Precise determination of stellar parameters of the ZZ Ceti and DAZ white dwarf GD 133 through asteroseismology

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 MNRA

Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

The lightcurves of variable DA stars are usually multi-periodic and non-sinusoidal, so that their Fourier transforms show peaks at eigenfrequencies of the pulsation modes and at sums and differences of these frequencies. These combination frequencies provide extra information about the pulsations, both physical and geometrical, that is lost unless they are analyzed. Several theories provide a context for this analysis by predicting combination frequency amplitudes. In these theories, the combination frequencies arise from nonlinear mixing of oscillation modes in the outer layers of the white dwarf, so their analysis cannot yield direct information on the global structure of the star as eigenmodes provide. However, their sensitivity to mode geometry does make them a useful tool for identifying the spherical degree of the modes that mix to produce them. In this paper, we analyze data from eight hot, low-amplitude DAV white dwarfs and measure the amplitudes of combination frequencies present. By comparing these amplitudes to the predictions of the theory of Goldreich & Wu, we have verified that the theory is crudely consistent with the measurements. We have also investigated to what extent the combination frequencies can be used to measure the spherical degree (ell) of the modes that produce them. We find that modes with ell > 2 are easily identifiable as high ell based on their combination frequencies alone. Distinguishing between ell=1 and 2 is also possible using harmonics. These results will be useful for conducting seismological analysis of large ensembles of ZZ Ceti stars, such as those being discovered using the Sloan Digital Sky Survey. Because this method relies only on photometry at optical wavelengths, it can be applied to faint stars using 4 m class telescopes.Comment: 73 pages, 22 figures, accepted in the Ap

High Resolution Spectroscopy of the Pulsating White Dwarf G29-38

We present the analysis of time-resolved, high resolution spectra of the cool white dwarf pulsator, G29-38. From measuring the Doppler shifts of the H-alpha core, we detect velocity changes as large as 16.5 km/s and conclude that they are due to the horizontal motions associated with the g-mode pulsations on the star. We detect seven pulsation modes from the velocity time-series and identify the same modes in the flux variations. We discuss the properties of these modes and use the advantage of having both velocity and flux measurements of the pulsations to test the convective driving theory proposed for DAV stars. Our data show limited agreement with the expected relationships between the amplitude and phases of the velocity and flux modes. Unexpectedly, the velocity curve shows evidence for harmonic distortion, in the form of a peak in the Fourier transform whose frequency is the exact sum of the two largest frequencies. Combination frequencies are a characteristic feature of the Fourier transforms of light curves of G29-38, but before now have not been detected in the velocities, nor does published theory predict that they should exist. We compare our velocity combination frequency to combination frequencies found in the analysis of light curves of G29-38, and discuss what might account for the existence of velocity combinations with the properties we observe. We also use our high-resolution spectra to determine if either rotation or pulsation can explain the truncated shape observed for the DAV star's line core. We are able to eliminate both mechanisms: the average spectrum does not fit the rotationally broadened model and the time-series of spectra provides proof that the pulsations do not significantly truncate the line.Comment: 24 pages, 9 figures, Accepted for publication in ApJ (June

Gravity-Modes in ZZ Ceti Stars: I.Quasiadiabatic Analysis of Overstability

We analyze the stability of g-modes in variable white dwarfs with hydrogen envelopes. In these stars, the radiative layer contributes to mode damping because its opacity decreases upon compression and the amplitude of the Lagrangian pressure perturbation increases outward. The overlying convective envelope is the seat of mode excitation because it acts as an insulating blanket with respect to the perturbed flux that enters it from below. A crucial point is that the convective motions respond to the instantaneous pulsational state. Driving exceeds damping by as much as a factor of two provided $\omega\tau_c\geq 1$, where $\omega$ is the radian frequency of the mode and $\tau_c\approx 4\tau_{th}$ with $\tau_{th}$ being the thermal time constant evaluated at the base of the convective envelope. As a white dwarf cools, its convection zone deepens, and modes of lower frequency become overstable. However, the deeper convection zone impedes the passage of flux perturbations from the base of the convection zone to the photosphere. Thus the photometric variation of a mode with constant velocity amplitude decreases. These factors account for the observed trend that longer period modes are found in cooler DAVs. The linear growth time, ranging from hours for the longest period observed modes ($P\approx 20$ minutes) to thousands of years for those of shortest period ($P\approx 2$ minutes), probably sets the time-scale for variations of mode amplitude and phase. This is consistent with observations showing that longer period modes are more variable than shorter period ones. Our investigation confirms many results obtained by Brickhill in his pioneering studies of ZZ Cetis.Comment: 26 pages, including 5 figures, uses aaspp4.sty, submitted to Ap

The period and amplitude changes in the coolest GW Virginis variable star (PG 1159-type) PG 0122+200

Context: The PG 1159 pre-white dwarf stars experiment a rapidly cooling phase with a time scale of a few 10 6 years. Theoretical models predict that the neutrinos produced in their core should play a dominant role in the cooling, mainly at the cool end of the PG 1159 sequence. Measuring the evolutionary time scale of the coolest PG 1159 stars could offer a unique opportunity to empirically constrain the neutrino emission rate. Aims. A subgroup of the PG 1159 stars are nonradial pulsators, the GW Vir type of variable stars. They exhibit g-mode pulsations with periods of a few hundred seconds. As the stars cool, the pulsation frequencies evolve according to the change in their internal structure. It was anticipated that the measurement of their rate of change would directly determine the evolution time scale and so constrain the neutrino emission rates. As PG 0122+200 (BB Psc) defines the red edge of the GW Vir instability strip, it is a good candidate for such a measurement. Methods. The pulsations of PG 0122+200 have been observed during 22 years from 1986 to 2008, through the fast photometry technique. We used those data to measure the rate of change of its frequencies and amplitudes. Results. Among the 24 identified ℓ = 1 modes, the frequency and amplitude variations have been obtained for the seven largest amplitude ones. We find changes of their frequency of much larger amplitudes and shorter time scales than the one predicted by theoretical models that assume that the cooling dominates the frequency variations. In the case of the largest amplitude mode at 2497 μHz (400 s), its variations are best fitted by a combination of two terms: one long term with a time scale of 5.4 × 10 4 years, which is significantly shorter than the predicted evolutionary time scale of 8 × 10 6 years; and one additional periodic term with a period of either 261 or 211 days. Some other mechanism(s) than the cooling must be responsible for such variations. We suggest that the resonant coupling induced within triplets by the star rotation could be such a mechanism. As a consequence, no useful constraints on the neutrino emission rate can presently be derived as long as the dominant mechanism is not properly understood. Conclusions. The temporal variations in the pulsation frequencies observed in PG 0122+200 cannot be simply attributed to the cooling of the star, regardless of the contribution of the neutrino losses. Our results suggest that the resonant coupling induced by the rotation plays a dominant role which must be further investigated.Facultad de Ciencias Astronómicas y Geofísica

White dwarf spins from low mass stellar evolution models

The prediction of the spins of the compact remnants is a fundamental goal of the theory of stellar evolution. Here, we confront the predictions for white dwarf spins from evolutionary models including rotation with observational constraints. We perform stellar evolution calculations for stars in the mass range 1... 3\mso, including the physics of rotation, from the zero age main sequence into the TP-AGB stage. We calculate two sets of model sequences, with and without inclusion of magnetic fields. From the final computed models of each sequence, we deduce the angular momenta and rotational velocities of the emerging white dwarfs. While models including magnetic torques predict white dwarf rotational velocities between 2 and 10 km s$^{-1}$, those from the non-magnetic sequences are found to be one to two orders of magnitude larger, well above empirical upper limits. We find the situation analogous to that in the neutron star progenitor mass range, and conclude that magnetic torques may be required in order to understand the slow rotation of compact stellar remnants in general.Comment: Accepted for A&A Letter

HD 51106 and HD 50747: an ellipsoidal binary and a triple system observed with CoRoT

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

Precise Modeling of the Exoplanet Host Star and CoRoT Main Target HD 52265

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 Astrophysic