We discuss two new slowly pulsating B stars for which it can be convincingly shown that they are multiperiodic variables. The group now contains ten confirmed and likely multiperiodic mid-B stars with periods between 0.7 and 4.4 days. The multiperiodicity and the length of the periods point to g-mode pulsations. The very high order of the modes implies that the modes are excited in the core or in the very outer layers of the star. A recently proposed mechanism, in which both the inner and outer layers intervene, is discussed.

Line-profile variations (LPVs) are often seen in early-type stars. They were first detected in the β Cephei stars, where they are due to radial as well as to nonradial pulsations (NRP). It is still a matter of debate whether NRP is also the cause of LPVs in broad-lined B- and Be stars.

The study of LPVs of nonradially pulsating stars is often considered to be especially interesting in the case of rapid rotators, because in such stars the line profiles may offer a Doppler image of the stellar surface. Almost all investigators conclude that only sectorial modes with high -values can properly account for the observations of LPVs in broad-lined stars; on the other hand, high-degree modes are almost never seen in slowly rotating stars.

We point out here that the expression for the velocity field which is usually adopted, is not valid for rapid rotators.

The star β CMa, prototype of the β CMa variables, is known to have been a double mode pulsator since the beginning of the century, with amplitudes of 12 and 7 km/sec for the 6.00 and 6.03 hour oscillations (Shobbrook, 1973). Recently, Dziembowski, Moskalik, and Pamyatnykh (1992) have produced models of B stars using OPAL opacities which have many radial and non-radial modes unstable. As only a few modes are observed in these stars, these authors suggest that modes might change amplitude in such a way that modes can appear, disappear, or be replaced by other modes. Based on unsubstantiated rumour that β CMa had, like α Vir, quit pulsating (Pesnell, priv. comm.), we undertook observations with the Mt. John University Observatory (New Zealand) echelle spectrograph and CCD camera on the 1-m McLelland telescope. We found that β CMa is still pulsating, but with reduced amplitude and substantial period change compared with earlier data.

In particular, quadratic ephemerides fit to all known times of spectroscopic maxima agree with our times of maxima [P1: HJD 2448611.8436; P2: HJD 2448611.8278] to better than two minutes, but an earlier linear ephemeris by Chappelier (1985) disagrees by over two hours. Our data is best fit with amplitudes of about 7 km/sec for both modes-this gives a nominal beat amplitude of nearly zero at the 49-day beat minimum (at a time when the linear ephemeris would have predicted a maximum amplitude). This may be the cause of the rumour mentioned above. Additional support for our conclusion of continuing pulsation comes from the fact that obvious line profile changes occur on the pulsation time scale.

We have obtained Voyager Ultraviolet Spectrometer (UVS) measurements of well-known β Cephei stars, which now total more than 1500 hours (> 300 pulsation cycles!) and which constitute the most comprehensive coherent data set that can address fundamental pulsation properties of a significant cross-section of the group. The extended measurement sequences for individual stars, which cover many successive pulsation cycles at wavelengths where pulsation amplitudes reach a maximum, can provide more comprehensive tests of pulsation stability than any ground-based data. During 1990-91, we acquired more than 100 hours of ground-based high-resolution spectroscopic observations and UBV photometric observations, simultaneous and near-simultaneous with the UVS data set. Analysis has been initiated at NASA's Goddard Spaceflight Center (NASA/GSFC), the University of Hawaii at Hilo (UH Hilo), and the Dominion Astrophysical Observatory (DAO).

Besides the well-known pulsation period of 4h34m, the B1 IV star β Cep has a very significant period of 6 or possibly 12 days in the equivalent width of the ultraviolet resonance lines. This was discovered by Fishel and Sparks (1972) with the OAO-2 satellite, and later confirmed with IUE data. Until now, no explanation has been put forward for this period.

We propose that the UV periodicity arises from a 12 day rotational period of the star and that the stellar wind is modulated by an oblique dipolar magnetic field at the surface.

Support for this hypothesis is given by the striking similarity between the UV-line behavior of β Cep and of known rotating magnetic B stars, for example the B2 V helium-strong star HD 184927 (Barker et al. 1982), and by the measured magnetic field strength of B ± σ = (810 ± 170) G for β Cep itself by Rudy and Kemp (1978). A rotational period of 12 days corresponds well with an adopted radius between 6 and 10 R⊙, given the reported values of 20 - 43 km/s for vsini.

To verify our hypothesis we carried out new magnetic field measurements simultaneously with UV spectroscopy. We confirm the 12 day UV period in the equivalent width of the stellar wind lines of CIV, Si III, Si IV and N V (see Figs. 1 and 2), but find a lower and likely variable field strength (Fig. 3), which is consistent with a 12 day period, but not conclusive.

It remains puzzling why our new magnetic field measurements show a lower field than in 1978. It is interesting to recall the recent discovery (Mathias et al. 1991) that β Cep has entered a new Be phase (July 1990), when Hα turned into emission (see Fig. 4). This opens the suggestion that the lower magnetic field is related to the emission phase. Because the UV period is still the same, the field must still be strong enough to modulate the wind. A possibly higher equivalent width of the 1991 UV data with respect to the 1979 data might also be related to this transition, but this needs to be confirmed.

The star β Cep appears to be the only star in its class which shows this wind variability and in this respect β Cep is an exceptional β Cep star.

HR 2680 (B5V) was used as a comparison star in a multi-site (ESO & SAAO) campaign organised in 1988 to observe Be stars. We found that the star is an eclipsing binary with a period of 8.1 days. The eclipse is partial with a depth of 0.18 mag. Radial velocity observations confirmed the period.

A light variation with an amplitude of as much as 0.03 mag was seen outside the eclipse (Fig. 1). This variation can be interpreted as two oscillations with approximate periods of 1.19 and 1.28 days. Further photometric observations were obtained in 1989, 1990 and 1991 at SAAO. The multiperiodicity was confirmed, but the periods were not constant from season to season.

We suspect that the star is a pulsator of the 53 Per class of line-profile variables. Being an eclipsing binary, this unique system is of potentially great importance as a test bed for stellar dynamics and nonradial pulsations.

Longitude-coordinated high-precision photometry has been obtained a few weeks before the beginning of a strong Be and shell phase (1988) in HR 8762 (o And). The star showed variations of a few millimagnitudes in amplitude; i.e., just over the detection threshold. The classical 1.57-day double-wave period is still detected, showing that it probably never fades out completely, whatever the phase of the star. These variations can be interpreted as normal photospheric activity in a regular rotating B star. Although the variations of HR 8762 during our campaign were quite small, we could detect their amplitudes at a level of a few mmag.

We still have to check whether they are still “in phase” with previous photometric observations: if this is the case, it means that in the “spot” hypothesis, these (superficial?) features would remain in the same position on the photosphere, changing only in surface area and/or brightness with the star's activity.

We have undertaken a multi-site, multi-wavelength observing campaign on the archetypal O stars ζ Puppis (O4 I(n)f) and ζ Ophiuchi (O9.5 V). Both stars are well known for the strength of their line profile variations (lpv's), and represent extremes of O spectral type and luminosity class. UV time-series spectroscopy of ζ Pup and ζ Oph is described by Prinja et al. (Ap.J. 1992, 390, 266), and Howarth et al. (Ap.J. 1992, submitted) respectively. The optical spectroscopic results of ζ Oph are reported by Reid et al. (1992, ApJ submitted), of which some of the principal results are given here.

During late April, and early May, 1989, we obtained high-resolution, high signal-to-noise optical spectra of the late O-type, rapid rotator ζ Oph. Time-series analysis, using the CLEAN algorithm, has shown that the characteristic lpv seen in HeI λ447lÅ, Si III λλ4552, 4567, 4575Å, and MgII λ448lÅ can be satisfactorily represented as a set of 4 sinusoids. No substantial variation is observed in HeII λ4541, or NIII λ4517Å. We attribute this behaviour to a combination of equatorial gravity-darkening and a latitudinally-confined origin for the lpv.

The phase changes over the line profiles indicate repetitive patterns of axial symmetry, rotating prograde in the co-rotating frame of the star. The periods are 3.339 hours (-m = 4), 2.435 hours (-m = 5 or -m = 6), 1.859 hours (-m = 9 ± 1), and either 1.366 hours or 1.292 hours (-m = 11 ± 1); -m represents the spatial frequency around the stellar equator. The first three periods confirm those found at earlier epochs, and we conclude that some lpv characteristics are reproduced over at least a 2-year interval.

Since no commensurate superperiod (|m|P) exists, and since the super-periods are less than our estimated minimum rotation period for ζ Oph (> 18 hours), we reject a rotational modulation origin for the lpv and conclude that the star is undergoing multi-mode, sectorial, non-radial pulsations.

The large-amplitude pulsation of long-period variables, together with a number of other interacting processes and phenomena, causes a rich variety of effects on the structure and behavior of the stars. Outflowing winds result, causing extensive mass loss, with profound consequences for stellar evolution. The present status of modeling calculations for LPVs will be discussed first, with various examples. Emphasis will be given to the great importance of complex, nonlinear, time-dependent interactions between things such as the waves and atmospheric shocks that result from pulsation; non-LTE radiative transfer; non-equilibrium chemistry; the growth, changing optical properties, and dynamics of grains; and radiation pressure on both grains and molecules. I will then survey the developing implications and insights from new results and from work now in progress. Some of these concern the structure and the behavior of individual stars (e.g. determination of the pulsation mode and limiting amplitude; properties of more massive stars); some relate to the evolution of individual stars (e.g. evolution of the wind and the mass loss rate; the wind and circumstellar region during helium shell flashes; effects of the star's metallicity); and some relate to the evolution of populations of stars (e.g. the white dwarf mass distribution). All of these, and many more, offer new perspectives and new understanding concerning the character of LPVs and their role in stellar evolution.

New results (∼last two years) on mainly observational properties of Long Period Variables (LPVs) in the Magellanic Clouds and the Galaxy are reviewed. These properties include the effects of metallicity variations on their mass loss rates, the use of AGB LPVs to map the stellar distributions of the Galactic disk and bulge, and using detailed observations of nearby Miras to investigate their structure and to obtain new parallax distances, with implications for the pulsation mode of Miras.

The first crude pictures of the structure of Mira photospheres were derived from velocity analyses of emission and absorption lines appearing shifted, doubled and doppler-broadened in Mira spectra. Positions and shapes of profiles change with phase and often do not repeat in successive cycles. Non-repeating cycles are also found in colors (e.g., TiO bands in Fig. 9 of Spinrad & Wing 1969) and in light curves and present, of course, a problem in matching specific observed and modeled cycles. The large geometric extension of Mira photospheres was demonstrated by monochromatic radius observations of o Ceti and R Leo by Labeyrie et al. (1977) and Bonneau et al. (1982) which, however, did not systematically follow the stars through different phases and cycles.

The structure of a Mira photosphere is essentially determined by the propagation of shock fronts. A shock front enters the bottom of the photosphere once each cycle and travels outwards.

We demonstrate that the dimension deduced from time series data of hydro-dynamic models for chaotic pulsation is a function of luminosity. The dimension is proposed as a good quantity to guess stellar parameters and the physics of stellar envelopes like as the pulsation periods and light curve shapes used for regular variables.

The presence of dust essentially affects the optical appearance and the dynamics of circumstellar shells around LPVs, while in turn the formation of solid particles as well as their properties critically depend on the actual local conditions. Thus, a reliable modelling of the structure and dynamics of such shells requires a detailed treatment of the dust complex.

In our hydrocode, which is described in more detail in Fleischer et al. (1992), the time evolution of the dust component is treated consistently by means of a moment method (Gauger et al. 1990). For the solution of the hydrodynamical and thermodynamical problem we essentially follow the approach of Bowen (1988), except for the shocks, which so far are assumed to be isothermal.

We present NLTE radiative transfer in hydrodynamic models representative of Mira-type variable stars. Calculations were carried out with the PANDORA code of the Bowen models using a snapshot approximation.

Nonlinear calculations of Mira variable stars of Population I are presented. Each model is 1 M⊙, with a luminosity of 5000 L⊙ and an effective temperature near 3000 K. These models incorporate our theory of time-dependent convection, which is based on a convective phase lag formalism and includes spatial averaging of convective eddies from adjacent zonal interfaces. The theory also includes turbulent pressure, energy, and viscosity terms and allows for negative convective luminosities in subadiabatic regions where overshooting occurs.

Results of the present study suggest that based upon the dynamic behavior of the models, fundamental mode pulsations are the preferred mode of oscillation. In particular, we do not obtain the chaotic behavior that has been noted in previous nonlinear studies of the fundamental mode oscillations of Miras.

Past attempts to model the Hα emission profiles from Mira stars have been hampered by the strong absorption bands produced by TiO (M-type Miras) or carbon-based molecules (C-type Miras). The S-type Miras, however, exhibit relatively clean emission lines. As part of a larger study of Mira variables, I have obtained a series of high-dispersion Hα profiles of S-type Miras at different phases, using the DAO 48” coudé spectrograph. Although most profiles were obtained from different stars, their shapes develop in a regular way with advancing phase, so it appears that the observations can be used together to provide a good data base for the fitting of evolutionary (rather than static) models for the shock waves in S-type Miras.

Initial experiments with fitting simple models to the profiles have been extremely encouraging. The profiles can be represented very well by three Gaussian components.

The object S Carinae is a bright, relatively hot, short (149d) period mira. As expected, the Mg II h and k lines dominate the ultraviolet line spectra during a large fraction of the pulsation cycle. There are also numerous emission lines of Fe I and Fe II produced by either fluorescense or possibly collisional excitation. The unifying “theme” for all the ultraviolet line emission is variability - during a pulsation cycle one observes changes in the intensity, the central wavelength and (for the stronger lines) the line profile.

We have continued to observe many of the R Coronae Borealis (RCB) stars and other related hydrogen-deficient carbon stars. We wish to more fully investigate the photometric and spectroscopic properties of these peculiar stars.

The UBVRI photometric data (acquired at Mount John University Observatory, MJUO) are being used to investigate whether the periods determined by Lawson et al. (1990), based on time intervals of up to 1100 d, are still evident in the larger datasets which now cover time intervals of up to 2200 d.

The long time baseline of photometric observations that we have been able to acquire has enabled us to accumulate an extensive database of decline photometry. These are used to investigate links with the pulsations at maximum light in order to get a better understanding of this remarkable phenomenon.

High resolution échelle spectra have been obtained of two Large Magellanic Cloud (LMC) and one galactic R Coronae Borealis (RCB) star with the Anglo-Australian Telescope. An analysis of these data using He- and C-rich models and the model atmosphere code WIDTH6 of Kurucz indicates that the galactic RCB star SU Tau and the two LMC stars, W Men and HV12842, have similar atmospheric parameters to the warmer galactic RCB and hydrogen-deficient Carbon (HdC) stars e.g., R CrB and XX Cam. Specifically, the new stars have Teff ∼7000 K, log g = 0.5-1.0, microturbulent velocities between 6 and 8 km.s-1 and C/He ratios from 0.004 to 0.006.

An abundance analysis has been performed on these stars for a wide range of species. Special emphasis has been placed on particular elements H, He, Li, C, N, O, & Fe (see figure 1), which are key indicators of the extent and relative importance of nuclear processes such as the CNO cycle and triple-alpha process, and also of the physical processes such as convective mixing and mass loss. Specific values for the abundances of [H/He], [Li/Fe] and [Fe/total] (expressed relative to the total abundance of all species) in SU Tau and HV12842 are -5.4 & -6.4, +2.5 & +2.4, -0.4 & -0.8.