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.     

AGB variables and the Mira period–luminosity relation

Published data for large-amplitude asymptotic giant branch variables in the Large Magellanic Cloud (LMC) are re-analysed to establish the constants for an infrared ( K ) period–luminosity relation of the form   M _K =ρ[log  P − 2.38]+δ  . A slope of  ρ=−3.51 ± 0.20  and a zero-point of  δ=−7.15 ± 0.06  are found for oxygen-rich Miras (if a distance modulus of 18.39 ± 0.05 is used for the LMC). Assuming this slope is applicable to Galactic Miras we discuss the zero-point for these stars using the revised Hipparcos parallaxes together with published very long baseline interferometry (VLBI) parallaxes for OH masers and Miras in globular clusters. These result in a mean zero-point of  δ=−7.25 ± 0.07  for O-rich Galactic Miras. The zero-point for Miras in the Galactic bulge is not significantly different from this value.
Carbon-rich stars are also discussed and provide results that are consistent with the above numbers, but with higher uncertainties. Within the uncertainties there is no evidence for a significant difference between the period–luminosity relation zero-points for systems with different metallicity.     

Observable effects of dust formation in dynamic atmospheres of M-type Mira variables

The formation of dust with temperature-dependent non-grey opacity is considered in a series of self-consistent model atmospheres at different phases of an O-rich Mira variable of mass  1.2 M_⊙  . Photometric and interferometric properties of these models are predicted under different physical assumptions regarding the dust formation. The iron content of the initial silicate that forms and the availability of grain nuclei are found to be critical parameters that affect the observable properties. For certain plausible parameter values, dust would form at 2–3 times the average continuum photospheric radius. This work provides a consistent physical explanation for the larger apparent size of Mira variables at wavelengths shorter than 1 μm than that predicted by dust-free fundamental-mode pulsation models.     

Pulsation–decline relationships in R Coronae Borealis stars

Decline onset times were measured in long-term visual light curves for five R Coronae Borealis (RCB) variable stars. These included RY Sgr and V854 Cen, the two RCB stars previously reported to have a relationship between dust formation events and pulsational variations. Analysis of the decline epochs showed that all decline onsets for a given star obey a linear ephemeris tied to the object's dominant radial pulsation period. Thus, in addition to confirming the pulsation–decline correlation for RY Sgr and V854 Cen, this same behaviour was demonstrated in UW Cen, R CrB and S Aps for the first time. This general result firmly establishes the connection between radial pulsation and mass loss in the RCB stars. The dominant pulsation period of ≈40 d for all of these objects therefore represents the characteristic time-scale on which these stars produce dust.     

Carbon-rich Mira variables: radial velocities and distances

Optical radial velocities have been measured for 38 C-type Mira variables (C-Miras). These data together with others in the literature are used to study the differences between optical and CO millimetre (mm) observations for C-Miras and the necessary corrections to the optical velocities are derived in order to obtain the true radial velocities of the variables. The difference between absorption and emission-line velocities is also examined. A particularly large difference  (+30 km s ⁻¹)  is found in the case of the Hα line. A catalogue is given of 177 C-Miras with estimated distances and radial velocities. The distances are based on bolometric magnitudes derived in Paper I using South African Astronomical Observatory (SAAO) observations or (for 60 of the stars) using non-SAAO photometry. In the latter case, the necessary transformations to the SAAO system are derived. These data will be used in Paper III to study the kinematics of the C-Miras.     

Globular clusters and the Mira period–luminosity relation

A globular cluster distance scale based on Hipparcos parallaxes of subdwarfs has been used to derive estimates of M _K for cluster Miras, including one in the Small Magellanic Cloud (SMC) globular cluster NGC 121. These lead to a zero-point of the Mira infrared period–luminosity (PL) relation, PL( K ), in good agreement with that derived from Hipparcos parallaxes of nearby field Miras. The mean of these two estimates together with data on LMC Miras yields a Large Magellanic Cloud (LMC) distance modulus of     in evident agreement with a metallicity-corrected Cepheid modulus     .
The use of luminous asymptotic giant branch (AGB) stars as extragalactic population indicators is also discussed.     

The variability of Magellanic cluster infrared stars

We report on the light variations of the infrared stars that were discovered recently in the Magellanic clusters NGC 419, 1783 and 1978. Their periods, of 528, 458 and 491 days, are among the longest known for carbon-rich Mira variables in the Clouds. All three IR stars were found to lie on the extension of the period– M _bol relation derived from the shorter-period C-rich Miras while they were 0.45–0.70 mag fainter than the extension of the period– M _K relation. Their main sequence masses were determined by isochrone fitting to be 1.5–1.6 M_⊙, consistent with the prediction of the evolutionary models of Vassiliadis & Wood.     

Continuum emission around AGB stars at 1.2 mm

It is generally acknowledged that the mass-loss of asymptotic giant branch (AGB) stars undergoes variations on different time-scales. We constructed models for the dust envelopes for a sample of AGB stars to assess whether mass-loss variations influence the spectral energy distribution. To constrain the variability, extra observations at millimetre wavelengths (1.2 mm) were acquired. From the analysis of the dust models, two indications for the presence of mass-loss variations can be found, being (1) a dust temperature at the inner boundary of the dust envelope that is far below the dust condensation temperature and (2) an altered density distribution with respect to  ρ( r ) ∝ r ⁻²  resulting from a constant mass-loss rate. For five out of the 18 studied sources a two-component model of the envelope is required, consisting of an inner region with a constant mass-loss rate and an outer region with a less steep density distribution. For one source an outer region with a steeper density distribution was found. Moreover, in a search for time variability in our data set at 1.2 mm, we found that WX Psc shows a large relative time variation of 34 per cent which might partially be caused by variable molecular line emission.     

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.