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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 form a debris disk around the star. We provide a grid of models for hydrogen rich white dwarfs accreting heavy material. We sweep a 3D parameter space involving different effective temperatures, envelope's hydrogen content and accretion rates. The grid is appropriate for determining accretion rates in white dwarfs showing the presence of heavy elements. 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, that 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. We obtain final (stationary or near stationary) and reliable abundances for a grid of models representing hydrogen rich white dwarfs of different effective temperatures and hydrogen contents, applied to various accretion rates. Our results provide estimates of accretion rates, accounting for thermohaline mixing, to be used for further studies on evolved planetary systems., Comment: 14 pages, 13 figures, 7 tables. Accepted for publication in A&A

An increasing number of white dwarf stars show atmospheric chemical composition polluted by heavy elements accreted from debris disk material. The existence of such debris disks strongly suggests the presence of one or more planet(s) whose gravitational interaction with rocky planetesimals is responsible for their disruption by tidal effect. The ZZ Ceti pulsator and polluted DAZ white dwarf GD 133 is a good candidate for searching for such a potential planet. We started in 2011 a photometric follow-up of its pulsations. As a result of this work in progress, we used the data gathered from 2011 to 2015 to make an asteroseismological analysis of GD 133, providing the star parameters from a best fit model with $M$/$M_{\odot}$ = 0.630 $\pm$ 0.002, $T_{\rm eff}$ = 12400 K $\pm$ 70 K, log($M_{\rm He}/M$) = -2.00 $\pm$ 0.02, log($M_{\rm H}/M$) = -4.50 $\pm$ 0.02 and determining a rotation period of $\approx$ 7 days., Comment: 10 pages, 13 figures, accepted by MNRAS

White dwarfs are compact objects with atmospheres containing mainly light elements, hydrogen or helium. Because of their surface high gravitational field, heavy elements diffuse downwards in a very short timescale compared to the evolutionary timescale, leaving the lightest ones on the top of the envelope. This results in the main classification of white dwarfs as hydrogen rich or helium rich. But many helium rich white dwarfs show also the presence of hydrogen traces in their atmosphere, whose origin is still unsettled. Here we study, by means of full evolutionary calculations, the case for a representative model of the "He-H-Z" white dwarfs, a sub-group of helium rich white dwarfs showing both heavy elements and a large amount of hydrogen in their atmosphere. We find it impossible to explain its hydrogen atmospheric content by the convective mixing of a primordial hydrogen present in the star. We conclude that the most likely explanation is the accretion of hydrogen rich material, presumably water-bearing, coming from a debris disk., Comment: 3 pages, 1 figure, Proceedings of the PHOST "Physics of Oscillating Stars" conference (2-7 Sept. 2018, Banyuls-sur-mer, France), Edited by J. Ballot, S. Vauclair, & G. Vauclair

Asteroseismology is a unique tool to explore the internal structure of stars through both observational and theoretical research. The internal structure of pulsating hydrogen shell white dwarfs (ZZ Ceti stars) detected by asteroseismology is regarded as the representative of all DA white dwarfs. Observations for KUV~08368+4026, which locates in the middle of the ZZ Ceti instability strip, have been carried out in 1999 and from 2009 to 2012 with either single-site runs or multisite campaigns. Time-series photometric data of about 300 hours were collected in total. Through data reduction and analysis, 30 frequencies were extracted, including four triplets, two doublets, one single mode and further signals. The independent modes are identified as either l=1 or l=2 modes. Hence, a rotation period of $5.52\pm 0.22$ days was deduced from the period spacing in the multiplets. Theoretical static models were built and a best fit model for KUV~08368+4026 was obtained with $0.692\pm0.002$ solar mass, $(2.92\pm0.02)\times 10^{-3}$ solar luminosity and the hydrogen mass fraction of $10^{-4}$ stellar mass., Comment: 9 pages, 7 figures

A precision of order one percent is needed on the parameters of exoplanet-hosts stars in order to correctly characterize the planets themselves. This will be achieved by asteroseismology. It is important in this context to test the influence on the derived parameters of introducing atomic diffusion with radiative accelerations in the models. In this paper, we begin this study with the case of the star 94 Ceti A. We performed a complete asteroseismic analysis of the exoplanet-host F-type star 94 Ceti A, from the first radial-velocity observations with HARPS up to the final computed best models. This star is hot enough to suffer from important effects of atomic diffusion, including radiative accelerations. We tested the influence of such effects on the computed frequencies and on the determined stellar parameters. We also tested the effect of including a complete atmosphere in the stellar models. The radial velocity observations were done with HARPS in 2007. The low degree modes were derived and identified using classical methods and compared with the results obtained from stellar models computed with the Toulouse Geneva Evolution Code (TGEC). We obtained precise parameters for the star 94 Ceti A. We showed that including atomic diffusion with radiative accelerations can modify the age by a few percents, whereas adding a complete atmosphere does not change the results by more than one percent., Comment: 7 pages, 6 figures, accepted for publication in A&A

A large fraction of white dwarf stars shows photospheric chemical composition polluted by heavy elements accreted from a debris disk. Such debris disks result from the tidal disruption of rocky planetesimals which had 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 towards estimating the mass of the planetesimals and towards understanding the ultimate fate of the planetary systems. The accretion of heavy material with a mean molecular weight, $\mu$, higher than the mean molecular weight of the white dwarf outer layers, induces a double-diffusive instability producing fingering convection and 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. We performed numerical simulations of the accretion of material with a chemical composition similar to the bulk Earth one. We considered accretion rates from $10^{4}$~g/s to $10^{10}$~g/s. The double-diffusive instability develops on a very short time scale. The accretion rate needed to reproduce the observed abundances exceeds by more than 2 orders of magnitude the rate estimated by neglecting the fingering convection in the case of GD~133, and by approximately 1.7 dex in the case of G~29-38. Our numerical simulations show that fingering convection is an efficient mechanism to mix the accreted material and that it must be taken into account in the determination of accretion rates., Comment: 6 pages, 6 figures, to be published in A&A

Aims. We use the Kepler data accumulated on the pulsating DB white dwarf KIC 08626021 to explore in detail the stability of its oscillation modes, searching in particular for evidences of nonlinear behaviors. Methods. We analyse nearly two years of uninterrupted short cadence data, concentrating in particular on identified triplets due to stellar rotation that show intriguing behaviors during the course of the observations. Results. We find clear signatures of nonlinear effects attributed to resonant mode coupling mechanisms. We find that a triplet at 4310 {\mu}Hz and this doublet at 3681 {\mu}Hz (most likely the two visible components of an incomplete triplet) have clear periodic frequency and amplitude modulations typical of the so-called intermediate regime of the resonance, with time scales consistent with theoretical expectations. Another triplet at 5073 {\mu}Hz is likely in a narrow transitory regime in which the amplitudes are modulated while the frequencies are locked. Using nonadiabatic pulsation calculations based on a model representative of KIC 08626021 to evaluate the linear growth rates of the modes in the triplets, we also provide quantitative information that could be useful for future comparisons with numerical solutions of the amplitude equations. Conclusions. The identified modulations are the first clear-cut signatures of nonlinear resonant couplings occurring in white dwarf stars. These should resonate as a warning to projects aiming at measuring the evolutionary cooling rate of KIC 08626021, and of white dwarf stars in general. Nonlinear modulations of the frequencies can potentially jeopardize any attempt to measure reliably such rates, unless they could be corrected beforehand. These results should motivate further theoretical work to develop nonlinear stellar pulsation theory., Comment: 14 pages, 13 Figures, 2 Tables, accepted to A&A

The Kepler spacecraft provides new opportunities to search for long term frequency and amplitude modulations of oscillation modes in pulsating stars. We ana- lyzed nearly two years of uninterrupted data obtained with this instrument on the DBV star KIC 08626021 and found clear signatures of nonlinear resonant mode coupling af- fecting several triplets. The behavior and timescales of these amplitude and frequency modulations show strong similarities with theoretical expectations. This may pave the way to new asteroseismic diagnostics, providing in particular ways to measure for the first time linear growth rates of pulsation modes in white dwarf stars.

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.

The pulsating DA white dwarfs (ZZ Ceti stars) are $g$-mode non-radial pulsators. Asteroseismology provides strong constraints on their global parameters and internal structure. Since all the DA white dwarfs falling in the ZZ Ceti instability strip do pulsate, the internal structure derived from asteroseismology brings knowledge for the DA white dwarfs as a whole group. HS 0507+0434B is one of the ZZ Ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study. We carried out multisite observation campaigns in 2007 and from December 2009 to January 2010. In total, 206 hours of photometric time-series have been collected. They have been analysed by means of Fourier analysis and simultaneous multi-frequency sine-wave fitting. In total, 39 frequency values are resolved including 6 triplets and a number of linear combinations. We identify the triplets as $\ell$=1 $g$-modes split by rotation. We derived the period spacing, the rotational splitting and the rotation rate. From the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star: its total mass M$_{*}$/M$_{\odot}$ = 0.675, its luminosity L/L$_{\odot}$=3.5$\times 10^{-3}$, and its hydrogen mass fraction M$_{H}$/M$_{*}$= 10$^{-8.5}$., Comment: 12 pages,8 figures, accepted for publication in MNRAS

Heavy elements are observed in the atmospheres of many DA and DB white dwarfs, and their presence is attributed to the accretion of matter coming from debris disks. Several authors have deduced accretion rates from the observed abundances, taking into account the mixing induced by the convective zones and the gravitational settling. The obtained values are different for DA and DB white dwarfs. Here we show that an important process was forgotten in all these computations: thermohaline mixing, induced by the inverse $\mu$-gradient built during the accretion process. Taking this mixing into account leads to an increase of the derived accretion rates, specially for DA white dwarfs, and modifies the conclusions., Comment: 4 pages, to appear in Eurowd2012, proceedings of the 18th European Workshop on White Dwarfs, Krakow, August 13-17, 2012, eds : Jurek Krzesinski, Greg Stachowski, Pawel Moskalik

This paper presents a detailed and precise study of the characteristics of the Exoplanet Host Star and CoRoT main target HD 52265, as derived from asteroseismic studies. The results are compared with previous estimates, with a comprehensive summary and discussion. The basic method is similar to that previously used by the Toulouse group for solar-type stars. Models are computed with various initial chemical compositions and the computed p-mode frequencies are compared with the observed ones. All models include atomic diffusion and the importance of radiative accelerations is discussed. Several tests are used, including the usual frequency combinations and the fits of the \'echelle diagrams. The possible surface effects are introduced and discussed. Automatic codes are also used to find the best model for this star (SEEK, AMP) and their results are compared with that obtained with the detailed method. We find precise results for the mass, radius and age of this star, as well as its effective temperature and luminosity. We also give an estimate of the initial helium abundance. These results are important for the characterization of the star-planet system., Comment: 9 pages, 6 figures, 7 tables, to be published in Astronomy and Astrophysics

We report on analysis of 308.3 hrs of high speed photometry targeting the pulsating DA white dwarf EC14012-1446. The data were acquired with the Whole Earth Telescope (WET) during the 2008 international observing run XCOV26. The Fourier transform of the light curve contains 19 independent frequencies and numerous combination frequencies. The dominant peaks are 1633.907, 1887.404, and 2504.897 microHz. Our analysis of the combination amplitudes reveals that the parent frequencies are consistent with modes of spherical degree l=1. The combination amplitudes also provide m identifications for the largest amplitude parent frequencies. Our seismology analysis, which includes 2004--2007 archival data, confirms these identifications, provides constraints on additional frequencies, and finds an average period spacing of 41 s. Building on this foundation, we present nonlinear fits to high signal-to-noise light curves from the SOAR 4.1m, McDonald 2.1m, and KPNO 2m telescopes. The fits indicate a time-averaged convective response timescale of 99.4 +/- 17 s, a temperature exponent 85 +/- 6.2 and an inclination angle of 32.9 +/- 3.2 degrees. We present our current empirical map of the convective response timescale across the DA instability strip., Comment: Accepted for publication in the Astrophysical Journal

The star HD 52265 is a G0V metal-rich exoplanet-host star observed in the seismology field of the CoRoT space telescope from November 2008 to March 2009. The satellite collected 117 days of high-precision photometric data on this star, showing that it presents solar-like oscillations. HD 52265 was also observed in spectroscopy with the Narval spectrograph at the same epoch. We characterise HD 52265 using both spectroscopic and seismic data. The fundamental stellar parameters of HD 52265 were derived with the semi-automatic software VWA, and the projected rotational velocity was estimated by fitting synthetic profiles to isolated lines in the observed spectrum. The parameters of the observed p modes were determined with a maximum-likelihood estimation. We performed a global fit of the oscillation spectrum, over about ten radial orders, for degrees l=0 to 2. We also derived the properties of the granulation, and analysed a signature of the rotation induced by the photospheric magnetic activity. Precise determinations of fundamental parameters have been obtained: Teff = 6100 +- 60 K, log g = 4.35 +- 0.09, [M/H] = 0.19 +- 0.05, as well as vsini = 3.6 +0.3 -1.0 km/s. We have measured a mean rotation period P_rot = 12.3 +- 0.15 days, and find a signature of differential rotation. The frequencies of 31 modes are reported in the range 1500-2550 micro-Hz. The large separation exhibits a clear modulation around the mean value = 98.3 +- 0.1 micro-Hz. Mode widths vary with frequency along an S-shape with a clear local maximum around 1800 micro-Hz. We deduce lifetimes ranging between 0.5 and 3 days for these modes. Finally, we find a maximal bolometric amplitude of about 3.96 +- 0.24 ppm for radial modes., Comment: published in A&A, 11 pages, 14 figures, 6 tables

KPD 1930+2752 is a short-period pulsating subdwarf B (sdB) star. It is also an ellipsoidal variable with a known binary period just over two hours. The companion is most likely a white dwarf and the total mass of the system is close to the Chandresakhar limit. In this paper we report the results of Whole Earth Telescope (WET) photometric observations during 2003 and a smaller multisite campaign from 2002. From 355 hours of WET data, we detect 68 pulsation frequencies and suggest an additional 13 frequencies within a crowded and complex temporal spectrum between 3065 and 6343 $\mu$Hz (periods between 326 and 157 s). We examine pulsation properties including phase and amplitude stability in an attempt to understand the nature of the pulsation mechanism. We examine a stochastic mechanism by comparing amplitude variations with simulated stochastic data. We also use the binary nature of KPD 1930+2752 for identifying pulsation modes via multiplet structure and a tidally-induced pulsation geometry. Our results indicate a complicated pulsation structure that includes short-period ($\approx 16$ h) amplitude variability, rotationally split modes, tidally-induced modes, and some pulsations which are geometrically limited on the sdB star., Comment: 30 pages, 17 figures, 11 tables. Accepted for publication by MNRAS

We present an analysis of the observations of HD 51106 and HD 50747 by the satellite CoRoT, obtained during its initial run, and of the spectroscopic preparatory observations. AIMS: We complete an analysis of the light curve, extract the main frequencies observed, and discuss some preliminary interpretations about the stars. Methods: We used standard Fourier transform and pre-whitening methods to extract information about the periodicities of the stars. Results: HD 51106 is an ellipsoidal binary, the light curve of which can be completely explained by the tidal deformation of the star and smaller secondary effects. HD 50747 is a triple system containing a variable star, which exhibits many modes of oscillation with periods in the range of a few hours. On the basis of this period range and the analysis of the physical parameters of the star, we conclude that HD 50747 is a Gamma-Doradus star., Comment: 7 pages, 8 figures, use (Astronomy-Astrophysics format/macro LAtex)