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The stability of planetary systems after stellar mass loss: Prospects for White Dwarf planets and pollution
Alexander James Mustill1*, Dimitri Veras2, Eva Villaver3, Amy Bonsor4, Boris GДnsicke2, Mark Wyatt
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Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-221 00 Lund, Sweden Department of Physics, University of Warwick, Coventry CV4 7AL, UK 3 Departamento de FМsica TeСrica, Universidad AutСmona de Madrid, Cantoblanco, 28049 Madrid, Spain 4 School of Physics, University of Bristol H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom 5 Institute of Astronomy, University of Cambridge, Madingley Road, CB3 9ET, UK *alex@astro.lu.se

Stars lose mass as they evolve to become white dwarfs (WDs), and this mass loss can induce instability in planetary systems as the planet:star mass ratio increases. We have numerically studied the dynamics of systems of two and three wide-orbit giant planets throughout their hosts' main sequence (MS), giant branch, and WD evolution. We find: Many giant planet systems spaced more closely than a 2:1 resonance, should they be stable on the MS, are destabilised following mass loss In triple-planet systems, instability around a WD can strike both systems that were stable on the MS, and those that relaxed into a metastable 2-planet configuration A few percent of unstable systems may dynamically deliver giant planets onto orbits close to a WD, where they may be detectable through timing or transits The instabilities around WDs occur at WD ages of 106 ­ 1010 yr, but more typically around 108 yr

Two-planet systems


1

Observational Implications
Planets around white dwarfs







Previous work had shown that mass loss experienced by stars on the RGB and AGB can induce instability in planetary systems 2. However, the consistent dynamics of planetary systems throughout the star's MS, giant and WD evolution, including the evolution of the star's mass and radius from stellar models, was required to properly understand the fates of planetary systems beyond the MS We adapted the MERCURY code3 to incorporate changes to the stellar mass and radius from the SSE stellar models4 In Veras et al. (2013) we studied the evolution of systems of two Jupiter-mass planets separated by a range of separations We restricted attention to stars >=3M to avoid the computational S ol cost of long MS lifetimes The inner planet is placed at 10au; closer planets require a treatment of tidal interaction with the star5,6 We find mass loss induces instability in systems stable on the MS, affecting systems closer than the 2:1 resonance

WD

Final semi-major axes and pericentres of planets around WDs in our three-planet simulations. Survivors have large semi-major axes (10s-100s of au) ~5% of our integrated systems have a planet that collides with the WD or attains a small pericentre (q<0.1au). Such planets may be tidally circularised before being destroyed, and be observed by timing or transits8 Pollution of white dwarfs


MS

Two-planet systems

Three-planet systems





Three-planet systems
WD MS


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Pollution of WD atmospheres asteroidal or cometary material Instabilities in our integrations Ages of polluted WDs may be observational bias is needed

is attributed to the accretion of destabilised by planets peak at ~108 yr older9, but more understanding of

In Mustill et al. (2014) we studied systems of three Jupitermass planets, separated by a range of Hill radii, again with the innermost planet at 10au As in the two-planet case, mass loss destabilises systems around WDs out to the 2:1 resonance

Next steps




Is using equal-mass planets unrealistic? Use a more realistic mass distribution What is the fate of multiple systems closer to the star? Incorporate the planets' tidal interaction with the giant star's envelope How does instability in a planetary system relate to WD pollution? Can low-mass planets be scattered onto detectable short-period orbits around WDs? Include small bodies in the integration to find probability of delivery close to WD, and its time evolution







Many systems lose more than one planet. In rare cases an AGB star destroys all three of its planets, by engulfment in the large envelope, or ejection by non-adiabatic mass loss Instability in WD systems affects both systems that were stable throughout the MS, as well as those that relaxed into a marginally stable two-planet configuration following a MS instability Overall, ~50% of our multiplanet systems around WDs are unstable Acknowledgements



Preliminary work suggests ~10% of a planetesimal belt may be accreted onto the WD during and after a giant planet instability References

AJM is grateful for support from Spanish grant AYA 2010/20630, Swedish Research Council grant 20113991, and grant number KAW 2012.0150 from the Knut and Alice Wallenberg foundation.

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Veras et al. 2013 Debes & Sigurdsson 2002 Chambers 1999

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Hurley et al. 2000 Mustill & Villaver 2012 Villaver et al. submitted

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Mustill et al. 2014 Faedi et al. 2011 Farihi et al. 2012