius depends on body shape, spin, composition, orbital state, and the definition of disruption.It defines a disruption or Roche sphere around the white dwarf.
9. White dwarf disc formation from first-generation substellar bodies: For strengthless bodies, rt ≈ 1.26R⋆(ρ⋆/ρSB)1/3, while broader formulations give coefficients of approximately 1.3-2.9.Internal tensile strength changes the disruption criterion for solid bodies.
9. White dwarf disc formation from first-generation substellar bodies: Simulations of highly eccentric rubble-pile asteroids show that disruption can create a highly collisionless eccentric ring retaining the original orbit’s shape.The disruption-sphere residence time is largely independent of semimajor axis, enabling scaled multi-orbit simulations.
9. White dwarf disc formation from first-generation substellar bodies: For collisionless rings with RSB ≈ 10^-5-10^-1 m, white-dwarf radiation compresses and circularises orbits inside the disruption radius.Outside this size range, Yarkovsky and radiation-scattering effects may dominate but remain unexplored.
9. White dwarf disc formation from first-generation substellar bodies: Radiation-driven shrinking depends on particle radius, so differently sized pebbles contract at different rates and fan out the original ring.General relativity becomes increasingly important as bodies approach the white dwarf, while collisions may alter subsequent shrinking.

10. White dwarf disc evolution

White-dwarf disc evolution involves coupled dust and gas dynamics, sublimation, collisions, viscosity, and secular effects. Major uncertainties remain in disc variability, gas production, thermal structure, and viscous transport.

10. White dwarf disc evolution: Observed dusty and gaseous disc structures remain difficult to explain, including dusty variability around WD J0959-0200 and gaseous asymmetries around SDSS J1228+1040.These uncertainties affect observational targeting and interpretations of disc formation and accretion.
10. White dwarf disc evolution: Gas should form through sublimation as the inner rim approaches the white dwarf, yet it is detected in only 7 of nearly 40 dusty discs.The detected gas overlaps radially with dust, creating an unresolved puzzle.
10. White dwarf disc evolution: Gas production through grain collisions is disputed: one study allows velocities up to 10^3 km/s, whereas another finds rapid inelastic damping makes the contribution negligible.The competing estimates imply different expectations for persistent gas generation.
10. White dwarf disc evolution: Disc temperature depends on optical thickness, shielding, white-dwarf and gas heating, sublimation cooling, and thermal radiation from particle surfaces.An isothermal disc would not produce detectable flux under the cited relation.
10. White dwarf disc evolution: Viscous-timescale estimates differ by six orders of magnitude, from 0.75 day to 2000 yr, because studies adopt different disc-formation and structural assumptions.The viscosity parameter itself remains unconstrained.
10. White dwarf disc evolution: Gas is expected inside dusty discs where r(out)d > rsub > r(in)d, and gas can also extend beyond the dusty disc boundaries.Gas accretes while viscously spreading outward to conserve angular momentum.
10. White dwarf disc evolution: Coupled gas-dust models support a buildup followed by runaway accretion, with eccentric gas motions as small as 10^-4 efficiently driving the runaway phase.Observed asymmetric gas-line profiles therefore indicate non-axisymmetric surface brightness rather than eccentric gas motions.
10. White dwarf disc evolution: Secular disc modes act over tens of years, about five orders of magnitude longer than orbital periods, and general-relativistic precession can match the observed timescale.External perturbers were excluded by simulations, while disc youth and self-generated perturbations require further modeling.

11. Accretion onto white dwarfs

Accretion onto white dwarfs connects polluted atmospheres and debris discs to the sizes, compositions, and delivery histories of substellar bodies. Inference is limited by sinking-time degeneracies, uncertain disc physics, and broad architectural variability.

11. Accretion onto white dwarfs: White-dwarf atmospheric pollution records externally accreted heavy metals and is therefore central to linking planetary-remnant composition with observations.Abundance ratios of different species are routinely reported.
11. Accretion onto white dwarfs: Element-abundance evolution models describe settling under assumptions about constant accretion, convection-zone mass, and diffusion timescales.These assumptions yield an explicit formula for the time-dependent mass fraction Xelm(t).
11. Accretion onto white dwarfs: Accretion modes remain degenerate in helium-rich white dwarfs because sinking times can reach Myr, whereas older hydrogen-rich white dwarfs have diffusion times of days to weeks.The degeneracy is absent for hydrogen-rich white dwarfs older than about 300 Myr.
11. Accretion onto white dwarfs: Pollution cannot be explained by mono-mass accretion distributions; a complex multi-mass distribution may also need to include a white-dwarf disc.The critical substellar-body radius separating continuous and stochastic accretion is about 1.7-170 km.
11. Accretion onto white dwarfs: Direct impacts allow boulders, asteroids, comets, and planets to accrete without passing through a disc, with explosion, ablation, and sublimation as possible outcomes.The cited impact outcomes are not mutually exclusive.
11. Accretion onto white dwarfs: Disc accretion proceeds through sublimated metallic gas between the dusty inner rim and white-dwarf surface, transported by viscous torques.Computing the mass flux requires modeling nontrivial dust-gas coupling and contributions such as Poynting-Robertson drag.
11. Accretion onto white dwarfs: Accretion-frequency and size-distribution predictions depend on planetary-system architecture and the instabilities experienced throughout its lifetime.The review emphasizes that the problem contains many free parameters.
11. Accretion onto white dwarfs: Cometary accretion rates are estimated at about one comet per 10^4 yr in two studies using different mass-loss prescriptions and environmental treatments.Both studies assume isotropic giant-branch mass loss without a natal kick.

12. Other dynamics

Post-main-sequence systems are shaped by stellar magnetism, Galactic tides, stellar flybys, and binary interactions, with effects varying across evolutionary phases and orbital scales.

Relativistic effects: General relativity can alter orbital elements on orbital timescales and drive pericentre precession on secular timescales.These effects may matter for volatile-rich substellar bodies with pericentres near the disruption radius.
Magnetism: Magnetic white dwarfs may reveal terrestrial planets with orbital periods shorter than about 30 hours through electron-cyclotron maser emission.The proposed mechanism is a unipolar-inductor circuit linking a conducting planet or core to the white dwarf’s magnetic poles.
Magnetism: Unipolar-inductor drag can drive inward migration, but the drift is negligible for r ≳200R⋆.At smaller distances, the body may already be undergoing tidal breakup, and the existence of a planet-mass conductor around GD 356 remains open.
External dynamics: Post-main-sequence mass loss enlarges orbital scales by at least a few and possibly orders of magnitude, increasing susceptibility to external Galactic forces.Systems previously protected from tides or flybys may therefore become externally perturbed.
External dynamics: AGB mass loss is decoupled from Galactic tides but not necessarily stellar flybys, whereas Galactic tides can become significant during the white-dwarf phase.The AGB result holds throughout the Milky Way.
Small-body dynamics: Oort-cloud comets can escape before, during, and after giant-branch evolution, with about three-quarters of the MS Hill-ellipsoid volume vulnerable for a 2M⊙ progenitor.The escape-prone semimajor-axis range is produced by post-main-sequence mass loss.
Binary systems: Galactic tides can trigger close encounters in wide binaries only after many Gyr of white-dwarf evolution, destabilizing previously quiescent planetary systems.This mechanism can provide an avenue for polluting very old white dwarfs.

13. The fate of the Solar system

The Solar system’s post-main-sequence fate depends on stellar expansion, mass loss, tides, radiation, and external perturbations, producing divergent outcomes across planets, belts, moons, and comets.

Remainder of MS: The Solar system’s outer architecture should remain broadly stable through the remaining main sequence, although the inner planets have a one to few percent collision or instability probability.The asteroid and Kuiper belts are expected to continue collisionally depleting.
Mercury and Venus: Mercury will be engulfed, and Venus will almost certainly share that fate because solar expansion and Sun-planet tides overcome their expanded orbits.The Sun may reach about 1 au, while Mercury and Venus expand to about 0.8 au and 1.5 au, respectively.
Earth: Earth’s fate is sensitive to the adopted Solar and tidal models, but one study finds engulfment unless all adjustable parameters lie at one edge of their uncertainty ranges.That study predicts Mercury, Venus, and Earth engulfment about 4.3, 1.5, and 0.5 Myr before the RGB phase ends, about 7.59 Gyr from now.
Earth: If Earth survives, it will not remain habitable, while the RGB-tip habitable zone may extend from about 49 to 71 au.The post-main-sequence state of Earth’s atmosphere and surface has not been modelled in detail.
Outer planets and asteroid belt: Mars and the giant planets should survive dynamically around the Solar white dwarf, but the asteroid belt likely will not.The giant planets are not expected to undergo instability, and Mars remains dynamically separated from Jupiter under adiabatic mass loss.
Moons: Solar-system moon orbits should become more stable after white-dwarf formation, but the effects of giant-branch radiation on icy crusts and oceans remain unexplored.The increased Hill radius and the absence of expected disruptive planetary scattering support orbital stability.
Kuiper belt and scattered disc: Kuiper-belt and scattered-disc evolution remains unclear because Yarkovsky redistribution and later stellar perturbations may alter depletion and resonant structure.An expanded scattered disc would be more susceptible to dynamical reshuffling.
Oort cloud: The Oort cloud will be dynamically excited by stellar mass loss, orbital expansion, Galactic tides, and stellar flybys, while depletion estimates during the giant branch disagree.The Milky Way–Andromeda collision changes the future prescriptions for tides and flybys.

14. Numerical codes

Post-main-sequence studies rely mainly on stellar-evolution and N-body codes, but full-lifetime integrations remain difficult because they must combine evolving stars, many forces, and long dynamical timescales.

Numerical tools: The two most widely used numerical-tool classes are stellar-evolution codes and N-body dynamics codes.Model-atmosphere codes are another relevant class but are not included in the listed code table.
Computational challenges: Full-lifetime integrations across the MS, GB, and much of the WD or NS phases remain computationally challenging.The main difficulties include coupling stellar and N-body evolution, timestep convergence, inclusion of additional forces, and sufficiently wide orbital configurations.
Code inventory: Table 2 categorizes cited numerical codes as stellar-evolution codes, N-body dynamics codes, or codes combining both.The table summarizes tools used by investigations discussed in the paper.
Computational challenges: Angular momentum is typically conserved and provides an important accuracy benchmark, although strong close encounters increase angular-momentum errors.Energy is not a conserved quantity in these integrations.
Recent codes: GENGA uses GPUs and is claimed to run up to 30 times faster than MERCURY and 8 times faster than PKDGRAV2.It can handle up to 2048 massive bodies or 10^6 test particles.

15. Future directions

Future progress requires coordinated observations and theory, including monitoring of white-dwarf systems, broader surveys, improved disruption and radiation models, and larger self-consistent simulations.

Observational priorities: Monitoring WD 1145+017 could constrain the number and masses of disintegrating bodies, future breakup events, disc changes, and white-dwarf accretion variability.The bodies reside within the disruption radius, making continued observations especially informative.
Observational priorities: A nearly 35% flux drop in WD J0959-0200 over 300 days motivates monitoring for disc flares and variable accretion rates.Simultaneous gas and dust observations may clarify their interplay with disc variability.
Observational priorities: More observations of giant-branch planets are needed because the observed planet-free region is too wide to be explained by tidal effects alone.This uncertainty bears directly on tidal dissipation mechanisms and planetary rheology.
Survey targets: High-mass polluted white dwarfs offer a route to constrain the masses of exoplanet host stars, since no main-sequence planet has yet been discovered around a star of about 4M⊙.The polluted WD SDSS J1228+1040 likely had such a progenitor mass.
Survey targets: JWST observations could distinguish young WD disc origins through brightness profiles and identify specific minerals for comparison with HST abundance measurements.The proposed origins include exo-Oort-cloud disruption and remnants of an exo-Kuiper belt.
Theoretical endeavours: Radiation modelling remains incomplete because no study has self-consistently integrated the relevant equations, and existing treatments assume restrictive body shapes and compositions.Highly eccentric objects, time-varying spin, nonspherical multilayered asteroids, and moons require more sophisticated models.
Theoretical endeavours: Mass-loss studies better understand substellar-body evolution than radiation and tides, but accretion, kicks, ram pressure, entrainment, drag, and resonance evolution remain insufficiently quantified.These uncertainties affect the transition between adiabatic and non-adiabatic motion and may influence white-dwarf pollution rates.
Theoretical endeavours: Self-consistent full-lifetime simulations remain limited in body count, simulated duration, and number of runs, despite the need for multi-planet systems containing asteroid or Kuiper belts.Computational hurdles remain the main boundary on broader architectures.