On the role of resonances in polluting white dwarfs by asteroids

Abstract

Pollution of white dwarf atmospheres may be caused by asteroids that originate from the locations of secular and mean-motion resonances in planetary systems. Asteroids in these locations experience increased eccentricity, leading to tidal disruption by the white dwarf. We examine how the ν 6 secular resonance shifts outwards into a previously stable region of the asteroid belt, as the star evolves to a white dwarf. Analytic secular models require a planet to be engulfed in order to shift the resonance. We show with numerical simulations that as a planet gets engulfed by the evolving star, the secular resonance shifts and the rate of tidal disruption events increases with the engulfed planet's mass and its orbital separation. We also investigate the behaviour of mean-motion resonances. The width of a mean-motion resonance increases as the star loses mass and becomes a white dwarf. The ν 6 secular resonance is more efficient at driving tidal disruptions than mean-motion resonances with Jupiter. By examining 230 observed exoplanetary systems whose central star will evolve into a white dwarf, we find that along with an Earth mass planet at 1 au, hot Jupiters at a semi-major axis a 0.05 au and super-Earths of mass 10 M ⊕ at a 0.3 au represent planet types whose engulfment shifts resonances enough to cause pollution of the white dwarfs to a degree in agreement with observations.

The post-main-sequence fate of the HR 8799 planetary system

“…The pollution is likely to occur soon after the star becomes a white dwarf because the planets are so massive. Terrestrial-mass planets would allow minor planets to meander for multiple Gyr (Frewen & Hansen 2014;Mustill et al 2018), whereas giant-mass planets would scatter the vast majority of minor planets within 1 Gyr (Veras et al 2021). We then might expect HR 8799 to be polluted at cooling ages under about 1 Gyr.…”

“…Overall, major planets, minor planets, dust, gas and metallic debris have all been discovered around or in white dwarfs; for a recent review, see Veras (2021). The HR 8799 system is an exemplar progenitor white dwarf planetary system, for several reasons.…”

“…These planets are also on the verge of instability, and instability during the white dwarf phase is necessary to perturb objects close to and later onto the star (Debes & Sigurdsson 2002;Veras et al 2013a). Finally, the HR 8799 system features multiple debris discs, and these could supply the metals that will be accreted by the white dwarf through interactions with the planets (Bonsor et al 2011;Debes et al 2012;Frewen & Hansen 2014;Mustill et al 2018;Smallwood et al 2018Smallwood et al , 2021Veras et al 2021).…”