Sublimation-induced orbital perturbations of extrasolar active asteroids and comets: application to white dwarf systems

The metal budgets in some white dwarf (WD) atmospheres reveal that volatile-rich circumstellar bodies must both exist in extrasolar systems and survive the giant branch phases of stellar evolution. The resulting behaviour of these active asteroids or comets which orbit WDs is not well-understood, but may be strongly influenced by sublimation due to stellar radiation. Here we develop a model, generally applicable to any extrasolar system with a main-sequence or WD star, that traces sublimation-induced orbital element changes in approximately km-sized extrasolar minor planets and comets travelling within hundreds of au. We derive evolution equations on orbital time-scales and for arbitrarily steep power-law sublimation dependences on distance, and place our model in a Solar system context. We also demonstrate the importance of coupling sublimation and general relativity, and the orbital consequences of outgassing in arbitrary directions. We prove that non-gravitational accelerations alone cannot result in orbit crossing with the WD disruption radius, but may shrink or expand the orbit by up to several au after a single pericentre passage, potentially affecting subsequent interactions with remnant debris and planets. Our analysis suggests that extant planets must exist in polluted WD systems.