Post-main-sequence planetary system evolution rsos.royalsocietypublishing.org Dimitri Veras Department of Physics, University of Warwick, Coventry CV4 7AL, UK Review The fates of planetary systems provide unassailable insights Cite this article: Veras D. 2016 into their formation and represent rich cross-disciplinary Post-main-sequence planetary system dynamical laboratories. Mounting observations of post-main- evolution. R. Soc. open sci. 3: 150571. sequence planetary systems necessitate a complementary level http://dx.doi.org/10.1098/rsos.150571 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 Received: 23 October 2015 interpretation and modelling of currently known systems and Accepted: 20 January 2016 upcoming discoveries. 1. Introduction Subject Category: Decades of unsuccessful attempts to find planets around other Astronomy Sun-like stars preceded the unexpected 1992 discovery of planetary bodies orbiting a pulsar [1,2]. The three planets around Subject Areas: the millisecond pulsar PSR B1257+12 were the first confidently extrasolar planets/astrophysics/solar system reported extrasolar planets to withstand enduring scrutiny due to their well-constrained masses and orbits. However, a retrospective Keywords: historical analysis reveals even more surprises. We now know that dynamics, white dwarfs, giant branch stars, the eponymous celestial body that Adriaan van Maanen observed pulsars, asteroids, formation in the late 1910s [3,4]isanisolatedwhitedwarf(WD)witha metal-enriched atmosphere: direct evidence for the accretion of planetary remnants. These pioneering discoveries of planetary material around Author for correspondence: or in post-main-sequence (post-MS) stars, although exciting, Dimitri Veras represented a poor harbinger for how the field of exoplanetary e-mail: [email protected] science has since matured. The first viable hints of exoplanets found around MS stars (γ Cephei Ab and HD 114762 b) [5,6], in 1987–1989, were not promulgated as such due to uncertainties in the interpretation of the observations and the inability to place upper bounds on the companion masses. A confident detection of an MS exoplanet emerged with the 1995 discovery of 51 Pegasi b [7], followed quickly by 70 Virginis b [8]and47 Ursae Majoris b [9], although in all cases the mass degeneracy remained. These planets ushered in a burgeoning and flourishing era of astrophysics. Now, two decades later, our planet inventory numbers in the thousands; over 90% of all known exoplanets orbit MS stars that will eventually become WDs, and WDs will eventually become the most common stars in the Milky Way. 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. NS abbreviations: GB 2 WD section 1: Introduction AGB: asymptotic giant branch rsos.royalsocietypublishing.org ................................................ section 2: Stellar evolution key points CE: common envelope 2.1: Single star evolution GB: giant branch 2.2: Common envelope and binary star evolution MS: main sequence section 3: Observational motivation NS: neutron star 3.1: Planetary remnants in and around WDs RGB: red giant branch 3.2: Major and minor planets around WDs SB: substellar body front matter front 3.3: Subgiant and giant star planet systems SN: supernova 3.4: Putative planets in post-CE binaries WD: white dwarf 3.5: Pulsar planets 3.6: Circumpulsar asteroid and disc signatures often-used variables: section 4: Stellar mass ejecta a semimajor axis R. Soc. open sci. 4.1: The mass-variable point-mass two-body problem e eccentricity 4.2: The mass-variable solid body two-body problem G gravitational constant 4.3: Stellar wind/gas/atmospheric drag i inclination section 5: Star–planet tides L luminosity M mass 3 5.1: Tidal theory : 150571 5.2: Simulation results r distance section 6: Stellar radiation R radius 6.1: Giant branch radiation t time 6.2: Compact object radiation T temperature v velocity section 7: Multi-body interactions r 7.1: Collisions within debris discs density 7.2: One star, one planet and asteroids 7.3: One star, multiple planets and no asteroids subscripts: 7.4: Two stars, planets and no asteroids none mutual property of SB and star star body 7.5: Two stars, one planet and asteroids 7.6: Three stars only b binary stellar companion section 8: Formation from stellar fallback d disc 8.1: Post-CE formation around WDs 8.2: Post-SN formation around NSs disambiguation equations: 8.3: Formation from tidal disruption of companions 2.3: initial-to-final mass relation section 9: WD disc formation from 1st-GEN SBs 2.4: WD radius-to-mass relation section 10: WD disc evolution 2.5: WD luminosity-to-mass relation section 11: Accretion onto WDs 3.2: probability of transit or occultation section 12: Other dynamics 3.3: duration of transit or occultation 12.1: General relativity 4.12: semimajor axis change from SN 12.2: Magnetism 4.13: escape condition from SN 12.3: External influences 4.14: eccentricity change from SN 12.4: Climate and habitability 4.16: accretion rate onto SB section 13: The fate of the solar system 4.20: gravitational drag force section 14: Numerical codes 4.21 + 10.8: frictional drag force section 15: Future directions 5.1: semimajor axis evolution from tides 15.1: Pressing observations 6.1: orbital evolution from stellar radiation end matter 15.2: Theoretical endeavours 9.1: tidal disruption radius Figure 1. Paper outline and nomenclature. Some section titles are abbreviated to save space. Variables not listed here are described in situ, and usually contain descriptive subscripts and/or superscripts. The important abbreviation ‘substellar body’ (SB) can refer to, for example, a brown dwarf, planet, moon, asteroid, comet or pebble. ‘Disambiguation equations’ refer to relations that have appeared in multipledifferentformsintheliterature.Inthispaper,theseotherformsarereferencedinthetextthatsurroundstheseequations,sothat readerscandecidewhichformisbesttouse(ornewlyderive)fortheirpurposes.Overdotsalwaysrefertotimederivatives.Theexpression refers to averaged quantities. Nevertheless, major uncertainties linger. MS exoplanet detection techniques currently provide minimal inferences about the bulk chemical composition of exoplanetary material. How planets form and dynamically settle into their observed states remains unanswered and represents a vigorous area of active research. Calls for a better understanding of post-MS evolution arise from MS discoveries of planets near the end of their lives [10] and a desire to inform planet formation models [11]. Direct observation of MS smaller bodies, such as exo-asteroids, exo-comets or exo-moons, remains tantalizingly out of reach, except in a handful of cases [12–16]. giant branch (GB) phases 3 mass ejecta orbital changes rsos.royalsocietypublishing.org section 4 ................................................ mass ejecta physical changes section 4 star–planet tides section 5 stellar radiation section 6 general relativity section 12a magnetic fields section 12b galactic tides R. Soc. open sci. section 12c stellar flybys section 12c distance in AU 10–3 10–2 10–1 110102 103 104 105 3 : 150571 white dwarf (WD) and neutron star (NS) phases mass ejecta orbital changes section 4 mass ejecta physical changes section 4 star–planet tides section 5 stellar radiation section 6 general relativity section 12a magnetic fields section 12b galactic tides section 12c stellar flybys section 12c distance in AU 10–3 10–2 10–1 110102 103 104 105 definitely non-negligible for at least some substellar bodies (SBs) possibly non-negligible for at least some substellar bodies (SBs) negligible for all substellar bodies (SBs) Figure 2. Important forces in post-MS systems. These charts represent just a first point of reference. Every system should be treated on a case-by-case basis. Magnetic fields include those of both the star and the SB, and external effects are less penetrative in theGBphases because they are relatively short. Post-MS planetary system investigations help alleviate these uncertainties, particularly with escalating observations of exoplanetary remnants in WD systems. Unlike for pulsar systems, planetary signatures are common in and around WD stars. The exquisite chemical constraints on rocky planetesimals that are gleaned from WD atmospheric abundance studies is covered in detail by the review of Jura & Young [17], and is not a focus of this article. Similarly, I do not focus on the revealing observational aspects of the nearly forty debris discs orbiting WDs, a topic recently reviewed by Farihi [18]. Instead, I place into context and describe the complex and varied dynamical processes that influence planetary bodies after the star has turned off of the MS. I attempt to touch upon all theoretical aspects of post-MS planetary science, although my focus is on the giant branch (GB) and WD phases of stellar evolution. The vital inclusion of bodies smaller than planets—e.g. exo-asteroids and exo-comets—in this review highlights both the necessity of incorporating Solar system constraints and models and the interdisciplinary nature of post-MS planetary science. Table 1. Some notable post-MS planetary systems. 4 rsos.royalsocietypublishing.org name type sections