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.     

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.     

An attempt to identify the pulsation modes in the δ Scuti star QQ Tel

We present simultaneous UBVRI photometry and high-dispersion spectroscopy of the δ Scuti star QQ Tel. At least seven periodicities are detected in the light curve, but there are likely to be many more. The line profile variations suggest that some of the observed frequencies may be due to modes of moderately high degree  (ℓ≳4)  .     

An asteroseismic study of the β Cephei star θ Ophiuchi: photometric results

We have carried out a three-site photometric campaign for the β Cephei star θ Oph from 2003 April to August. 245 h of differential photoelectric u v y photometry were obtained during 77 clear nights. The frequency analysis of our measurements has resulted in the detection of seven pulsation modes within a narrow frequency interval between 7.116 and 7.973 c d⁻¹. No combination or harmonic frequencies have been found. We have performed a mode identification of the individual pulsations from our colour photometry that shows the presence of one radial mode, one rotationally split  ℓ= 1  triplet and possibly three components of a rotationally split  ℓ= 2  quintuplet. We discuss the implications of our findings and point out the similarity of the pulsation spectrum of θ Oph to that of another β Cephei star, V836 Cen.     

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.     

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.     

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.     

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     .     

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.     

Mode identification from time-resolved spectroscopy of the pulsating white dwarf G29‐38

We have used time-resolved spectroscopy to measure the colour dependence of pulsation amplitudes in the DAV white dwarf G29-38. 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 G29-38 reveals one mode with a colour dependence different from the other five, permitting us to identify the ℓ-value of all six modes and to test the model predictions. The Keck observations also show pulsation amplitudes that are unexpectedly asymmetric within absorption lines. We show that these asymmetries arise from surface motions associated with the non-radial pulsations (which are discussed in detail in a companion paper). By incorporating surface velocity fields into line profile calculations, we are able to produce models that more closely resemble the observations.     

Fitting the young main-sequence: distances, ages and age spreads

We use several main-sequence models to derive distances (and extinctions), with statistically meaningful uncertainties for 11 star-forming regions and young clusters. The model dependency is shown to be small, allowing us to adopt the distances derived using one model. Using these distances, we have revised the age order for some of the clusters of Mayne et al. The new nominal ages are: ≈2 Myr for NGC 6530 and the ONC, ≈3 Myr for λ Orionis, NGC 2264 and σ Orionis, ≈4–5 Myr for NGC 2362, ≈13 Myr for h and χ Per, ≈20 Myr for NGC 1960 and ≈40 Myr for NGC 2547. In cases of significantly variable extinction, we have derived individual extinctions using a revised Q-method. These new data show that the largest remaining uncertainty in deriving an age ordering (and necessarily ages) is metallicity. We also discuss the use of a feature we term the radiative–convective gap overlap to provide a diagnostic of isochronal age spreads or varying accretion histories within a given star formation region. Finally, recent derivations of the distance to the ONC lie in two groups. Our new more precise distance of 391⁺¹²₋₉ pc allows us to decisively reject the further distance; we adopt 400 pc as a convenient value.     

Time-dependent convection seismic study of five γ Doradus stars

We apply for the first time the time-dependent convection (TDC) treatment of Gabriel and Grigahcène et al. to the photometric mode identification in γ Doradus (γ Dor) stars. We consider the influence of this treatment on the theoretical amplitude ratios and phase differences. Comparison with the observed amplitudes and phases of the stars γ Dor, 9 Aurigae, HD 207223 = HR 8330, HD 12901 and 48501 is presented and enables us to identify the degree ℓ of the pulsation modes for four of them. We also determine the mode stability for different models of these stars. We show that our TDC models agree better with observations than with frozen convection models. Finally, we compare the results obtained with different values of the mixing-length parameter α.     

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.     

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.     

Semiclassical approximation for low-degree stellar p modes – I. The classical eigenfrequency equation

A new eigenfrequency equation for low-degree solar-like oscillations in stars is developed, based on the assumption of purely classical propagation in the stellar interior of acoustic waves modified by buoyancy and gravity . Compared with high-frequency asymptotic analysis, the eigenfrequency equation has a new functional form, with expansion in powers of ℓ(ℓ+1) instead of 1/ ω . Basic observable quantities, the 'large' and 'small' frequency separations , are interpreted as the dependence on frequency and refraction angle of a classical action integral for waves propagating close to the stellar diameter. The new eigenfrequency equation gives a significant improvement in accuracy over previous analyses when tested with solar p modes, suggesting this as an alternative and more powerful tool for applications in stellar seismology.     

Cosmic microwave background anisotropies resulting from feedback-regulated inhomogeneous reionization

We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z _i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C _χ , and obtain the power spectrum of the anisotropies, C _ℓ, in the range 5000<ℓ<10⁶. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10⁻¹². We also show that the ionization correlation function C _χ is not Gaussian, but at separation angles θ ≲10⁻⁴ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C _χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.     

Towards mode selection in δ Scuti stars: regularities in observed and theoretical frequency spectra

Only a fraction of the theoretically predicted non-radial pulsation modes have so far been observed in δ Scuti stars. Nevertheless, the large number of frequencies detected in recent photometric studies of selected δ Scuti stars allow us to look for regularities in the frequency spacing of modes. Mode identifications are used to interpret these results.
Statistical analyses of several δ Scuti stars (FG Vir, 44 Tau, BL Cam and others) show that the photometrically observed frequencies are not distributed at random, but that the excited non-radial modes cluster around the frequencies of the radial modes over many radial orders.
The observed regularities can be partly explained by modes trapped in the stellar envelope. This mode selection mechanism was proposed by Dziembowski & Królikowska and shown to be efficient for  ℓ= 1  modes. New pulsation model calculations confirm the observed regularities.
We present the s – f diagram, which compares the average separation of the radial frequencies ( s ) with the frequency of the lowest frequency unstable radial mode ( f ). This provides an estimate for the  log  g   value of the observed star, if we assume that the centres of the observed frequency clusters correspond to the radial mode frequencies. This assumption is confirmed by examples of well-studied δ Scuti variables in which radial modes were definitely identified.     

Eight new δ Scuti stars

HD 23194, a member of the Pleiades, was found to pulsate with a period of about 30 min. The literature on the star is reviewed, and it is concluded that it may be a marginal Am star in a binary system. HD 95321 is an evolved Am ( ρ Puppis) star with a 5.1-h periodicity. Mode identification of its pulsation, based on multicolour photometry, suggests that the oscillation is probably non-radial with ℓ=2. We also report on the discovery of six other new δ Scuti stars, some of which may be pulsating in gravity modes.     

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.     

Discovery and asteroseismological analysis of a new pulsating DB white dwarf star, PG 2246+121

We report 36.6 h of time-resolved CCD photometry of the DB white dwarf star PG 2246+121 and the discovery that it is a new pulsating variable. Analysis of our compact single-site data set allowed the detection of three mode multiplets, two triplets at 256 and 329 s, respectively, and one doublet at 286 s. The frequency splitting within those structures is exactly the same within the length and accuracy of our data set.
We argue that these multiplets are the result of non-radial g-mode pulsations, most probably of spherical degree ℓ=1, which then yields a formal stellar rotation period of 2.00±0.12 d. We suggest that the excited modes are three consecutive radial overtones of order 3–7, most likely k =4,5,6. This discovery's impact on the understanding of pulsating DB white dwarfs is discussed.