Magnetic perturbations to the acoustic modes of roAp stars

We study the effect of a large-scale surface magnetic field on the non-radial acoustic modes of roAp stars. Special attention is given to the use of a variational principle which is used for determining the shifts in the frequencies with relative ease, enabling us to avoid having to calculate the perturbed eigenfunctions. With knowledge of the frequency shifts we then estimate the eigenfunctions in a simpler, albeit approximate way. The results indicate frequency shifts of the order of few μHz, which depend on the order, degree and azimuthal order of the mode. The loss of energy through Alfvén waves is also estimated from the imaginary parts of the frequency shifts. The results indicate that the loss is particularly high near specific frequencies. This might indicate the presence of a selection effect, which could make some modes more likely to be excited than others. However, our results do not explain why the modes observed appear always to be aligned with the axis of the magnetic field. Finally, the estimated perturbed eigenfunctions contain strong components of spherical harmonics that differ from those of the original unperturbed modes.     

On the excitation mechanism in roAp stars

We investigate a model for the excitation of high-order oscillations in roAp stars. In this model we assume that the strong concentration of magnetic field about the magnetic poles is enough to suppress convection. Thus the model considered is composed of two polar regions, in which convection is presumed to be suppressed totally, and an equatorial region, where the convection is unaffected. This model is generated by building pairs of locally spherically symmetrical equilibria to represent the polar and equatorial regions of the star, which are patched together below the base of the convection zone. Gravitational settling of heavy elements is taken into account by choosing appropriate chemical composition profiles for both the polar and equatorial regions. Our results indicate that the composite model is unstable against axisymmetric non-radial high-order modes of pulsation that are aligned with the magnetic poles. The oscillations are excited by the κ mechanism acting principally in the hydrogen ionization zones of the polar regions. The effect of the lateral inhomogeneity on the second frequency differences is also investigated; we find that the perturbation to them by the inhomogeneity is of the same order as the second differences themselves, thereby hindering potential attempts to use such differences to identify the degrees of the modes in a straightforward way.     

OH masers and magnetic fields near the cometary H ii region G34.3+0.2

The mechanism responsible for exciting high-order acoustic oscillations in rapidly oscillating Ap stars is still an open issue. Recently, Balmforth et al. (hereafter BCDGV) proposed a model according to which high-frequency oscillations may be excited in roAp stars if the intensities of the magnetic fields present in these stars are sufficiently large to suppress convection at least in some region of their envelopes. Using models similar to those proposed by BCDGV, we predict the theoretical edges of the instability strip appropriate to roAp stars and compare them with the observations. Moreover, we discuss our results in the light of some of the systematic differences found between roAp stars, noAp stars and Ap stars in general. We suggest that a combination of intrinsic differences between these types of stars and a bias related to the frequencies of the unstable oscillations might hold the explanation to some of the differences observed.     

A non-adiabatic analysis for axisymmetric pulsations of magnetic stars

This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M_⊙  , main-sequence model  (log  T _eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.     

A frequency analysis of the p-mode pulsations of the Ap SrEu(Cr) star HD 119027

We present new high-speed, multisite photometric observations of the rapidly oscillating Ap star HD 119027 acquired over seven nights during 1996. A frequency analysis of these observations reveals the presence of oscillations at 1835, 1875, 1888, 1913, 1940, 1942 and (possibly) 1953 μHz. These frequencies are consistent with a spacing of either 13 or 26 μHz, depending on the reality of the oscillations at 1875 and 1953 μHz. The data in hand do not permit us to discriminate between the two possible spacings. If the smaller value of the spacing is correct, it suggests that HD 119027 is outside the main-sequence band. Two of the frequencies listed above are separated by only 1.95 μHz, suggesting that they are modes of ( n ,ℓ) and ( n  − 1, ℓ + 2), which in roAp stars is a quantity governed by the internal magnetic field.     

Confirmation of the oblique pulsator model for the rapidly oscillating Ap star HR 3831

We have detected pulsational radial velocity variations in the rapidly oscillating Ap star HR 3831 which are amplitude- and phase-modulated in the same manner as the photometric variations. In particular, the radial velocities show the same 180° phase reversal at magnetic quadrature as the photometric variations. This confirms the oblique pulsator model, and rules out the spotted pulsator model for these stars.     

The Dushak-Erekdag survey of roAp stars

The search of roAp stars at Mt. Dushak-Erekdag Observatory was started in 1992 using the 0.8 m Odessa telescope equipped with a two-star high-speed photometer. We have observed more than a dozen stars so far and discovered HD 99563 as roAp star while BD+8087 is suspected to have rapid oscillations. Negative results of our observations for the search of rapid oscillations in four stars in NGC 752 are also discussed.     

The pulsating hydrogen-deficient star LSS 3184 (BX Cir)

We present extensive photometry and spectroscopy of the extremely hydrogen-deficient star, LSS 3184, recently discovered to be a rapid variable (period ∼0.1066 d) strikingly similar to V652 Her. Over 95 h of photometry confirms the reported variability, which is of rather low amplitude (Δ V ∼0.03 mag), defines the light curve with greater precision and establishes a much more accurate ephemeris (period ∼0.106 578 4 d) to form a basis for detecting period change. Attention is drawn to the usefulness of a period-finding technique that fits harmonic components to the photometric observations. Spectroscopy shows a peak-to-peak variation in radial velocity of about 30 km s⁻¹, which, when combined with the photometric observations, confirms the pulsational nature of the variability and strongly indicates that the pulsations are radial in nature.     

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.     

Time-series spectroscopy of the rapidly oscillating Ap star HR 3831

We present time-series spectroscopy of the rapidly oscillating Ap (roAp) star HR 3831. This star has a dominant pulsation period of 11.7 min and a rotation period of 2.85 d. We have analysed 1400 intermediate-resolution spectra of the wavelength region 6100–7100 Å obtained over one week, using techniques similar to those we applied to another roAp star, α  Cir.
We confirm that the H α velocity amplitude of HR 3831 is modulated with rotation phase. Such a modulation was predicted by the oblique pulsator model, and rules out the spotted pulsator model. However, further analysis of H α and other lines reveals rotational modulations that cannot easily be explained using the oblique pulsator model. In particular, the phase of the pulsation as measured by the width of the H α line varies with height in the line.
The variation of the H α bisector shows a very similar pattern to that observed in α Cir, which we have previously attributed to a radial node in the stellar atmosphere. However, the striking similarities between the two stars, despite the much shorter period of α Cir (6.8 min), argues against this interpretation unless the structure of the atmosphere is somewhat different between the two stars. Alternatively, the bisector variation is a signature of the degree ℓ of the mode and not the overtone value n .
High-resolution studies of the metal lines in roAp stars are needed to understand fully the form of the pulsation in the atmosphere.     

A photometric and spectroscopic study of the hottest pulsating extreme helium star, V2076 Oph (HD 160641)

We present results from a three-site photometric and high-resolution spectroscopic campaign on the hottest known extreme helium star V2076 Oph (HD 160641). A core programme of intensive observations covered two weeks and a much lower sampling rate extended over another two months. Despite the fact that the data seem to indicate periodicity near half a day (though the light curves are clearly not formed by a single periodicity), conventional Fourier analysis of the data fails to reveal coherent frequencies. Furthermore, we are unable to recover frequencies which were apparently clear in an earlier campaign on the star. Evidence of monotonic pulsation amplitude changes is seen at the higher frequencies from a wavelet analysis, but more data are needed before this study can be extended to lower frequencies. The application of linear stochastic differential equation (LSDE) methods indicates that the observed light variations could be a result of random variations giving the appearance of intermittent periodicity. High-resolution spectroscopic observations were obtained during the campaign and additional observations were made three years later. Complex line profile variations were observed. It is proposed that the different behaviour of the emission line studied may indicate it is associated with a stellar wind or resident circumstellar material. The frequencies that are extracted from the velocity data do not conform to those identified in the current or previous photometric campaigns.     

The sixth frequency of roAp star HR 1217

The frequency of the sixth mode observed in HR 1217 cannot currently be understood in the light of the asymptotic theory for high-frequency acoustic modes, valid for adiabatic pulsations in spherically symmetric stars. Deviations from spherical symmetry will change the frequency of the observed oscillations away from the frequencies predicted by the asymptotic theory. Among other things, the presence of a magnetic field in the star will introduce such deviations from spherical symmetry. In the present work we inspect the effect of the magnetic field on the oscillations of HR 1217. Although we model HR 1217 in a rather simplified manner, we believe, as argued in the text, that the essence of the conclusions would not be modified if a more sophisticated model were to be used instead. The results show that the frequency of the sixth mode observed in HR 1217 might be understood if the effect of the magnetic field on the frequencies of the oscillations is fully taken into account. Moreover, we interpret the sixth frequency as a mode of even degree, and explain the absence from the observations of an intermediate l =1 , m =0 mode as the result of large energy losses associated with the coupling of the latter with Alfvénic waves, in the strongly magnetized outer layers of the star. Finally, we show how, in the light of this explanation, the frequency of the sixth mode might be used in order to put constraints on the parameters characterizing the star.     

Unstable non-radial modes in radial pulsators: theory and an example

We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.     

Determining temperature amplitude as a function of depth in the atmospheres of rapidly oscillating Ap stars

We present numerical models based on realistic treatment of the intensity spectrum (from model atmospheres), and demonstrate that they are consistent with Kurtz and Medupe's recent formula in showing that limb darkening is too small an effect to explain the observed sharp decline of pulsation light amplitude with wavelength in rapidly oscillating Ap stars. Kurtz and Medupe's formula is shown to be a special form of Watson's earlier general formula for non-radial light variations of a star pulsating in any mode ( l m ). Using a technique suggested by Kurtz and Medupe we derive temperature semi-amplitude as a function of depth in the atmospheres of α Cir and HR 3831, assuming that we can neglect non-adiabatic effects.     

Confirmation of simultaneous p and g mode excitation in HD 8801 and γ Peg from time-resolved multicolour photometry of six candidate 'hybrid' pulsators

We carried out a multicolour time-series photometric study of six stars claimed as 'hybrid' p and g mode pulsators in the literature. γ Peg was confirmed to show short-period oscillations of the β Cep type and simultaneous long-period pulsations typical of Slowly Pulsating B (SPB) stars. From the measured amplitude ratios in the Strömgren uvy passbands, the stronger of the two short period pulsation modes was identified as radial; the second is  ℓ= 1  . Three of the four SPB-type modes are most likely  ℓ= 1  or 2. Comparison with theoretical model calculations suggests that γ Peg is either a  ∼8.5 M_⊙  radial fundamental mode pulsator or a  ∼9.6 M_⊙  first radial overtone pulsator. HD 8801 was corroborated as a 'hybrid'δ Sct/γ Dor star; four pulsation modes of the γ Dor type were detected, and two modes of the δ Sct type were confirmed. Two pulsational signals between the frequency domains of these two known classes of variables were confirmed and another was newly detected. These are either previously unknown types of pulsation or do not originate from HD 8801. The O-type star HD 13745 showed small-amplitude slow variability on a time-scale of 3.2 d. This object may be related to the suspected new type of supergiant SPB stars, but a rotational origin of its light variations cannot be ruled out at this point. 53 Psc is an SPB star for which two pulsation frequencies were determined and identified with low spherical degree. Small-amplitude variability was formally detected for 53 Ari but is suspected not to be intrinsic. The behaviour of ι Her is consistent with non-variability during our observations, and we could not confirm light variations of the comparison star 34 Psc previously suspected. The use of signal-to-noise criteria in the analysis of data sets with strong aliasing is critically discussed.