Diffusion in white dwarfs - New results and comparative study

Paquette, C.; Pelletier, C.; Fontaine, G.; Michaud, G.

doi:10.1086/191112

Cited by 218 publications

(205 citation statements)

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“…Given the utility of the accretion rate diagnostic, it is important to examine when the steadystate equations might be valid, and the implications otherwise. 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).…”

Section: Accretion Rates and Historymentioning

confidence: 98%

Circumstellar debris and pollution at white dwarf stars

Farihi

2016

New Astronomy Reviews

300

265

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Circumstellar disks of planetary debris are now known or suspected to closely orbit hundreds of white dwarf stars. To date, both data and theory support disks that are entirely contained within the preceding giant stellar radii, and hence must have been produced during the white dwarf phase. This picture is strengthened by the signature of material falling onto the pristine stellar surfaces; disks are always detected together with atmospheric heavy elements. The physical link between this debris and the white dwarf host abundances enables unique insight into the bulk chemistry of extrasolar planetary systems via their remnants. This review summarizes the body of evidence supporting dynamically active planetary systems at a large fraction of all white dwarfs, the remnants of first generation, main-sequence planetary systems, and hence provide insight into initial conditions as well as long-term dynamics and evolution.

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Section: Accretion Rates and Historymentioning

confidence: 98%

Circumstellar debris and pollution at white dwarf stars

Farihi

2016

New Astronomy Reviews

300

265

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“…For the calculation of diffusion timescales we follow closely the fundamental works of Paquette et al (1986a) and Paquette et al (1986b). From the tables in the first paper, we take the fit coefficients for the calculation of Coulomb collision integrals and the diffusion coefficients as well as thermal diffusion coefficients.…”

Section: Diffusion Coefficients and Timescalesmentioning

confidence: 99%

“…We therefore calculated atmosphere and envelope models for hydrogen and helium atmosphere white dwarfs throughout the interesting temperature range and calculated the timescales for many elements. In this work, we follow the ground work laid by the Montreal group, using their data on the Coulomb collision integrals (Paquette et al 1986a) and to a large extent the methods outlined in Paquette et al (1986b).…”

Section: Introductionmentioning

confidence: 99%

Accretion and diffusion in white dwarfs

Koester¹

2009

A&A

282

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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.

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“…As pointed out in Paquette et al 1986, they all reached the same qualitative conclusion: the gravitational settling time scales of metals in cool white dwarfs are small compared to their evolutionary time scales. These stars should therefore have their photospheres depleted of metals if there is no extrinsic source such as accretion for example.…”

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confidence: 57%

“…Several investigators have been interested by the problem of gravitational settling in white dwarfs (Fontaine and Michaud 1979;Vauclair, Vauclair, and Greenstein 1979; Alcock and Illarianov 1980; Muchmore 1984;Paquette et al 1986). As pointed out in Paquette et al 1986, they all reached the same qualitative conclusion: the gravitational settling time scales of metals in cool white dwarfs are small compared to their evolutionary time scales. These stars should therefore have their photospheres depleted of metals if there is no extrinsic source such as accretion for example.…”

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confidence: 99%

Time-Dependent Studies of the Settling of Heavy Elements in the Envelopes of Cool White Dwarfs

Dupuis

Pelletier

Fontaine

et al. 1989

International Astronomical Union Colloquium

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Gravitational settling is widely accepted as being a fundamental physical process acting upon superficial layers of white dwarfs and resulting in an important alteration of their atmospheric composition. Several investigators have been interested by the problem of gravitational settling in white dwarfs (Fontaine and Michaud 1979;Vauclair, Vauclair, and Greenstein 1979; Alcock and Illarianov 1980; Muchmore 1984;Paquette et al. 1986). As pointed out in Paquette et al. 1986, they all reached the same qualitative conclusion: the gravitational settling time scales of metals in cool white dwarfs are small compared to their evolutionary time scales. These stars should therefore have their photospheres depleted of metals if there is no extrinsic source such as accretion for example. This is consistent with the observational fact that most of the cool white dwarfs spectra just show hydrogen and helium lines while the absence of metallic lines indicates a strong depletion of metals. Although the qualitative agreement between theory and observations is satisfactory, only time-dependent calculations can lead to a thorough understanding of the heavy element abundance patterns in cool white dwarfs. In particular, the predicted abundance of an element within the framework of the accretion-diffusion model does depend explicitly on the results of such calculations. We have already presented some preliminary results of numerical simulation of accretion episodes of heavy elements into white dwarfs (Dupuis et al. 1987). As part of an ongoing detailed investigation of these processes, we focus here exclusively on the mechanism of gravitational settling in white dwarfs in order to clear some confusion which has appeared in the literature.The usual notion of an e-folding diffusion time scale strictly applies at the base of the convection zone of a stellar model after having made a number of approximations. If an element can be considered as trace and if ordinary diffusion can be neglected (i.e. the concentration gradient is much smaller than its equilibrium value; see Fontaine and Michaud 1979), then it is a simple matter to show that, at the base of a convection zone, the abundance of a given element is given by,where 8, the diffusion or settling time scale, is given by,where G is the gravitational constant, g is the local gravity, q is the fractional mass, p is the density, and u is the diffusion velocity of the trace element with respect to the background (w < 0). The exponential behavior shown in equation (1) is not valid in regions below the convection zone and the notion of an e-folding diffusion time scale loses its significance there. The time-dependence of the abundance at a given shell can only be obtained from a solution of the continuity equation and, generally, the behavior is very different from an exponential 359 available at https://www.cambridge.org/core/terms. https://doi

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Diffusion in white dwarfs - New results and comparative study

Cited by 218 publications

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Circumstellar debris and pollution at white dwarf stars

Circumstellar debris and pollution at white dwarf stars

Accretion and diffusion in white dwarfs

Time-Dependent Studies of the Settling of Heavy Elements in the Envelopes of Cool White Dwarfs

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