Surface motion in the pulsating DA white dwarf G29‐38

We present time-resolved spectrophotometry of the pulsating DA white dwarf G29-38. As in previous broad-band photometry, the light curve shows the presence of a large number of periodicities. Many of these are combination frequencies, i.e. periodicities occurring at frequencies that are sums or differences of frequencies of stronger, real modes. We identify at least six real modes, and at least five combination frequencies. We measure line-of-sight velocities for our spectra and detect periodic variations at the frequencies of five of the six real modes, with amplitudes of up to 5 km s⁻¹. We argue that these variations reflect the horizontal surface motion associated with the g-mode pulsations. No velocity signals are detected at any of the combination frequencies, confirming that the flux variations at these frequencies do not reflect physical pulsation, but rather reflect mixing of frequencies owing to a non-linear transformation in the outer layers of the star. We discuss the amplitude ratios and phase differences found for the velocity and light variations, as well as those found for the real modes and their combination frequencies, both in a model-independent way and in the context of models based on the convective-driving mechanism. In a companion paper, we use the wavelength dependence of the amplitudes of the modes to infer their spherical degree.     

Non-linear behaviour of the pulsating white dwarf G29-38 – III. Relative amplitudes of the cross-frequencies

In each season when the DA pulsating white dwarf G29-38 has been observed, its period spectrum appears very different, but it always contains a forest of harmonics and cross-frequencies. The ratio of the amplitude of these non-linear frequencies A _c to the product of the amplitudes of the corresponding parent modes A ₁ A ₂ has been measured. The results are compared with the predictions given by three existing theoretical models. Our analysis shows that the non-linear frequencies present in the period spectrum of G29-38 owe their presence mostly to the inelastic response of the stellar medium to the perturbation travelling through it, rather than to the non-linear response of the emergent luminous flux to the surface temperature variation. This analysis also confirms that most identified modes are ℓ=1, as previously asserted by Kleinman et al.     

Non-linear behaviour of the pulsating white dwarf G29-38 – I. Evolution of the temporal spectrum

An analysis of the evolution of the amplitude spectrum over many seasons of the DA pulsating white dwarf G29-38 has been performed. Neither beating nor resonant mode coupling can account for the observed appearance and disappearance of modes, although some of them clearly grow while others get damped. Therefore some unknown non-adiabatic, non-linear process has to be invoked that affects both the mode selection mechanism and the driving efficiency on a time-scale as short as a day.     

Non-linear behaviour of the pulsating white dwarf G29-38 – II. Analysis of the phase spectrum

An analysis of the phase spectrum of the DA pulsating white dwarf G29-38 over many seasons has been performed. This complements a companion paper which analyses the evolution of the temporal spectrum of G29-38.
We show that, with one exception, the relative phases of the harmonics and combination frequencies are all oscillating in phase with their parent modes. This not only suggests that these non-linear frequencies owe their presence to harmonic distortion and not to resonant mode coupling, but also explains the typical pulse shapes observed in the light curves of large-amplitude variable white dwarfs.
The one exceptional cross-frequency that does not show a phasing with its parent modes is thought to be a resonance.     

Deciphering the pulsations of G 29-38 with optical time series spectroscopy

We present optical time series spectroscopy of the pulsating white dwarf star G 29-38 taken at the Very Large Telescope (VLT). By measuring the variations in brightness, Doppler shift and line shape of each spectrum, we explore the physics of pulsation and measure the spherical degree (ℓ) of each stellar pulsation mode. We measure the physical motion of the g modes correlated with the brightness variations for three of the eight pulsation modes in this data set. The varying line shape reveals the spherical degree of the pulsations, an important quantity for properly modelling the interior of the star with asteroseismology. Performing fits to the Hβ, Hγ and Hδ lines, we quantify the changing shape of the line and compare them to models and previous time series spectroscopy of G 29-38. These VLT data confirm several ℓ identifications and add four new values, including an additional ℓ= 2 and a possible ℓ= 4. In total, from both sets of spectroscopy of G 29-38, eleven modes now have known spherical degrees.     

Asteroseismology of DAV white dwarf stars and G29-38

Asteroseismology is a powerful tool used for detecting the inner structure of stars, which is also widely used to study white dwarfs. We discuss the asteroseismology of DAV stars. The period-to-period fitting method is discussed in detail, including its reliability in detecting the inner structure of DAV stars. If we assume that all observed modes of some DAV stars are the l = I cases, the errors associated with model fitting will be always large. If we assume that the observed modes are com- posed of I = 1 and 2 modes, the errors associated with model fitting in this case will be small. However, there will be modes identified as l = 2 that do not have ob- served quintuplets. G29-38 has been observed spectroscopically and photometrically for many years. Thompson et al. made 1 modes identifications in the star through the limb darkening effect. With 11 known I modes, we also study the asteroseismology of G29-38, which reduces the blind l fittings and is a fair choice. Unfortunately, our two best-fitting models are not in line with the previous atmospheric results. Based on factors like only a few observed modes, stability and identification of eigenmodes, identification of spherical degrees, construction of physical and realistic models and so on, detecting the inner structure of DAV stars by asteroseismology needs further development.     

The pulsating DA white dwarf star EC 14012−1446: results from four epochs of time-resolved photometry

The pulsating DA white dwarfs are the coolest degenerate stars that undergo self-driven oscillations. Understanding their interior structure will help us to understand the previous evolution of the star. To this end, we report the analysis of more than 200 h of time-resolved CCD photometry of the pulsating DA white dwarf star EC 14012−1446 acquired during four observing epochs in three different years, including a coordinated three-site campaign. A total of 19 independent frequencies in the star's light variations together with 148 combination signals up to fifth order could be detected. We are unable to obtain the period spacing of the normal modes and therefore a mass estimate of the star, but we infer a fairly short rotation period of  0.61 ±0.03 d  , assuming the rotationally split modes are  ℓ= 1  . The pulsation modes of the star undergo amplitude and frequency variations, in the sense that modes with higher radial overtone show more pronounced variability and that amplitude changes are always accompanied by frequency variations. Most of the second-order combination frequencies detected have amplitudes that are a function of their parent mode amplitudes, but we found a few cases of possible resonantly excited modes. We point out the complications in the analysis and interpretation of data sets of pulsating white dwarfs that are affected by combination frequencies of the form   f _A + f _B − f _C   intruding into the frequency range of the independent modes.     

Lessons for asteroseismology from white dwarf stars

The interpretation of pulsation data for sun-like stars is currently facing challenges quite similar to those faced by white dwarf modelers ten years ago. The observational requirements for uninterrupted long-term monitoring are beginning to be satisfied by successful multi-site campaigns and dedicated satellite missions. But exploration of the most important physical parameters in theoretical models has been fairly limited, making it difficult to establish a detailed best-fit model for a particular set of oscillation frequencies. I review the past development and the current state of white dwarf asteroseismology, with an emphasis on what this can tell us about the road to success for asteroseismology of other types of stars.     

The low-mass white dwarf companion to β Crateris

We present FUSE H Lyman series spectroscopy of the hot white dwarf companion to the 4th magnitude A1 III star β  Crt, which shows that it has an unusually low mass,     , and has almost certainly evolved through binary interaction. This system could be a long-sought remnant of Algol-type evolution, although radial velocity measurements appear to show that the pair are not close. Instead, micro-variations in the proper motion of β  Crt as measured by Hipparcos suggest that the period could be as high as ∼10 yr. However, a low-mass white dwarf in a system with a period ≳3 yr is difficult to explain by conventional models for binary evolution. We speculate on alternative models for the evolution of this system which involve an eccentric binary or multiple components.     

Two new pulsating DB Stars from the EC survey, EC 04207−4748 and EC 05221−4725

We report the discovery of pulsations in two DB stars found in the Edinburgh–Cape blue object survey. The light curve of EC 04207−4748 appears to be dominated by a strong variation at  2235 μHz  (447 s) and its first overtone near 4475 μHz (223 s). Two other peaks appear in the periodograms of all three data sets for this star; near  2370 μHz  (∼420 s) and  3000 μHz  (∼333 s), though these are less accurately defined. EC 05221−4725 is less easy to specify with the currently available data; it appears to have one coherent frequency near  1114 μHz  (898 s), but is obviously multiperiodic and probably has several more frequencies near the one clearly observed.     

Normal modes and discovery of high-order cross-frequencies in the DBV white dwarf GD 358

We present a detailed mode identification performed on the 1994 Whole Earth Telescope (WET) run on GD 358. The results are compared with that obtained for the same star from the 1990 WET data. The two temporal spectra show very few qualitative differences, although amplitude changes are seen in most modes, including the disappearance of the mode identified as k =14 in the 1990 data. The excellent coverage and signal-to-noise ratio obtained during the 1994 run lead to the secure identification of combination frequencies up to fourth order, i.e. peaks that are sums or differences of up to four parent frequencies, including a virtually complete set of second-order frequencies, as expected from harmonic distortion. We show how the third-order frequencies are expected to affect the triplet structure of the normal modes by back-interacting with them. Finally, a search for ℓ=2 modes was unsuccessful, not verifying the suspicion that such modes had been uncovered in the 1990 data set.