Horizontal spreading of planetary debris accreted by white dwarfs

Abstract

White dwarfs with metal-polluted atmospheres have been studied widely in the context of the accretion of rocky debris from evolved planetary systems. One open question is the geometry of accretion and how material arrives and mixes in the white dwarf surface layers. Using the 3D radiation-hydrodynamics code CO5BOLD, we present the first transport coefficients in degenerate star atmospheres which describe the advection-diffusion of a passive scalar across the surface-plane. We couple newly derived horizontal diffusion coefficients with previously published vertical diffusion coefficients to provide theoretical constraints on surface spreading of metals in white dwarfs. Our grid of 3D simulations probes the vast majority of the parameter space of convective white dwarfs, with pure-hydrogen atmospheres in the effective temperature range 6000–18 000 K and pure-helium atmospheres in the range 12 000–34 000 K. Our results suggest that warm hydrogen-rich atmospheres (DA; ≳ 13 000 K) and helium-rich atmospheres (DB, DBA; ≳ 30 000 K) are unable to efficiently spread the accreted metals across their surface, regardless of the time dependence of accretion. This result may be at odds with the current non-detection of surface abundance variations at white dwarfs with debris discs. For cooler hydrogen- and helium-rich atmospheres, we predict a largely homogeneous distribution of metals across the surface within a vertical diffusion timescale. This is typically less than 0.1 per cent of disc lifetime estimates, a quantity which is revisited in this paper using the overshoot results. These results have relevance for studies of the bulk composition of evolved planetary systems and models of accretion disc physics.

The entry geometry and velocity of planetary debris into the Roche sphere of a white dwarf

“…This homogenising timescale range is a subset of the disc lifetime range from theoretical constraints (Veras & Heng 2020), which has no lower limit and an upper limit of 10 7 yr. Empirical evidence from the currently observable sample (Girven et al 2012;Cunningham et al 2021) indicates a more restricted disc lifetime range of ∼ 10 4 − 10 6 yr. Either way, the homogenising timescale may be longer than the disc lifetime.…”

“…Accreted debris not only sinks radially towards the white dwarf core, but also spreads across the photospheric surface. Cunningham et al (2021) showed that homogenising debris across the surface of convective white dwarfs occurs on timescales on the order of 10 1 -10 5 yr. This range implies that surface abundances could exhibit some heterogeneity if metal accretion is highly localised, which will occur if this homogenising timescale is greater than the disc lifetime.…”

“…The detectability of a single accretion event depends on, amongst other factors, the geometry of asteroid entry into the white dwarf Roche sphere and photosphere. For example, Cunningham et al (2021) performed a spectroscopic analysis of a metal-polluted DAZ white dwarf (SDSS J104341.53+085558.2) with a cooling age of ≈150 Myr. They found that a sufficiently metallic spot covering just ≈10 per cent of the visible surface could be detectable in spectroscopic observations, although a more homogeneous distribution of surface metals better fit the observational data.…”

Spectral analysis of cool white dwarfs accreting from planetary systems: from the UV to the optical

“…Furthermore, no evidence of Zeeman splitting is observed in any lines, in particular the components of the Ca infra-red triplet which is particularly sensitive to small fields due to its red wavelength and large Landé-𝑔 factors, allowing us to place an upper-limit of 40 kG from the GTC 𝑖-band spectrum. A heterogeneous abundance distribution is also ruled out as the horizontal spreading timescale for metals across the surface of cool white dwarfs with helium-dominated atmospheres should be around four orders of magnitude faster than the sinking timescale (Cunningham et al 2021). With no ready explanation for the peculiar change in abundances, we conduct the rest of our analysis into SDSS J0956+5912 referring to results for both the SDSS and GTC abundances.…”

“…While the corresponding diffusion timescales are on the order of Myrs, these are still much shorter than the 1-10 Gyr white dwarf cooling ages, thus maintaining the requirement of accretion as the origin of the metals. On the other hand, the Myr diffusion timescales are likely longer than the dusty debris disc lifetime (Girven et al 2012;Cunningham et al 2021), and so DZs are rarely observed with the infrared excesses characteristic of debris discs. Because of the low opacity of helium in the outer layers of cool DZs, their atmospheres reach fluid-like densities at the deepest layers relevant to atmospheric modelling (Blouin et al 2018).…”