Constraining the origin of the planetary debris surrounding ZTF J0139+5245 through rotational fission of a triaxial asteroid

Abstract

White dwarfs containing orbiting planetesimals or their debris represent crucial benchmarks by which theoretical investigations of post-main-sequence planetary systems may be calibrated. The photometric transit signatures of likely planetary debris in the ZTF J0139+5245 white dwarf system has an orbital period of about 110 days. An asteroid which breaks up to produce this debris may spin itself to destruction through repeated close encounters with the star without entering its Roche radius and without influence from the white dwarf's luminosity. Here, we place coupled constraints on the orbital pericentre (q) and the ratio (β) of the middle to longest semiaxes of a triaxial asteroid which disrupts outside of this white dwarf's Roche radius (r Roche ) soon after attaining its 110-day orbit. We find that disruption within tens of years is likely when β 0.6 and q ≈ 1.0 − 2.0r Roche , and when β 0.2 out to q ≈ 2.5r Roche . Analysing the longer-timescale disruption of triaxial asteroids around ZTF J0139+5245 is desirable but may require either an analytical approach relying on ergodic theory or novel numerical techniques.

The lifetimes of planetary debris discs around white dwarfs

“…We have shown here that the survival timescales for spin discs are strongly dependent on the values of Rp and M disc , and can vary from seconds to about 1 Myr (despite some cold disc cases with small numbers of planetesimals where the survival timescales exceed this value). If the disc mass in ZTF J0139+5245 is 10 14 − 10 15 kg (Veras et al 2020a), then Fig. 5 demonstrates that the lifetime of this disc is at least hundreds if not thousands of years; only if the star was brighter would the disc be influenced by the Yarkovsky effect.…”

“…Makarov & Veras (2019) demonstrated the concept of YORP-less spin-up to destruction due solely to close passages with a white dwarf, and Veras et al (2020a) applied the idea to the ZTF J0139+5245 system, where the semimajor axis of the debris is just 0.42 au (Vanderbosch et al 2020). Veras et al (2020a) found that rotational fission could occur at separations up to 3R Roche across the progenitor density range of 1 − 8 g/cm 3 . We adopt max(ro) = 4.5R⊙ here for these discs, but acknowledge that spin discs may extend further pending future parameter space explorations.…”

“…We can also look for theoretical constraints in studies of disc formation, whether it be from tidal disruption (Graham et al 1990;Jura 2003;Debes et al 2012;Veras et al 2014a;Malamud & Perets 2020a,b) or rotational disruption (Makarov & Veras 2019;Veras et al 2020a). Malamud & Perets (2020b) illustrated that tidal disruption can produce planetesimals ranging in size from their numerical resolution limit of a few km up to hundreds of km.…”

“…YORP discs have not yet been observed. For tidal systems with transiting debris, the amount of dust may be estimated by assuming that a homogeneous rectangular or cylindrical dust cloud creates the transits (Gänsicke et al 2016;Xu et al 2018a;Vanderbosch et al 2020;Veras et al 2020a). For both WD 1145+017 and ZTF J0139+5245, this mass was estimated to be about 10 14 kg.…”

“…For the debris discs generated from exo-planetesimals approaching the white dwarf, there are (at least) two formation channels: tidal disruption within the Roche radius of the white dwarf (Graham et al 1990;Jura 2003;Debes et al 2012;Veras et al 2014a;Malamud & Perets 2020a,b) and spin disruption outside of the Roche radius (Makarov & Veras 2019;Veras et al 2020a). The spin disruption mechanism occurs when the exchange between spin and angular momentum of exo-planetesimals on highly eccentric orbits becomes chaotic, and can spin these objects up to break-up speed.…”