Accretion and diffusion in white dwarfs

Abstract

Context. A number of cool white dwarfs with metal traces, of spectral types DAZ, DBZ, and DZ have been found to exhibit infrared excess radiation due to circumstellar dust. The origin of this dust is possibly a tidally disrupted asteroid that formed a debris disk now supplying the matter accreting onto the white dwarf. To reach any clear conclusions from the observed composition of the white dwarf atmosphere to that of the circumstellar matter, we need a detailed understanding of the accretion and diffusion process, in particular the diffusion timescales. Aims. We aim to provide data for a wide range of white dwarf parameters and all possible observed chemical elements. Methods.Starting from atmosphere models, we calculate the structure of the outer envelopes, obtaining the depth of the convection zone and the physical parameters at the lower boundary. These parameters are used to calculate the diffusion velocities using calculations of diffusion coefficients available in the literature. Results. With a simple example, we demonstrate that the observed element abundances are not identical to the accreted abundances. Reliable conclusions are possible only if we know or can assume that the star has reached a steady state between accretion and diffusion. In this case, most element abundances differ only by factors in the range 2−4 between atmospheric values and the circumstellar matter. Knowing the diffusion timescales, we can also accurately relate the accreted abundances to the observed ones. If accretion has stopped, or if the rates vary by large amounts, we cannot determine the composition of the accreted matter with any certainty.

Circumstellar debris and pollution at white dwarf stars

“…This theoretical expectation is corroborated by high-resolution spectra that typically exhibit pure hydrogen or helium compositions (Zuckerman et al, 2003;Koester et al, 2005). Once the stellar ember has cooled below 25 000 K, metals can no longer be radiatively supported and diffuse from the atmosphere in a matter of days to years (Koester, 2009). At least 20 Myr is required to reach this temperature, and roughly 0.5 Myr is spent as a hot and luminous star with T eff ∼ 10 5 K, L ∼ 50 L ; (Fontaine et al, 2001).…”

“…While the diffusion timescales for all heavy elements in all white dwarfs 7 are universally orders or magnitude shorter than their cooling ages, they vary substantially as a function of effective temperature and between hydrogen-and helium-rich atmospheres (Paquette et al, 1986). For 25 000 K > T eff > 6000 K, typical sinking timescales are on the order of days to 10 4 yr for pure hydrogen atmospheres, and from 10 to 10 6 yr for pure helium atmospheres (Koester, 2009). If a white dwarf is observed to have photospheric metals, the probability that it is in a transient phase of accretion, and not a steady-state, is proportional to the diffusion timescale divided by the lifetime of the pollution event; p trans ∝ τ/t disk ; the probability of being in a steady state is p ss = 1 − p trans .…”

“…In this case, the heavy element ratios in the star and circumstellar disk are identical as any significant sinking has yet to occur. After the passage of one to a few diffusion timescales, the system will approach a steady-state; in this condition the metal-to-metal ratios in the circumstellar disk and stellar atmosphere are related by the ratio of their sinking timescales (Koester, 2009). Finally, when accretion from the disk is complete, the photospheric metals will remain detectable for up to several diffusion timescales, depending on the observational sensitivity.…”

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

“…We follow previous work and use white dwarf atmosphere models (Koester 2010), kindly provided by the author, to fit the observed stellar spectrum in the optical, making use of previously derived stellar effective temperatures. For the Mullally et al (2007) sample, we use the J, H and Ks 2MASS photometry, and effective temperatures presented in their Rocchetto et al (2015), we use the temperatures quoted in their Table A1 and a mixture of 2MASS, SDSS, APASS and GALEX photometry, as available for the different stars.…”

“…Fig. 10 shows the distribution of gravitational settling timescales for calcium in the sample, taken from Table 5 and 6 of Koester (2009), based on the stellar effective temperature and atmospheric composition. The stellar type classification are taken from Kleinman et al (2013) for the Debes et al (2011a) sample.…”