Abstract
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 three-dimensional (3D) radiation hydrodynamics code co5bold, we present the first transport coefficients in degenerate star atmospheres that 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 of 6000–18 000 K and pure-helium atmospheres in the range of 12 000–34 000 K. Our results suggest that warm hydrogen-rich atmospheres (DA; ${\gtrsim} 13\, 000$ K) and helium-rich atmospheres (DB and DBA; ${\gtrsim} 30\, 000$ 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 in 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 time-scale. This is typically less than 0.1 per cent of disc lifetime estimates, a quantity that 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.
Highlights
It is accepted that 25–50 per cent of all white dwarfs show clear evidence of metal pollution in their surface layers (Zuckerman et al 2010; Koester, Gansicke & Farihi 2014; Farihi et al 2016)
A major limitation with this approach, is the large range of advective time-scales spanned by a single simulation box, where the vertical diffusion coefficient was found in CU19 to vary by up to seven orders of magnitude
We have presented the first diffusion coefficients of stellar surfaceplane transport derived from 3D tracer experiments for white dwarfs
Summary
It is accepted that 25–50 per cent of all white dwarfs show clear evidence of metal pollution in their surface layers (Zuckerman et al 2010; Koester, Gansicke & Farihi 2014; Farihi et al 2016). The canonical model is that a circumstellar disc born of one or many tidally disrupted planetesimals is able to constantly feed planetary material on to the white dwarf surface (Jura 2003). These metals disappear from the observable layers at rates defined by the sinking time-scale (Koester 2009). In all cases, surviving planets are required to gravitationally scatter asteroids and minor planets on to the central regions (Debes & Sigurdsson 2002; Debes, Walsh & Stark 2012; Veras 2016)
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