Stochastic accretion of planetesimals on to white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution

Abstract

This paper explores how the stochastic accretion of planetesimals onto white dwarfs would be manifested in observations of their atmospheric pollution. Archival observations of pollution levels for unbiased samples of DA and non-DA white dwarfs are used to derive the distribution of inferred accretion rates, confirming that rates become systematically lower as sinking time (assumed here to be dominated by gravitational settling) is decreased, with no discernable dependence on cooling age. The accretion rates expected from planetesimals that are all the same mass (i.e., a mono-mass distribution) are explored both analytically and using a Monte Carlo model, quantifying how measured accretion rates inevitably depend on sinking time, since different sinking times probe different times since the last accretion event. However, that dependence is so dramatic that a mono-mass distribution can be excluded within the context of this model. Consideration of accretion from a broad distribution of planetesimal masses uncovers an important conceptual difference: accretion is continuous (rather than stochastic) for planetesimals below a certain mass, and the accretion of such planetesimals determines the rate typically inferred from observations; smaller planetesimals dominate the rates for shorter sinking times. A reasonable fit to the observationally inferred accretion rate distributions is found with model parameters consistent with a collisionally evolved mass distribution up to Pluto-mass, and an underlying accretion rate distribution consistent with that expected from descendants of debris discs of main sequence A stars. With these parameters, while both DA and non-DA white dwarfs accrete from the same broad planetesimal distribution, this model predicts that the pollution seen in DAs is dominated by the continuous accretion of < 35 km objects, and that in non-DAs by > 35 km objects (though the dominant size varies between stars by around an order of magnitude from this reference value). Further observations that characterise the dependence of inferred accretion rates on sinking time and cooling age (including a consideration of the effect of thermohaline convection on models used to derive those rates), and the decadal variability of DA accretion signatures, will improve constraints on the mass distribution of accreted material and the lifetime of the disc through which it is accreted.

Infrared observations of white dwarfs and the implications for the accretion of dusty planetary material

“…A disc lifetime of 100yrs remains short compared to most estimates (e.g. Girven et al 2012), although it is longer, but of the same order of magnitude as the ∼ 20yr disc lifetime estimated by Wyatt et al (2014). Thus, to conclude, whilst a finite dust lifetime cannot explain the absence of an infrared excess for the full population, it provides a good explanation for those white dwarfs with sinking timescales greater than five hundred years.…”

Circumstellar debris and pollution at white dwarf stars

“…This formulation yields an instantaneous, ongoing rate for those stars actually in accretion-diffusion equilibrium, while for stars that are unlikely (or uncertain) to be in a steady state, the equation provides a historical, average rate over a single sinking timescale (Farihi et al, 2012b). In the simplistic case of constant accretion over disk lifetime or diffusion timescale (whichever is shorter), both the instantaneous and historical rates among the DAZ and DBZ stars, respectively, should be comparable in the early or steady-state phases Wyatt et al, 2014). Figure 10 depicts infrared excess detections and non-detections, as a function of instantaneous or average accretion rate, for all the polluted white dwarfs observed with Spitzer during its first seven cycles (Bergfors et al, 2014).…”

Post-Main Sequence Evolution of Icy Minor Planets: Implications for Water Retention and White Dwarf Pollution

“…According to Wyatt et al (2014) and Veras et al (2014b), direct accretion is far less likely, since the WD radius is about ∼70 times smaller than the tidal disruption radius.…”