Accretion from debris disks onto white dwarfs : Fingering (thermohaline) instability and derived accretion rates

Recent observations of a large number of DA and DB white dwarfs show evidence of debris disks, which are the remnants of old planetary systems. The infrared excess detected with \emph{Spitzer} and the lines of heavy elements observed in their atmospheres with high-resolution spectroscopy converge on the idea that planetary material accretes onto these stars. Accretion rates have been derived by several authors with the assumption of a steady state between accretion and gravitational settling. The results are unrealistically different for DA and DB white dwarfs. When heavy matter is accreted onto stars, it induces an inverse $\mu$-gradient that leads to fingering (thermohaline) convection. The aim of this letter is to study the impact of this specific process on the derived accretion rates in white dwarfs and on the difference between DA and DB. We solve the diffusion equation for the accreted heavy elements with a time-dependent method. The models we use have been obtained both with the IRAP code, which computes static models, and the La Plata code, which computes evolutionary sequences. Computations with pure gravitational settling are compared with computations that include fingering convection. The most important result is that fingering convection has very important effects on DAs but is inefficient in DBs. When only gravitational settling is taken into account, the time-dependent computations lead to a steady state, as postulated by previous authors. When fingering convection is added, this steady state occurs much later. The surprising difference found in the past for the accretion rates derived for DA and DB white dwarfs disappears. The derived accretion rates for DAs are increased when fingering convection is taken into account, whereas those for DBs are not modified. More precise and developed results will be given in a forthcoming paper

Thermohaline mixing and the photospheric composition of low-mass giant stars

We compute full evolutionary sequences of red giant branch stars close to the luminosity bump by including state of the art composition transport prescriptions for the thermohaline mixing regimes. In particular we adopt a self-consistent double-diffusive convection theory, that allows to handle the instabilities that arise when thermal and composition gradients compete against each other, and a very recent empirically motivated and parameter free asymptotic scaling law for thermohaline composition transport. In agreement with previous works, we find that during the red giant stage, a thermohaline instability sets in shortly after the hydrogen burning shell (HBS) encounters the chemical discontinuity left behind by the first dredge-up. We also find that the thermohaline unstable region, initially appearing at the exterior wing of the HBS, is unable to reach the outer convective envelope, with the consequence that no mixing of elements that produces a non-canonical modification of the stellar surface abundances occurs. Also in agreement with previous works, we find that by artificially increasing the mixing efficiency of thermohaline regions it is possible to connect both unstable regions, thus affecting the photospheric composition. However, we find that in order to reproduce the observed abundances of red giant branch stars close to the luminosity bump, thermohaline mixing efficiency has to be artificially increased by about 4 orders of magnitude from that predicted by recent 3D numerical simulations of thermohaline convection close to astrophysical environments. From this we conclude the chemical abundance anomalies of red giant stars cannot be explained on the basis of thermohaline mixing alone.Comment: 7 pages, 6 figures, accepted for publication in A&

Importance of fingering convection for accreting white dwarfs in the framework of full evolutionary calculations: the case of the hydrogen-rich white dwarfs GD 133 and G 29-38

Context. A large fraction of white dwarfs show photospheric chemical composition that is polluted by heavy elements accreted from a debris disk. Such debris disks result from the tidal disruption of rocky planetesimals that have survived to whole stellar evolution from the main sequence to the final white dwarf stage. Determining the accretion rate of this material is an important step toward estimating the mass of the planetesimals and understanding the ultimate fate of the planetary systems. Aims. The accretion of heavy material with a mean molecular weight, μ, higher than the mean molecular weight of the white dwarf outer layers, induces a double-diffusive instability producing the fingering convection and an extra-mixing. As a result, the accreted material is diluted deep into the star. We explore the effect of this extra-mixing on the abundance evolution of Mg, O, Ca, Fe and Si in the cases of the two well-studied polluted DAZ white dwarfs: GD 133 and G 29-38. Methods. We performed numerical simulations of the accretion of material that has a chemical composition similar to the bulk Earth composition. We assumed a continuous and uniform accretion and considered a range of accretion rates from 104 g/s to 1010 g/s. Two cases are simulated, one using the standard mixing length theory (MLT) and one including the double-diffusive instability (fingering convection). Results. The double-diffusive instability develops on a very short timescale. The surface abundance rapidly reaches a stationary value while the depth of the zone mixed by the fingering convection increases. In the case of GD 133, the accretion rate needed to reproduce the observed abundances exceeds by more than two orders of magnitude the rate estimated by neglecting the fingering convection. In the case of G 29-38 the needed accretion rate is increased by approximately 1.7 dex. Conclusions. Our numerical simulations of the accretion of heavy elements on the hydrogen-rich white dwarf GD 133 and G 29-38 show that fingering convection is an efficient mechanism to mix the accreted material deeply. We find that when fingering convection is taken into account, accretion rates higher by 1.7 to 2 dex than those inferred from the standard MLT are needed to reproduce the abundances observed in G 29-38 and GD 133

New simulations of accreting DA white dwarfs: Inferring accretion rates from the surface contamination

International audienceContext. A non-negligible fraction of white dwarf stars show the presence of heavy elements in their atmospheres. The most accepted explanation for this contamination is the accretion of material coming from tidally disrupted planetesimals, which forms a debris disk around the star. Aims: We provide a grid of models for hydrogen-rich white dwarfs accreting heavy material. We sweep a 3D parameter space that has different effective temperatures, envelope hydrogen contents, and accretion rates. The grid is appropriate for determining accretion rates in white dwarfs that show the presence of heavy elements. Methods: Full evolutionary calculations of accreting white dwarfs were computed including all relevant physical processes, particularly the fingering (thermohaline) convection, a process neglected in most previous works, which has to be considered to obtain realistic estimations. Accretion is treated as a continuous process, and bulk-Earth composition is assumed for the accreted material. Results: We obtain final (stationary or near-stationary) and reliable abundances for a grid of models that represent hydrogen-rich white dwarfs of different effective temperatures and hydrogen contents, which we apply to various accretion rates. Conclusions: Our results provide estimates of accretion rates, accounting for thermohaline mixing, to be used for further studies on evolved planetary systems

RevMexAA (Serie de Conferencias), 14, 69--69 (2002)

Merritt 1990) to follow the evolution of a satellite similar to the one considered by Carpintero et al. (CelMechDynAstr, 73, 159, 1999), except that the 10 5 particles that make it up were randomly chosen from a HR model with W 0 = 0:5. We followed the satellite for 62.83 time units, which correspond to five periods of the circular orbit, or 110 crossing times of the satellite. The original satellite was on a circular orbit of 100 units radius and, besides, we also considered the same satellite on elongated orbits, starting at the apocenter and characterizing the orbit by the amount of departure of the apocenter distance from the original circular orbit. Figure 1 shows the evolution of the semiaxes of the satellite 0 10 20 30 40 50 60 Time 0.185 0.195 0.205 0.215 Semiaxes, departure Circular orbit Elongated orbit (10) Elongated orbit (20) Departure from circular Fig. 1. Evolution of the HR models placed on circular and elongated (10% and 20% departures from the circu