On the frequency and amplitude variations of the δ Scuti star CD−24 7599 (=XX Pyx)

We present 132 h of new time-series photometric observations of the δ Scuti star CD−24 7599 acquired during 86 nights from 1993 to 1996 to study its frequency and amplitude variations. By using all published observations we demonstrate that the three dominating pulsation modes of the star can change their photometric amplitudes within one month at certain times, while the amplitudes can remain constant within the measurement errors at other times. CD−24 7599 also exhibits frequency variations, which do not show any correspondence between the different modes.   The typical time-scale for the amplitude variations is found to be several hundred days, which is of the same order of magnitude as the inverse linear growth rates of a selected model. We find no evidence for periodic amplitude modulation of two of the investigated modes ( f ₂ and f ₃), but f ₁ may exhibit periodic modulation. The latter result could be spurious and requires confirmation. The observed frequency variations may either be continuous or reflect sudden frequency jumps. No evidence for cyclical period changes is obtained.   We exclude precession of the pulsation axis and oblique pulsation for the amplitude variations. Beating of closely spaced frequencies cannot explain the amplitude modulations of two of the modes, while it is possible for the third. Evolutionary effects, binarity, magnetic field changes or avoided crossings cannot be made responsible for the observed period changes. Only resonance between different modes may be able to explain the observations. However, at this stage a quantitative comparison is not possible. More observations, especially data leading to a definite mode identification and further measurements of the temporal behaviour of the amplitudes and frequencies of CD−24 7599, are required.     

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.     

The multiperiodic δ Scuti star 4 Canum Venaticorum: amplitude variability

Recent multisite campaigns of the Delta Scuti Network have revealed 34 frequencies of pulsation for the star 4 CVn. Our present knowledge of the frequencies makes it possible to reanalyse the shorter data sets in the literature, photometric observations from 1966 to 1997.
4 CVn shows strong amplitude variability with time-scales of ten years or longer, although for neighbouring years the amplitudes usually are similar. Seven of the eight dominant modes show annual variability of ∼12 per cent. The variability increases to ∼40 per cent over a decade. The formally derived time-scale of variation of 30 years can only be a rough estimate, since this is also the length of the available data span. The variability is compared with that of FG Vir, which shows lower amplitude variability.
The cyclic behaviour of the amplitude variations excludes an evolutionary origin. There exists some evidence that a mode at 6.12 d⁻¹, which appeared during 1996 and 1997, may have been present with small amplitudes in the 1976–1978 time period.
The pulsation mode at 7.375 d⁻¹ exhibited the most rapid decrease found so far: the V amplitude dropped from the highest known value of 15 mmag in 1974 to 4 mmag in 1976 and 1 mmag in 1977. After that the mode has been increasing in amplitude. There exists a phase jump between 1976 and 1977, suggesting the growth of a new mode. It is interesting to note that this mode also has the strongest coupling with other modes with combination frequencies, f _i ± f _j . The amplitudes of these combination frequencies are also strongly variable from year to year. We speculate that power is transferred between the modes through mode-coupling.     

Photometric properties of the δ Scuti star BR Cancri

We present the results of a three-year Johnson V and Strömgren uvby H β photometric study of the δ Scuti star BR Cancri (BR Cnc). Our data sets consist of 1293 discrete differential magnitudes in Johnson V and yellow y filters, 883 in Strömgren v and 239 in ub filters. The Fourier analysis of the data suggests four pulsation frequencies for the variable: f ₁=24.978, f ₂=11.358, f ₃=11.808 and f ₄=27.914 cycle d⁻¹. During the three observing years, the main frequency f ₁ kept its V ( y ) amplitude constant at about 6 mmag but its v amplitude seems to be changing. Amplitude variations for all the three other frequencies are also claimed. The pulsation modes of the frequencies are discussed based on the colour data. Using uvbyβ data and calibrations in the literature, we derive the physical parameters for BR Cnc.     

An asteroseismic study of the β Cephei star 12 Lacertae: multisite spectroscopic observations, mode identification and seismic modelling

We present the results of a spectroscopic multisite campaign for the β Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high-resolution high S/N spectra gathered with eight different telescopes in a time span of 11 months. In addition, we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the slowly pulsating B-stars (SPB)-like g -mode with frequency 0.3428 d⁻¹ reported before is detected in our spectroscopy. We identify the four main modes as  (ℓ₁, m ₁) = (1, 1), (ℓ₂, m ₂) = (0, 0), (ℓ₃, m ₃) = (1, 0)  and  (ℓ₄, m ₄) = (2, 1)  for   f ₁= 5.178 964 d⁻¹, f ₂= 5.334 224 d⁻¹, f ₃= 5.066 316 d⁻¹  and   f ₄= 5.490 133 d⁻¹  , respectively. Our seismic modelling shows that f ₂ is likely the radial first overtone and that the core overshooting parameter  α_ov  is lower than 0.4 local pressure scale heights.     

Low-frequency variability and binarity of the δ Scuti star XX Pyx

We analyse 147 h of single-site CCD time series photometry of the multiperiodic low-amplitude δ Scuti star XX Pyx with the aim of investigating variability at low frequencies. Part of the data were obtained in the context of the 1998 multisite campaign on XX Pyx, the results of which were described by Handler et al. We find that periodic low-frequency variations are present in the XX Pyx light curves, and we detect two frequencies at f _A=0.8695 cycle d⁻¹ and f _B=1.7352 cycle d⁻¹ , respectively, with amplitudes of 4.5 and 5.4 mmag. The low-frequency variability is intrinsic to XX Pyx, and cannot be attributed to instrumental or atmospheric effects. The near 2:1 ratio of the frequencies leads us to suggest that XX Pyx is a δ Scuti star in a binary system, with a possible binary period of 27.6 h. This is strongly supported by the detection of radial velocity variations from the re-analysis of echelle spectra obtained by Handler et al. However, in the absence of a spectroscopic period, alternative explanations of the photometric variability involving pulsation are also possible; the variations occur close to possible combination frequencies of the short-period ( δ Scuti) variations, but high Q values of 0.57 and 0.28 d suggest that the variations are not a result of normal (p-)modes. They could possibly be due to g-modes excited to observable amplitudes as a result of resonance effects. Surface features (spots) are unlikely to be the cause of the variations.
We searched for combination frequencies (  f _i − f _j ) , f being the normal δ Scuti frequencies detected by Handler et al., but failed to detect any.     

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.     

Resonant excitation of white dwarf oscillations in compact object binaries – I. The no back reaction approximation

We consider the evolution of white dwarfs with compact object companions (specifically black holes with masses up to  ∼10⁶  M_⊙  , neutron stars, and other white dwarfs). We suppose that the orbits are initially quite elliptical and then shrink and circularize under the action of gravitational radiation. During this evolution, the white dwarfs will pass through resonances when harmonics of the orbital frequency match the stellar oscillation eigenfrequencies. As a star passes through these resonances, the associated modes will be excited and can be driven to amplitudes that are so large that there is a back reaction on the orbit which, in turn, limits the growth of the modes. A formalism is presented for describing this dynamical interaction for a non-rotating star in the linear approximation when the orbit can be treated as non-relativistic. A semi-analytical expression is found for computing the resonant energy transfer as a function of stellar and orbital parameters for the regime where back reaction may be neglected. This is used to calculate the results of passage through a sequence of resonances for several hypothetical systems. It is found that the amplitude of the  ℓ= m = 2  f -mode can be driven into the non-linear regime for appropriate initial conditions. We also discuss where the no back reaction approximation is expected to fail, and the qualitative effects of back reaction.     

Radial velocity variations of the pulsating subdwarf B star PG 1605+072

We present an analysis of high-speed spectroscopy of the pulsating subdwarf B star PG 1605+072. Periodic radial motions are detected at frequencies similar to those reported for photometric variations in the star, with amplitudes of up to 6 km s⁻¹. Differences between relative strengths for given frequency peaks for our velocity data and previously measured photometry are probably a result of shifting of power between modes over time. Small differences in the detected frequencies may also indicate mode-shifting. We report the detection of line-shape variations using the moments of the cross-correlation function profiles. It may be possible to use the moments to identify the pulsation modes of the star.     

Multiple frequency analysis of the large-amplitude SX Phoenicis star BL Camelopardalis

A multifrequency analysis of the SX Phoenicis star BL Camelopardalis is presented on the basis of new high-speed photometry, along with fitting a total of 136 maxima. BL Cam is a multiple periodic pulsator. We find f ₀=25.5768, f ₁=25.2982, f ₂=25.8622, f ₃=31.5912, f ₄=25.1065, f ₅=25.5147 and f ₆=25.6188 cycle d⁻¹ together with the harmonics 51.1513 and 76.7268 cycle d⁻¹ and combination frequencies f ₀+ f ₁, f ₀+ f ₂ and f ₀+ f ₃. The new frequency solution represents the light curves of BL Cam quite well. The observed minus calculated (O-C) analysis indicates that the fundamental frequency is in good agreement with the results of Fourier analysis.     

Characterizing the pulsations of the ZZ Ceti star KUV 02464+3239

We present the results on period search and modelling of the cool DAV star KUV 02464+3239. Our observations resolved the multiperiodic pulsational behaviour of the star. In agreement with its position near the red edge of the DAV instability strip, it shows large amplitude, long-period pulsation modes, and has a strongly non-sinusoidal light curve. We determined six frequencies as normal modes and revealed remarkable short-term amplitude variations. A rigorous test was performed for the possible source of amplitude variation: beating of modes, effect of noise, unresolved frequencies or rotational triplets. Among the best-fitting models resulting from a grid search, we selected three that gave   l = 1  solutions for the largest amplitude modes. These models had masses of 0.645, 0.650 and  0.680  M _⊙  . The three 'favoured' models have   M _H  between  2.5 × 10⁻⁵ and 6.3 × 10⁻⁶  M _*  and give 14.2–14.8 mas seismological parallax. The  0.645  M _⊙  (11 400 K) model also matches the spectroscopic  log  g   and   T _eff  within 1σ. We investigated the possibility of mode trapping and concluded that while it can explain high amplitude modes, it is not required.     

Radial velocities of pulsating subdwarf B stars: KPD 2109+4401 and PB 8783

High-speed spectroscopy of two pulsating subdwarf B stars, KPD 2109+4401 and PB 8783, is presented. Radial motions are detected with the same frequencies as reported from photometric observations and with amplitudes of ∼2 km s⁻¹ in two or more independent modes. These represent the first direct observations of surface motion arising from multimode non-radial oscillations in subdwarf B stars. In the case of the sdB+F binary PB 8783, the velocities of both components are resolved; high-frequency oscillations are found only in the sdB star and not the F star. There also appears to be evidence for mutual motion of the binary components. If confirmed, it implies that the F-type companion is ≳1.2 times more massive than the sdB star, while the amplitude of the F-star acceleration over 4 h would constrain the orbital period to lie between 0.5 and 3.2 d.     

An asteroseismic signature of helium ionization

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent γ is a superposition of two decaying periodic functions of frequency ν, with 'frequencies' that are approximately twice the acoustic depths of the centres of the He  i and He  ii ionization regions. That variation is probably best exhibited in the second frequency difference  Δ₂ν _{n ,  l} ≡ν _{n −1,  l} − 2ν _{n ,  l} +ν _{n +1,  l}   . We show how an analytic approximation to the variation of γ leads to a simple representation of this oscillatory contribution to Δ₂ν which can be used to characterize the γ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize γ, not merely to find a formula for Δ₂ν that reproduces the data.     

Photospheric phosphorus in the FUSE spectra of GD71 and two similar DA white dwarfs

We report the detection, from the Far Ultraviolet Spectroscopic Explorer (FUSE) data, of phosphorus in the atmospheres of GD71 and two similar DA white dwarfs. This is the first detection of a trace metal in the photosphere of the spectrophotometric standard star GD71. Collectively, these objects represent the coolest DA white dwarfs in which photospheric phosphorus has been observed. We use a grid of homogeneous non-local thermodynamic equilibrium synthetic spectra to measure abundances of  [P/H]=−8.57^+0.09_−0.13, −8.70^+0.23_−0.37  and  −8.36^+0.14_−0.19  in GD71, RE J1918+595 and RE J0605−482 respectively. At the observed level we find that phosphorus has no significant impact on the overall energy distribution of GD71. We explore possible mechanisms responsible for the presence of this element in these stars, concluding that the most likely is an interplay between radiative levitation and gravitational settling, possibly modified by weak mass loss.     

A period study and light-curve synthesis for the Algol-type semidetached binary XX Cephei

We obtained CCD photometric observations of the Algol-type semidetached binary XX Cephei (XX Cep) during 15 nights from 2002 September 17 to 2003 February 2, and also on 2005 January 21. Except for those data taken on the last night of the concentrated observing season, the 3881 measurements were obtained over an interval of only 106 nights. From these data, four new times of minimum light were calculated. The  (O− C)  diagram formed from all available timings, and thus the orbital period of the system, can be partly represented as a beat effect between two cyclical variations with different periods (      yr,      yr) and amplitudes  ( K ₁=0.015 d, K ₂=0.103 d)  , respectively. Both physical and non-physical interpretations of these cycles were investigated. The long-term sinusoidal variation is too long for magnetic cycling in solar-type single and close binary stars. In addition, we have studied the effect of a possible secular period variation. By analysing the residuals from our Wilson–Devinney (WD) binary model, we found small light variations with a period of 5.99 d with amplitudes growing toward longer wavelengths. We think that these oscillations may be produced by instabilities at the systemic L ₁ point (also occupied by the point of the cool star) and that these instabilities are, in turn, caused by non-uniform and sporadic convection. There is also a short-period oscillation of about 45 min in the WD light residuals that is attributed to accretion on to the mass-gaining primary component from a feeble gas stream originating on the cool donor star.     

The mass of the neutron star in the binary millisecond pulsar PSR J 1012 + 5307

We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J 1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (≡ M ₁/ M ₂) = 10.5 ± 0.5. Our optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M ₂ = 0.16 ± 0.02 M⊙, and hence the mass of the neutron star is 1.64 ± 0.22 M⊙, where the error is dominated by that of M ₂. The orbital inclination is 52 ± 4°. For an initial neutron star mass of ∼ 1.4 M⊙, only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was ∼ 1 M⊙, our result suggests that the mass transfer may have been non-conservative.     

The pulsating λ Bootis star HD 105759

We present spectroscopic and multisite time series photometric observations of the star HD 105759 which confirm that this is a new pulsating λ Bootis star. Our spectroscopy indicates an overall metallicity of [Z] = log Z − log Z_⊙ = −1 and that T _eff = 8000 ± 300 K and log  g  = 4.0 ± 0.2. The photometric data reveal that this star pulsates with at least five frequencies: 8.62, 12.69, 20.15, 21.27 and 23.66 d⁻¹. These frequencies do not all match those found in an earlier single-site study, indicating that the pulsation spectrum changes with time.     

Combination frequencies in the Fourier spectra of white dwarfs

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs, along with frequencies that are associated with stellar gravity modes. They appear at the sum and difference frequencies of the stellar modes. Brickhill proposed that the combination frequencies result from mixing of the eigenmode signals by a depth-varying surface convection zone when undergoing pulsation. The depth changes cause time-dependent thermal impedance.
Following Brickhill's proposal, we developed analytical expressions for the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in the stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly the spherical degrees of the eigenmodes involved in the mixing. Adopting credible values for these parameters, we apply our expressions to DA and DB variable white dwarfs. We find reasonable agreement between theory and observation, although some discrepancies remain unexplained. It is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.     

The influence of Hall drift on the magnetic fields of neutron stars

We consider the evolution of magnetic fields under the influence of Hall drift and Ohmic decay. The governing equation is solved numerically, in a spherical shell with   r _i / r _o = 0.75  . Starting with simple free-decay modes as initial conditions, we then consider the subsequent evolution. The Hall effect induces so-called helicoidal oscillations, in which energy is redistributed among the different modes. We find that the amplitude of these oscillations can be quite substantial, with some of the higher harmonics becoming comparable with the original field. Nevertheless, this transfer of energy to the higher harmonics is not sufficient to accelerate significantly the decay of the original field, at least not at the   R _B = O (100)  parameter values accessible to us, where this Hall parameter   R _B   measures the ratio of the Ohmic time-scale to the Hall time-scale. We do find clear evidence though of increasingly fine structures developing for increasingly large   R _B   , suggesting that perhaps this Hall-induced cascade to ever-shorter length-scales is eventually sufficiently vigorous to enhance the decay of the original field. Finally, the implications for the evolution of neutron star magnetic fields are discussed.     

Orbital parameters, masses and distance to β Centauri determined with the Sydney University Stellar Interferometer and high-resolution spectroscopy

The bright southern binary star β Centauri (HR 5267) has been observed with the Sydney University Stellar Interferometer (SUSI) and spectroscopically with the European Southern Observatory Coude Auxiliary Telescope and Swiss Euler telescope at La Silla. The interferometric observations have confirmed the binary nature of the primary component and have enabled the determination of the orbital parameters of the system. At the observing wavelength of 442 nm the two components of the primary system have a magnitude difference of  0.15 ± 0.02  . The combination of interferometric and spectroscopic data gives the following results: orbital period  357.00 ± 0.07 d  , semimajor axis  25.30 ± 0.19 mas  , inclination  674 ± 03  , eccentricity  0.821 ± 0.003  , distance  102.3 ± 1.7 pc  , primary and secondary masses   M ₁= M ₂= 9.1 ± 0.3 M_⊙  and absolute visual magnitudes of the primary and secondary   M _{1 V} =−3.85 ± 0.05  and   M _{2 V} =−3.70 ± 0.05  , respectively. The high degree of accuracy of the results offers a fruitful starting point for future asteroseismic modelling of the pulsating binary components.