In the light of the recent and unexpected discovery of a brand new type of white dwarfs, those with carbon-dominated atmospheres, we examine the asteroseismological potential of such stars. The motivation behind this is based on the observation that past models of carbon-atmosphere white dwarfs have partially ionized outer layers that bear strong resemblance with those responsible for mode excitation in models of pulsating DB (helium-atmosphere) and pulsating DA (hydrogen-atmosphere) white dwarfs. Our exciting main result is that, given the right location in parameter space, some carbon-atmosphere white dwarfs are predicted to show pulsational instability against gravity modes. We are eagerly waiting the results of observational searches for luminosity variations in these stars.
We review the basic concepts, the present state of theoretical models, and the future prospects for theory and observations of pulsating stellar atmospheres. Our emphasis is on radially pulsating cool stars, which dynamic atmospheres provide a general example for the differences with standard static model atmospheres.
We report on our findings of the bright, pulsating, helium atmosphere white dwarf GD 358, based on time-resolved optical spectrophotometry. We identify 5 real pulsation modes and at least 6 combination modes at frequencies consistent with those found in previous observations. The measured Doppler shifts from our spectra show variations with amplitudes of up to 5.5 km/s at the frequencies inferred from the flux variations. We conclude that these are variations in the line-of-sight velocities associated with the pulsational motion. We use the observed flux and velocity amplitudes and phases to t…
We present detailed analysis of the vertical pulsation mode cross-section in ten rapidly oscillating Ap (roAp) stars based on spectroscopic time-series observations. The aim of this analysis is to derive from observations a complete picture of how the amplitude and phase of magnetoacoustic waves depend on depth. We find common features in the pulsational behaviour of roAp stars. Within a sample of representative elements the lowest amplitudes are detected for Eu II (and Fe in 33 Lib and in HD 19918), then pulsations go through the layers where Halpha core, Nd, and Pr lines are formed. There RV…
Pulsation influences atmospheric structures of variable AGB stars (Miras) considerably. Spectral lines of the CO dv=3 vibration-rotation bands (at 1.6mue) therefore have a very characteristic appearance in time series of high-resolution spectra. Coupled to the light cycle they can be observed blue- or red-shifted, for some phases even line doubling is found. This is being explained by radial pulsations and shock fronts emerging in the atmospheres. Based on dynamic model atmospheres synthetic CO line profiles were calculated consistently, reproducing this scenario qualitatively.
This work presents a new method to compute time and wavelength dependent center-to-limb brightness distributions for Classical Cepheids. Our model atmospheres are based on second-order accurate 1-D hydrodynamic calculations, performed in spherical geometry. The brightness intensity distributions, and the resulting limb darkening, are computed through the dynamic atmospheres by using a full set of atomic and molecular opacities. Our results confirm important differences with respect to equivalent hydrostatic models. The amount of limb darkening, and the shape of the limb profiles, show a strong…
We report the discovery of a strong magnetic field in the unique pulsating carbon-atmosphere white dwarf SDSS J142625.71+575218.3. From spectra gathered at the MMT and Keck telescopes, we infer a surface field of B_s ~1.2 MG, based on obvious Zeeman components seen in several carbon lines. We also detect the presence of a Zeeman-splitted He I 4471 line, which is an indicator of the presence of a non-negligible amount of helium in the atmosphere of this Hot DQ star. This is important for understanding its pulsations, as nonadabatic theory reveals that some helium must be present in the envelope…
We present the analysis of a total of 177h of high-quality optical time-series photometry of the helium atmosphere pulsating white dwarf (DBV) EC 20058-5234. The bulk of the observations (135h) were obtained during a WET campaign (XCOV15) in July 1997 that featured coordinated observing from 4 southern observatory sites over an 8-day period. The remaining data (42h) were obtained in June 2004 at Mt John Observatory in NZ over a one-week observing period. This work significantly extends the discovery observations of this low-amplitude (few percent) pulsator by increasing the number of detected …
We present precise relative radial velocity (RV) measurements for the rapidly oscillating Ap (roAp) star 33 Librae measured from high resolution data spanning the wavelength interval 5000--6200 A. We find that pulsational radial velocity amplitude determined over a broad wavelength range (~100 A) depends on the spectral region that is examined and can be as high as 60 m/s at 5600 A and as low as 7 m/s in the 5900 A region. RV measurements of individual spectral lines can show even higher RV amplitudes. The acoustic cross-sections of the atmosphere, i.e. the phase and amplitude of the pulsation…
Four members of the new class of pulsating sdB stars are analysed from Keck HIRES spectra using NLTE and LTE model atmospheres. Atmospheric parameters (Teff, log g, log(He/H)), metal abundances and rotational velocities are determined. Balmer line fitting is found to be consistent with the helium ionization equilibrium for PG1605+072 but not so for PG1219+534 indicating that systematic errors in the model atmosphere analysis of the latter have been underestimated previously. All stars are found to be helium deficient probably due to diffusion. The metals are also depleted with the notable exce…
We present an improved version of the method of photometric mode identification of Heynderickx et al. (1994). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al.(2002). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our improved met…
We are searching for new He atmosphere white dwarf pulsators (DBVs) based on the newly found white dwarf stars from the spectra obtained by the Sloan Digital Sky Survey. DBVs pulsate at hotter temperature ranges than their better known cousins, the H atmosphere white dwarf pulsators (DAVs or ZZ Ceti stars). Since the evolution of white dwarf stars is characterized by cooling, asteroseismological studies of DBVs give us opportunities to study white dwarf structure at a different evolutionary stage than the DAVs. The hottest DBVs are thought to have neutrino luminosities exceeding their photon l…
GW Vir variables are the pulsating members in the spectroscopic class of PG 1159 stars. In order to understand the characteristic differences between pulsating and non-pulsating PG 1159 stars, we analyse FUSE spectra of eleven objects, of which six are pulsating, by means of state-of-the-art NLTE model atmospheres. The numerous metal lines in the FUV spectra of these stars allow a precise determination of the photospheric parameters. We present here preliminary results of our analysis.
PG 1605+072 has unique pulsational properties amongst the members of the new class of pulsating sdB (EC 14026) stars. It has the longest periods and the richest, most puzzling frequency spectrum (55 periods). We present a quantitative analysis of a Keck HIRES spectrum using NLTE and LTE model atmospheres. Atmospheric parameters (Teff, log g, log(He/H)), metal abundances, and the rotational velocity are determined. He, C, N and O are subsolar as well as the intermediate mass elements Mg and Si, whereas Ne and Fe are solar. This abundance pattern is caused by diffusion. PG 1605+072 displays cons…
Phase differences and amplitude ratios at different colour photometric bands are currently being used to discriminate pulsation modes in order to facilitate mode identification of kappa-driven non-radial pulsating stars. In addition to physical inputs (e.g., mass, T_eff, etc.), these quantities depend on the non-adiabatic treatment of the atmosphere. This paper presents theoretical results concerning Delta Scuti pulsating stars. The envelope of each of these stellar structures possesses a convection zone whose development is determined by various factors. An interacting pulsation-atmosphere ph…
We present time-resolved optical spectrophotometry of the pulsating hydrogen atmosphere (DA) white dwarf G 117-B15A. We find three periodicities in the pulsation spectrum (215s, 272s, and 304s) all of which have been found in earlier studies. By comparing the fractional wavelength dependence of the pulsation amplitudes (chromatic amplitudes) with models, we confirm a previous report that the strongest mode, at 215s, has l=1. The chromatic amplitude for the 272s mode is very puzzling, showing an increase in fractional amplitude with wavelength that cannot be reproduced by the models for any l a…
This paper reviews the results obtained so far with the newly developed tomographic technique, which probes the velocity field across the atmosphere of long-period variable (LPV) stars. The method cross-correlates the optical spectrum with numerical masks constructed from synthetic spectra and probing layers of increasing depths. This technique reveals that the line doubling often observed in LPV stars around maximum light is the signature of the shock wave propagating in the atmosphere of these pulsating stars. Applications to the Mira variables RT Cyg and RY Cep are presented, revealing the …
The helium-atmosphere (DB) white dwarfs are commonly thought to be the descendants of the hotter PG 1159 stars, which initially have uniform He/C/O atmospheres. In this evolutionary scenario, diffusion builds a pure He surface layer which gradually thickens as the star cools. In the temperature range of the pulsating DB white dwarfs (T_eff ~ 25,000 K) this transformation is still taking place, allowing asteroseismic tests of the theory. Objective global fitting of our updated double-layered envelope models to recent observations of the pulsating DB star CBS 114, and to existing observations of…
We investigate the potential of multi-colour photometry for partial mode identification in both long- and short-period variable subdwarf B stars. The technique presented is based on the fact that the frequency dependence of an oscillation's amplitude and phase bears the signature of the mode's degree index l, among other things. Unknown contributing factors can be eliminated through the evaluation of the amplitude ratios and phase differences arising from the brightness variation in different wavebands, theoretically enabling the inference of the degree index from observations in two or more b…
We suggest that high-order g modes can be used as a probe of the internal magnetic field of SPB (slowly pulsating B) stars. The idea is based on earlier work by the authors which analytically investigated the effect of a vertical magnetic field on p and g modes in a plane-parallel isothermal stratified atmosphere. It was found that even a weak field can significantly shift the g-mode frequencies -- the effect increases with mode order. In the present study we adopt the classical perturbative approach to estimate the internal field of a 4 solar mass SPB star by looking at its effect on a low-de…
We have used time-resolved spectroscopy to measure the colour dependence of pulsation amplitudes in the DAV white dwarf G 29-38. Model atmospheres predict that mode amplitudes should change with wavelength in a manner that depends on the spherical harmonic degree l of the mode. This dependence arises from the convolution of mode geometry with wavelength-dependent limb darkening. Our analysis of the six largest normal modes detected in Keck observations of G 29-38 reveals one mode with a colour dependence different from the other five, permitting us to identify the l value of all six modes and …
Three members of the new class of pulsating sdB stars (sdBV or EC 14026 stars) are analysed from Keck HIRES spectra using line blanketed NLTE and LTE model atmospheres. Atmospheric parameters (Teff, log g, He/H), metal abundances and rotational velocities are determined. As is typical for sdB stars, all programme stars are found to be helium deficient, with a He abundance ranging from 1/80 solar for Feige 48 to 1/3 solar for PG 1219+534, probably due to diffusion. Most metals are also depleted. The abundances of C, O, Ne, Mg, Al and Si in the high gravity programme stars KPD 2109+4401 and PG 1…
Aims: We test the hypothesis that the pulsations in sdB stars are correlated with the surface abundances of iron-group elements. Any correlation might explain why, when given two spectroscopically similar stars, one will pulsate while the other will not. Methods: We have obtained high-resolution ultraviolet spectra two pulsating and three non-pulsating sdB stars using the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope. We determined abundances for 25 elements including the iron group and even heavier elements such as tin and lead using LTE curve-of-growth and spectrum …
The potential of photometric methods for the identification of l, the degree of spherical surface harmonic of a pulsating star, is investigated with special emphasis on Stromgren photometry applied to delta Scuti and gamma Dor variables. Limitations of actual model atmospheres when fine precision is required for the calculations of partial derivatives and integrals, which depend on limb darkening coefficients, are discussed. Two methods are discussed to calculate the phase lags, the angle between maximum temperature and minimum radius, and R, a parameter which describes departure from adiabati…
Atmospheres of evolved AGB stars are heavily affected by pulsation, dust formation and mass loss, and they can become very extended. Time series of observed high-resolution spectra proved to be a useful tool to study atmospheric dynamics throughout the outer layers of these pulsating red giants. Originating at various depths, different molecular spectral lines observed in the near-infrared can be used to probe gas velocities there for different phases during the lightcycle. Dynamic model atmospheres are needed to represent the complicated structures of Mira variables properly. An important asp…
We present a quantitative and homogeneous analysis of the broadband multicolor photometric data sets gathered so far on rapidly pulsating hot B subdwarf stars. This concerns seven distinct data sets related to six different stars. Our analysis is carried out within the theoretical framework developed by Randall et al., which includes full nonadiabatic effects. The goal of this analysis is partial mode identification, i.e., the determination of the degree index l of each of the observed pulsation modes. We assume possible values of l from 0 to 5 in our calculations. For each target star, we com…
We report the discovery of two new ZZ Ceti pulsators, LP 133-144 and HE 1258+0123, selected on the basis of model atmosphere fits to optical spectroscopic data. The atmospheric parameters for LP 133-144, Teff = 11,800 +/- 200 K and log g = 7.87 +/- 0.05, and for HE 1258+0123, Teff = 11,410 +/- 200 K and log g = 8.04 +/- 0.05, place them within the empirical boundaries of the ZZ Ceti instability strip. This brings the number of known ZZ Ceti stars to a total of 36, a quarter of which have now been discovered using the spectroscopic approach for estimating their atmospheric parameters. This meth…
The helium-atmosphere (DB) white dwarfs are commonly thought to be the descendants of the hotter PG1159 stars, which initially have uniform He/C/O atmospheres. In this evolutionary scenario, diffusion builds a pure He surface layer which gradually thickens as the star cools. In the temperature range of the pulsating DB white dwarfs (T_eff ~ 25,000 K) this transformation is still taking place, allowing asteroseismic tests of the theory. We have obtained dual-site observations of the pulsating DB star CBS114, to complement existing observations of the slightly cooler star GD358. We recover the 7…
The metal-poor post-AGB star HD 46703 is shown to be a single-line spectroscopic binary with a period of 600 days, a high velocity of -94 km/s, and an orbital eccentricity of 0.3. Light curve studies show that it also pulsates with a period of 29 days. High-resolution, high signal-to-noise spectra were used for a new abundance study. The atmospheric model determined is T(eff) = 6250 K, log(g) = 1.0, V(t) = 3.0 km/s, and a metal abundance of [M/H] = -1.5. A low carbon abundance and lack of s-process element enhancement indicate that the star has not experienced third dredge-up on the AGB. The s…
Element abundances of three roAp stars, HD 166473, HD 203932, and HD 217522, were determined using Kurucz model atmospheres with metal abundances scaled to solar ones and the results were compared with data from the literature concerning three further roAp stars, normal B and A stars and two lambda Bootis stars. Up to 38 elements could be identified and therefore, this work represents the most complete chemical investigation hitherto published, which can be summarized as follows: - all investigated roAp stars have a similar abundance pattern, - the overabundances of rare earth and other heavy …
Frequencies in oscillating $β$ Cephei stars are usually inferred by means of radial velocities measured from the SiIII triplet 4552-4574 A. These lines, relatively insensitive to the variation of Teff through a pulsation cycle, show small equivalent width variations. In this study we aimed to verify if the behavior of radial velocities and equivalent widths measured from other ions are compatible with the one observed from SiIII lines and than to verify the possible vertical stratification along the stellar atmosphere. For this reason we selected from our spectra a number of, unblended and wel…
We have investigated the structure of the pulsating atmosphere of one of the best studied rapidly oscillating Ap stars, HD 24712. For this purpose we analyzed spectra collected during 2001-2004. An extensive data set was obtained in 2004 simultaneously with the photometry of the Canadian MOST mini-satellite. This allows us to connect directly atmospheric dynamics observed as radial velocity variations with light variations seen in photometry. We directly derived for the first time and for different chemical elements, respectively ions, phase shifts between photometric and radial velocity pulsa…
The location of the red edge of the ZZ Ceti instability strip is defined observationally as being the lowest temperature for which a white dwarf with a H-rich atmosphere (DA) is known to exhibit periodic brightness variations. Whether this cut-off in flux variations is actually due to a cessation of pulsation or merely due to the attenuation of any variations by the convection zone, rendering them invisible, is not clear. The latter is a theoretical possibility because with decreasing effective temperature, the emergent flux variations become an ever smaller fraction of the amplitude of the fl…
Some of the rapidly oscillating (roAp) stars, have frequencies which are larger than the theoretical acoustic cut-off frequency. We have computed models and adiabatic frequencies for pulsating Ap stars with T(tau) laws based on Kurucz model atmospheres and on the Hopf's purely radiative relation. We compare the values of the cut-off frequency derived from expressions for the potential from Vorontsov & Zarkhov (1989), from Gough (1986), and from the approximation of an isothermal atmosphere. Kurucz model atmospheres increase the theoretical acoustic cut-off frequency for roAp stars by about 200…
We explore different evolutionary scenarios to explain the helium deficiency observed in H1504+65, the most massive known PG1159 star. We concentrate mainly on the possibility that this star could be the result of mass loss shortly after the born-again and during the subsequent evolution through the [WCL] stage. This possibility is sustained by recent observational evidence of extensive mass-loss events in Sakurai's object and is in line with the recent finding that such mass losses give rise to PG1159 models with thin helium-rich envelopes and large rates of period change, as demanded by the …
We have carried out a detailed asteroseismic analysis of PG 1219+534. Our analysis leads to the identification of the (k,l) indices of nine periods observed in the star PG 1219+534, and to the determination of its structural parameters. The periods all correspond to low-order acoustic modes with adjacent values of k and with l=0, 1, 2, and 3. They define a band of unstable modes, in close agreement with nonadiabatic pulsation theory. Furthermore, the average dispersion between the nine observed periods and the periods of the corresponding nine theoretical modes of the optimal model is only ~0.…
Originating in different depths of the very extended atmospheres of AGB stars, various molecular spectral lines observable in the near-infrared show diverse behaviours and can be used to probe atmospheric dynamics throughout the outer layers of these pulsating red giants. In Nowotny et al. (2005, Paper I) time series of synthetic high-resolution spectra were presented, computed from a dynamic model atmosphere for a typical carbon-rich Mira. In this work, line profile shapes, their variations during the lightcycle and radial velocities derived from wavelength shifts are analyzed and compared wi…
Some of the rapidly oscillating (CP2) stars, have frequencies which are larger than the theoretical acoustic cut-off frequency. As the cut-off frequency depends on the T(tau) relation in the atmosphere, we have computed models and adiabatic frequencies for pulsating Ap stars with T(tau) laws based on Kurucz model atmospheres and on Hopf's purely radiative relation. The frequency-dependent treatment of radiative transfer as well as an improved calculation of the radiative pressure in Kurucz model atmospheres increase the theoretical acoustic cut-off frequency by about 200 microHz, which is clos…
For many years, astronomers have promised that the study of pulsating white dwarfs would ultimately lead to useful information about the physics of matter under extreme conditions of temperature and pressure. We can now make good on that promise. Using observational data from the Whole Earth Telescope and a new analysis method employing a genetic algorithm, we empirically determine the central oxygen abundance of the helium-atmosphere variable white dwarf GD 358. We use this value, combined with detailed evolutionary calculations of the internal chemical profiles to place constraints on the 12…
HS\,2324+3944 is a peculiar PG\,1159 star, with a high amount of H in its atmosphere (Dreizler et al. 1995). Its location in the $\log T_{\rm eff}$ -- $\log g$ plane is well inside the GW Vir instability strip. In this paper I report the results of two photoelectric observations of HS\,2324+39, which clearly show that the luminosity of this star presents periodical variations with a period of (2140 $\pm$ 11) s. This photometric behaviour is most easily explained by the presence of non-radial oscillations. Therefore HS\,2324+39 is a new member of the GW Vir group, and is characterized by the lo…
We reexamine the theoretical instability domain of pulsating DB white dwarfs (DBV or V777 Her variables). We performed an extensive $g$-mode nonadiabatic pulsation analysis of DB evolutionary models considering a wide range of stellar masses, for which the complete evolutionary stages of their progenitors from the ZAMS, through the thermally pulsing AGB and born-again phases, the domain of the PG1159 stars, the hot phase of DO white dwarfs, and then the DB white dwarf stage have been considered. We explicitly account for the evolution of the chemical abundance distribution due to time-dependen…
We present the results of a search for pulsations in six of the recently discovered carbon-atmosphere white dwarf ("hot DQ") stars. Based on our theoretical calculations, the star SDSS J142625.71+575218.3 is the only object expected to pulsate. We observe this star to be variable, with significant power at 417.7 s and 208.8 s (first harmonic), making it a strong candidate as the first member of a new class of pulsating white dwarf stars, the DQVs. Its folded pulse shape, however, is quite different from that of other white dwarf variables, and shows similarities with that of the cataclysmic va…
Due to a new global analysis method, it is now possible to measure the internal composition of pulsating white dwarf stars, even with relatively simple theoretical models. The precise internal mixture of carbon and oxygen is the largest single source of uncertainty in ages derived from white dwarf cosmochronometry, and contains information about the rate of the astrophysically important, but experimentally uncertain, ^12C(alpha,gamma)^16O nuclear reaction. Recent determinations of the internal composition and structure of two helium-atmosphere variable (DBV) white dwarf stars, GD 358 and CBS 1…
For many years, astronomers have promised that the study of pulsating white dwarfs would ultimately lead to useful information about the physics of matter under extreme conditions of temperature and pressure. In this paper we finally make good on that promise. Using observational data from the Whole Earth Telescope and a new analysis method employing a genetic algorithm, we empirically determine that the central oxygen abundance in the helium-atmosphere variable white dwarf GD 358 is 84+/-3 percent. We use this value to place preliminary constraints on the 12C(alpha,gamma)16O nuclear reaction …
