We review radio maser observations of the circumstellar envelopes of oxygen-rich Mira variables, OH/IR stars and M-type supergiants.

The identification of the mode of pulsation of Mira variables remains a major problem. Recent angular diameter measurements of solar neighbourhood Miras suggest large radii consistent with first overtone pulsation. On the other hand, the pulsation velocity amplitudes of Mira variables point to fundamental mode pulsation. There is some marginal evidence from multiple modes in Miras that the prime pulsation mode is the first overtone, while distinct (K,logP) sequences in the Magellanic Clouds point to the Miras being fundamental mode pulsators. The above confusing evidence is presented and discussed. Finally, the (K,logP) relations in the SMC and LMC are compared in order to determine if there is any metallicity dependence.

The main conclusions that can be drawn from most of previous non-linear simulations of LPV (Keeley 1970, Rose & Smith 1972, Wood 1974, Tuchman et al. 1978, 1979) are the following:

In all cases where the fundamental mode is predicted, by the linear analysis, to be the dominant, the pulsations are seen to diverge and lead to a rather violent mass-loss process (Wood 1974, Tuchman, Sack & Barkat 1979).

A steady pulsation with (roughly) a limit cycle does set in only in those cases where the linear analysis predicts that the dominant mode (with the largest value of the growth rate) is the first overtone (or higher). In all these cases the actual limit cycle is found to be in a good agreement with the linear predictions, with regard to the pulsation mode and period (Wood 1974, Tuchman, Sack & Barkat 1979). However, it is important to note that periods, for these overtone pulsators, are always found to be smaller than 300 days (Wood 1974, Tuchman, Sack & Barkat 1979). Increasing the luminosity of these models, in order to increase their periods, results in a switch to the fundamental mode, followed by the violent relaxation oscillations, mentioned above.

The relation between mass loss rate and pulsation period in carbon Miras is discussed. The dust mass loss rate is very low (about 2 10−10 M⊙yr) up to about P = 380 days, where there is a sudden increase. For P > 400 days there is a linear relation between log and P. The change in the mass loss rate near 380 days may be related to radiation pressure on dust becoming effective in driving the outflow.

The study of luminous variable stars has important consequences both with respect to the scale of the Universe and for our understanding of the later stages of stellar evolution.

This review will look at a number of groups of these stars, in particular the RV Tauri stars, the hydrogen-deficient Carbon (HdC) stars, including the R Coronae Borealis (RCB) stars and some aspects of Cepheid variables.

Both photometric and spectroscopic observations will be presented to show the amount of progress that has been made in this area over the last several years. Links will be made to various models which are being used to understand the observational data.

The most important conclusion is that there is still enormous scope for the acquisition and detailed analysis of data on the relatively bright members of these groups of stars. These can be used to provide further understanding of the more distant objects of each group and of the wider problems in astrophysics.

In this review I consider recent results on the space distribution of classical Cepheids, first dealing with their Z-distribution normal to the galactic plane, and second considering their X,Y components in the plane. In doing so, use is made of a new database of 505 stars known to be or likely to be classical Cepheids which has recently been compiled by Fernie et al. (1995) and which is available electronically on the World Wide Web at the URL http://ddo.astro.utoronto.ca/cepheids.html, and by anonymous ftp at perseus.astro.utoronto.ca (128.100.77.18) in the directory pub/cepheids.

Following the discussion of space distribution, a review of recent work on Cepheid kinematics and the resulting determination of the distance to the galactic centre will be given.

The review concerns the use of Miras and OH/IR stars as probes of Galactic structure and concentrates on groups of stars with both kinematic and luminosity data. The reliability of distance determinations for these stars is covered in some depth. Kinematic and scale height data for local Miras suggest that those with pulsation periods of around 200 day are members of the thick disk or inner halo. Longer-period stars are kinematically cooler and have smaller scale heights. Stars with moderate dust shells, which may be more evolved, seem to belong to the same population as thin-shelled sources with the same pulsation period. Our current knowledge of the structure of the Galactic Bulge is reviewed, as is our understanding of its rotation as derived from observations of SiO Masers from Mira variables. Infrared and radio surveys, in progress or planned, offer us the potential to extend the study of low-mass metal-rich stars well beyond the solar neighbourhood.

The different types of variations of LBVs are discussed. The “typical LBV variations” have amplitudes of ΔV ≃ 0.5 to 2.0 magnitudes and irregular time-scales of months to years. This is due to changes in the stellar radius and the effective temperature. Modelling of this variability for one star, S Dor, shows that the radius of the star varies between 100 and 380 R⊙, the effective temperature between 20,000 and 9,000 K, and the luminosity between log L* = 6.10 to 5.9. The variation of the radius is not an apparent variation of the effective radius of the wind due to a variable mass loss rate (which has often been assumed) but it is a true variation of the radius of the star itself. The changes in L* suggest that about 10−3 to 10−2M* takes part in the expansion of the star. The irregular microvariations with amplitudes of about ΔV ≃ 0.2m on timescales of weeks are probably due to non-adiabatic pulsations with mode-interaction. We argue that LBVs are close to their effective Eddington Limit and discuss a qualitative scenario to explain their location in the HR-diagram.

Both radial and low degree and order g-mode nonradial pulsations are predicted for luminous blue variables that occur in the blue supergiant region of the Hertzsprung-Russell diagram. It is found that the radial strange modes have very large growth rates due to helium ionization in models at surface effective temperatures between 10,000 and 20,000 K.

A group of faint, remote Cepheids in the outer disc of the Galaxy has been observed in spectroscopy and photometry. These Cepheids are used as tracers to measure the rotation curve of the disc beyond R=11 kpc, and to study the metallicity gradient in the outer disc.

The doubly-periodic semiregular variable V Hydrae became redder and developed resonance emission lines and bands during the 1992-94 deep minimum, which therefore resulted from the production of a circumstellar dust cloud. This removes the need to postulate a secondary pulsation period, ten times as long as the main pulsation period, in the stellar as opposed to circumstellar envelope.

A summary is given of recent measurements, by various methods, of the absolute magnitudes for RR Lyrae stars. Calibrations within our galaxy, using the Baade-Wesselink method and by Statistical Parallaxes, give a result that is some 0.2–0.3 mag fainter than is obtained by all other methods considered. The resolution of this conundrum will be likely in the near future when new and improved datasets become available.

The properties of variable blue stragglers (i.e., SX Phe stars) in the extremely metal-poor globular cluster NGC 5053 are reviewed. Pulsation modes are derived for three of the SX Phe stars recently discovered in the central regions of 47 Tuc by Gilliland et al. (1995a,b).

The current Cepheid zero-point is equivalent to an LMC distance modulus of 18.57 ± 0.10. The zero-point from corrected Baade-Wesselink data is probably not significantly different from this. A reexamination of the Baade-Wesselink data for RR Lyrae variables leads to an LMC modulus of 18.51, an age difference between β- and α-group galactic globular clusters of +1.46±0.70 Gyr, and an Mv - [Fe/H] slope in agreement with theory. Other questions discussed include; Avoiding bias in using the Cepheid PL relation; Metallicity spread amongst Cepheids; Cepheids and Ho.

The MACHO Collaboration’s search for baryonic dark matter via its gravitational microlensing signature has generated a massive database of time ordered photometry of millions of stars in the LMC and the bulge of the Milky Way. The search’s experimental design and capabilities are reviewed and the dark matter results are briefly noted. Preliminary analysis of the ~ 39,000 variable stars discovered in the LMC database is presented and examples of periodic variables are shown. A class of a periodically variable Be star is described which is the closest background to microlensing which has been found. Plans for future work on variable stars using the MACHO data are described.

In the past few years, the Magellanic Clouds have been the targets for several major variable star surveys. The results of these surveys are now becoming available and it is clear that a Renaissance in LMC and SMC variable star research will result. In this review, I will describe the results of such surveys and review the questions that are likely to be answered by further work.

With respect to results, I will concentrate on LMC MACHO Project data, including beat Cepheids, discovery statistics, mode identification, Fourier decomposition of lightcurves, and the differences between the LMC and galactic sample.

The preliminary astrometric and photometric results obtained from the first 30 months of HIPPARCOS data are presented. Examples of the results obtained for the various categories of pulsating variables included in the HIPPARCOS programme are given. The perspectives opened by GAIA (Global Astrometric Interferometer for Astrophysics), the concept for an astrometric interferometer submitted in September 1994 to the ESA Horizon 2000+ survey committee, are briefly exposed.

Ultraviolet spectroscopy with the IUE satellite has been used to survey all Cepheids brighter than 8th magnitude to identify blue companions. The derived binary frequency is 21% with blue companions which implies that 34% would have been found from a large radial velocity survey. A second study has used deep IUE exposures of Cepheids showing orbital motion to determine the distribution of mass ratios in Cepheid binaries. Low mass companions are strongly preferred, especially when corrections for incompleteness are included.

Laney & Stobie (1995) (LS95) have determined Baade-Wesselink radii for 49 galactic Cepheids using BVRI and JHK photometry. Four of the possible magnitude-colour combinations were studied in detail — namely, (V,B–V), (V,V–Ic), (K,V–K) and (K,J–K). In that paper and in the present note we have used the maximum likelihood method of Balona (1977) as recently modified to allow for the nonlinear effects of the non-negligible radius excursions of Cepheids.

One major advantage of infrared photometry is that the light variation at K is dominated by the change in surface area, unlike the light variation at V which is dominated by temperature changes. Another is that (as shown both empirically and by model atmospheres) one may use a J–K or V–K colour index to calculate the surface brightness at K without having to worry very much about the effects of varying surface gravity or Doppler broadening velocity, while the same is definitely not true when optical colour indices are used to calculate the surface brightness at V.

Comments in the literature in recent years reveal a variety of misconceptions about the role and value of galactic clusters for calibrating the Cepheid period-luminosity-colour (PLC) relation. This paper attempts to clarify some of these points using personal experiences gained from studies of the sparse galactic clusters and groups in which some classical Cepheids are located.

Reddening is often blamed for problems originating from other causes. Three features of reddening are sometimes overlooked: (i) no universal reddening law applies to all fields, (ii) mean reddening laws are not applicable to samples of dispersed objects, and (iii) patchy extinction is the norm.