Tomography of stellar non‐radial pulsations

The stellar surface imaging technique is used for studying stellar non‐radial pulsations on the basis of inversions of time series of variable line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which sectoral and tesseral modes can be distinguished in many cases and the pulsational degree and the azimuthal order can be determined. The capability of the technique is studied with simulated data. Then, the surface imaging technique is applied to high‐resolution spectra of the rapidly rotating Beta Cep‐type star ω¹ Sco, which shows strong line‐profile variations. Stellar surface imaging is concluded to be a useful technique for pulsation‐mode identification. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short-period line profile variations in the Be star ε Cap

We present new high-dispersion spectroscopic data for the Be star ε Cap. The purpose of these data is to study the short-period line profile variations. By using a two-dimensional period-finding technique, we confirm that the photometric period of 0.99 d is present in the helium line profiles. We show that the variations are not easily explained by non-radial pulsation and suggest that corotating circumstellar material is responsible.     

Abundances in intermediate-mass AGB stars undergoing third dredge-up and hot-bottom burning

High-dispersion near-infrared spectra have been taken of seven highly evolved, variable, intermediate-mass (4–6 M_⊙) asymptotic giant branch (AGB) stars in the Large Magellanic Cloud and Small Magellanic Cloud in order to look for C, N and O variations that are expected to arise from third dredge-up and hot-bottom burning. The pulsation of the objects has been modelled, yielding stellar masses, and spectral synthesis calculations have been performed in order to derive abundances from the observed spectra. For two stars, abundances of C, N, O, Na, Al, Ti, Sc and Fe were derived and compared with the abundances predicted by detailed AGB models. Both stars show very large N enhancements and C deficiencies. These results provide the first observational confirmation of the long-predicted production of primary nitrogen by the combination of third dredge-up and hot-bottom burning in intermediate-mass AGB stars. It was not possible to derive abundances for the remaining five stars: three were too cool to model, while another two had strong shocks in their atmospheres which caused strong emission to fill the line cores and made abundance determination impossible. The latter occurrence allows us to predict the pulsation phase interval during which observations should be made if successful abundance analysis is to be possible.     

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.     

Discovery of the 'missing' mode in HR 1217 by the Whole Earth Telescope

HR 1217 is a prototypical rapidly oscillating Ap star that has presented a test to the theory of non-radial stellar pulsation. Prior observations showed a clear pattern of five modes with alternating frequency spacings of 33.3 and 34.6 μHz, with a sixth mode at a problematic spacing of 50.0 μHz (which equals  1.5×33.3 μHz)  to the high-frequency side. Asymptotic pulsation theory allowed for a frequency spacing of 34 μHz, but Hipparcos observations rule out such a spacing. Theoretical calculations of magnetoacoustic modes in Ap stars by Cunha predicted that there should be a previously undetected mode 34 μHz higher than the main group, with a smaller spacing between it and the highest one. In this Letter, we present preliminary results from a multisite photometric campaign on the rapidly oscillating Ap star HR 1217 using the 'Whole Earth Telescope'. While a complete analysis of the data will appear in a later paper, one outstanding result from this run is the discovery of a newly detected frequency in the pulsation spectrum of this star, at the frequency predicted by Cunha.     

The semi-detached binary system IU Per and its intrinsic oscillation

We present a long-term time-resolved photometry of the short-period eclipsing binary IU Per. It confirms the intrinsic δ Scuti-like pulsation of the system reported by Kim et al.. With the obtained data, an orbital period study and an eclipsing light curve synthesis based on the Wilson-Devinney method were carried out. The photometric so- lution reveals a semi-detached configuration with the less-massive component filling its own Roche-lobe. By subtracting the eclipsing light changes from the data, we obtained the pure pulsating light curve of the mass-accreting primary component. A Fourier anal- ysis reveals four pulsation modes with confidence larger than 99%. A mode identification based on the results of the photometric solution was made. It suggests that the star may be in radial pulsation with a fundamental period of about 0.0628 d. A brief discussion concerning the evolutionary status and the pulsation nature is finally given.     

Analysis of the oscillations in HST observations of the quiescent SU UMa type dwarf nova WZ Sagittae

An analysis of the UV oscillations in WZ Sge is presented, in which we obtain the oscillation amplitude spectra. We find a strong 27.9-s oscillation in our Hubble Space Telescope ( HST ) UV and zeroth-order light curves as well as weaker oscillations at 28.4 s in the UV and 29.1 s in the zeroth order. We find that the main oscillation amplitude spectrum can be fitted with static white dwarf spectra of about 17 000 K, an accretion hotspot of only a few 100 K hotter than the underlying white dwarf temperature or a variety of cool (<14 500 K) white dwarf pulsation amplitude spectra. A pulsating white dwarf can also explain the very blue colour of oscillations of different periods previously found in the optical. Comparing our results with those of Welsh et al., we see that the amplitude spectra of the main oscillations in WZ Sge measured with different periods in data sets from different epochs are similar to each other. Our results raise questions about using the magnetically accreting rotating white dwarf model to explain the oscillations. We suggest that the pulsating white dwarf model is still a viable explanation for the oscillations in WZ Sge.     

The rapidly oscillating Ap star HD 99563 and its distorted dipole pulsation mode

We undertook a time-series photometric multisite campaign for the rapidly oscillating Ap (roAp) star HD 99563 and also acquired mean light observations over four seasons. The pulsations of the star, which show flatter light maxima than minima, can be described with a frequency quintuplet centred on 1557.653 μHz and some first harmonics of it. The amplitude of the pulsation is modulated with the rotation period of the star that we determine with 2.91179 ± 0.00007 d from the analysis of the stellar pulsation spectrum and of the mean light data. We break up the distorted oscillation mode into its pure spherical harmonic components and find it is dominated by the ℓ= 1 pulsation, and also has a notable ℓ= 3 contribution, with weak ℓ= 0 and 2 components. The geometrical configuration of the star allows us to see both pulsation poles for about the same amount of time; HD 99563 is only the fourth roAp star for which both pulsation poles are seen and only the third where the distortion of the pulsation modes has been modelled. We point out that HD 99563 is very similar to the well-studied roAp star HR 3831. Finally, we note that the visual companion of HD 99563 is located in the δ Scuti instability strip and may thus show pulsation. We show that if the companion was physical, the roAp star would be a 2.03-M_⊙, object, seen at a rotational inclination of 44°, which then predicts a magnetic obliquity     .     

Resolving the pulsations of the subdwarf B star KPD 2109 + 4401

We present the results of extensive time-series photometry of the pulsating subdwarf B star KPD 2109 + 4401. Our data set consists of 29 data runs with a total length of 182.6 h over 31 d, collected at five observatories in 2004. These data comprised high signal-to-noise ratio observations acquired with larger telescopes and wider time-coverage observations obtained with smaller telescopes. They are sufficient to resolve the pulsation structure to 0.4 μHz and are the most extensive data set for this star to date. With these data, we identify eight pulsation frequencies extending from 4701 to 5481 μHz, corresponding to periods of 182–213 s. The pulsation frequencies and their amplitudes are examined over several time-scales with some frequencies showing amplitude variability.     

Hipparcos parallaxes for Mira-like long-period variables

This paper concerns the calibration of the K period–luminosity relation for Mira variables using Hipparcos parallaxes. K magnitudes are available for 255 Mira-like variables which were observed by Hipparcos . Period–luminosity zero-points are evaluated for various subgroups of data. The best solution for oxygen-rich Miras, which uses 180 stars, omitting the short-period red group (which had different kinematics from the short-period blue stars) and the low-amplitude variables, provides a zero-point of     which implies a distance modulus for the Large Magellanic Cloud of     or perhaps slightly greater if a metallicity correction is required, in good agreement with the value derived from Cepheids. The zero-point of the period–luminosity relation for carbon stars is briefly discussed.
Linear diameters are derived for red variables with measured angular diameters and parallaxes, and are used to examine the long-standing question of the pulsation mode(s) of these stars. Evidence is presented to suggest that most of them are pulsating in the same mode and, if published model atmospheres are correct, this is probably the first overtone. Some discussion is given of sequences in the period–luminosity and period–colour diagrams and their bearing on the pulsation mode problem.     

UBVRIJH photometry of two new luminous δ Scuti stars and the discovery of δ Scuti pulsation in the most evolved Ap star known

Time-series photometry of the Hipparcos variable stars HD 199434 and 21190 is reported. Both stars are pulsators of the δ Scuti type. Reclassifications of the MK types of the stars, based on new spectrograms, are given. HD 21190 is found to be F2III SrEuSi:, making it the most evolved Ap star known. Its Strömgren photometric indices support the peculiar spectral type. It is also one of the most evolved δ Scuti stars known. Its combined Ap– δ Scuti nature makes it an important test of models of pulsation in peculiar stars recently developed by Turcotte et al., although it is more extreme than any model they examined. Physical parameters of both stars are estimated from Strömgren and H β photometry, and Hipparcos absolute magnitudes. We attempt mode identifications based on amplitude ratios and phase differences from our photometry. The dominant pulsation of HD 21190 may be an overtone radial mode. The model fits for HD 199434 are even less satisfactory, but favour an ℓ=2 mode. Given the good quality and wavelength coverage of our data, the poor results from the application of the photometric theory of mode identification may call into question the use of that technique.     

Discovery of a New Multiperiodic δ Scuti Variable Star

We report on the discovery of a new short-periodic pulsating variable star in the field of the pulsating sdB star KPD 2109+4401. The star was observed on 10 consecutive nights. Based on the light curves, we detect three pulsation frequencies at 10.308, 4.023 and 11.075 cycle d⁻¹ with amplitudes of 11.1, 4.3 and 4.2 milli-magnitudes, respectively. Using the existing data from other sky surveys, we estimate a spectral type of late F and other atmospheric parameters. Then we discuss the observational properties of the star. Finally it is classified to be a new low-amplitude multiperiodic δ Scuti star. A future interest addressed is to accurately determine the star's spectral type and then to judge a possible link to γ Doradus-type pulsation.     

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.     

Radial velocity study of the roAp star α Circinus

We present results of 548 high-dispersion spectra of the roAp star α Circinus over a five-night period. The pulsational radial velocities measured from the rare-earth elements, Nd iii , Hα and Hβ are easily measured and occur at the photometric period. The amplitude is largest in Nd iii and Hα, is lower in the rare earths and Hβ, and cannot be measured in other metal lines. This behaviour can be understood in terms of an increase of pulsational amplitude with height in the atmosphere coupled with abundance stratification. The radial velocities show a significant variation at the rotational period of 4.463 d and a marginally significant periodicity at a frequency of 8.16 cycle d⁻¹. The latter may be a very low-amplitude δ Scuti pulsation.     

Do red giant stars pulsate in high overtones?

About 30 photometrically variable red giant stars have periods less than 10 d, as determined by the compilers of the Hipparcos Catalogue from Hipparcos photometric measurements. These periods, when combined with estimates of the radii and masses of these stars, and with pulsation theory, imply that these stars are pulsating in very high overtones. We present several pieces of evidence which suggest that the periods may be spurious, as a result of the particular aliasing properties of the Hipparcos photometry. We conclude that the evidence for high-overtone pulsation in red giant stars is equivocal.     

Surface trapping and leakage of low-frequency g modes in rotating early-type stars – II. Global analysis

A global analysis of the surface trapping of low-frequency non-radial g modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. The dimensionless pulsation equations governing these modes are reviewed, and the boundary conditions necessary for solution of the equations are considered; in particular, an outer mechanical boundary condition, which does not enforce complete wave trapping at the stellar surface, is derived and discussed in detail. The pulsation equations are solved for a 7-M_⊙ model star over a range of rotation rates, using a numerical approach.
The results of the calculations confirm the findings of the preceding paper in the series: modes with eigenfrequencies below a cut-off cannot be fully trapped within the star, and exhibit leakage in the form of outwardly propagating waves at the surface. The damping rates resulting from leakage are calculated for such 'virtual' modes, and found to be appreciably larger than typical growth rates associated with opacity-driven pulsation. Furthermore, it is demonstrated that the surface perturbations generated by virtual modes are significantly changed from those caused by fully trapped modes; the latter result suggests differences in the line-profile variations exhibited by these two types of mode.
The findings are discussed in the context of the 53 Per, SPB and pulsating Be classes of variable star. Whilst wave leakage will probably not occur for overstable g modes in the 53 Per and slowly rotating SPB stars, the adoption of the new outer mechanical boundary condition may still affect the pulsational stability of these systems. Wave leakage for overstable modes remains a possibility in Be stars and the more rapidly rotating SPB stars.     

The double‐mode RR Lyrae variable BS Com

We present the frequency analysis of the multicolour time series photometry of the field RRd variable BS Comae. The large number of data points in each of the BV (RI)_C bands and the ∼0.01 magnitude accuracy of the individual measurements allow us a high precision analysis of the properties of the combination frequencies due to nonlinear coupling. Through the combination of the frequency spectra in different colors we show that except for the components corresponding to the linear combinations of the two pulsation modes, there are no other components present above the millimagnitude amplitude level. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the moving subfeatures in the Be star ζ Oph

We analyse a series of line profile observations of the He  i 6678 line in ζ Oph. A period analysis on these data using the mode and moments of the line profile confirms the two previously known periods. We describe a new method of mode identification for pulsating stars in which the calculated profiles are directly fitted to observed profiles. The method yields the full set of pulsational parameters including the spherical harmonic degree, ℓ, and azimuthal number, m . Application of the method to these data confirms the mode identifications previously suggested for the two periodicities. We find that the derived pulsational parameters are physically realistic and conclude that non-radial pulsation is the most likely explanation for the travelling subfeatures. However, a unique mode identification is still not possible – several non-sectorial modes fit the data as well as the usually adopted sectorial identifications. The predicted photometric amplitudes are in good accord with upper limits derived from photometric observations. We conclude that ζ Oph is a star in the β Cep instability strip in which two modes of high degree (probably ℓ=4 and ℓ=8) are excited. We present an interpretation of these findings in which the cause of the low-order line profile and light variations in periodic Be stars is corotating photospheric clouds, while the travelling subfeatures are incidental to the Be phenomenon and are a result of non-radial pulsation.     

Resolving the pulsations of subdwarf B stars: PG 0154+182, HS 1824+5745 and HS 2151+0857

We continue our programme of extended single-site observations of pulsating subdwarf B (sdB) stars and present the results of extensive time-series photometry to resolve the pulsation spectra for use in asteroseismological analyses. PG 0154+182, HS 1824+5745 and HS2151+0857 were observed at the MDM Observatory during 2004 and 2005. Our observations are sufficient to resolve the pulsations of all three target stars. We extend the number of known frequencies for PG 0154+182 from one to six, confirm that HS 1824+5745 is a monoperiodic pulsator and extend the number of known frequencies to five for HS 2151+0857. We perform standard tests to search for multiplet structure, measure amplitude variations as pertains to stochastic excitation and examine the mode density to constrain the mode degree ℓ.     

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.