The pulsation of long-period variables

Abstract

The long- period variables are a class of star about which comparatively little is known , despite a long history of observations. In this thesis , the results are presented of pulsation analyses of long-period variables, and of investigations into the shock waves associated with the pulsation. Chapter 2 describes a grid of linear non-adiabatic pulsation models appropriate to galactic disk , population II and supergiant red variables. These are designed to provide a sound theoretical basis for pulsation analyses of the long-period variables. The effects of altering surface boundary conditions, effective temperatures, and of including molecular opacity are examined . Values of the pulsation constant , Q, can sometimes be substantially different from those found in earlier pulsation studies for both fundamental and first overtone modes. Observed secondary periodicities and observationally derived values of Q are compared with theoretical models and favour the first overtone mode as the primary pulsation mode in the long-period variables. In Chapter 3 , intrinsic properties (Teff and L) and pulsation constants are derived for a sample of red variables in 47 Tucanae . Merits of available temperature and luminosity calibrations are discussed. Comparisons of derived Q values with appropriate theoretical models of Chapter 2 favour overtone pulsation for the semi-regular variables and, if black-body temperatures are used, for the Hiras as well . A systematic high-dispersion survey of Balmer emissioll lines in a sample of nine Mira variables is presented in Chapter 4 . Observations are centred on phases around maximum light when the hydrogen lines Hγ, Hδ , Hζ; and Hη are in emission. Variations in emission line characteristics with phase and where available , between cycles, are discussed. The Balmer lines appear to become narrower and bluer with increasing phase , because of diminishing emission on the red side. All observations of the abovementioned Balmer lines have been calibrated to absolute flux levels. It is evident that the line ratios are significantly different to theoretical pure recombination values; Hδ is the strongest of the four lines in the majority of observations when effects of overlying absorption are small. A simple shock model is presented in Chapter 4 in which hydrogen Balmer photons undergoe a substantial degree of scattering in the hot, immediate post- shock region . A theoretical model from which shock structure may be computed is described in Chapter 5. This detailed theoretical shock model is the first that allows the shock structure and resultant photon emission to be determined consistently for conditions typical of the atmospheres of long-period variables. A grid of shock models is generated in Chapter 6 for a variety of physical conditions and shock speeds likely to be found in the outer atmospheres of long-period variables. The structure of the shocks is described, and the effects on the shock structure and resultant line emission of altering physical input parameters are examined . Theoretical models with shock velocities and pre- shock densities and temperatures derived from infrared spectroscopy of Mira variables predict -levels of emission in the Balamer lines much higher than the levels observed in Miras at maximum light. Line ratios near to pure recombination values are predicted , in contrast to the observations. Possible interpretations to the broad observed line profiles are discussed. The theoretical model in its current fo rm does not permit accurate comparisons with the observational data. However, a number of arguments indicate that the shock speed slows from - 30 kms⁻¹ around maximum - 20 kms⁻¹ at phase 0.25. light to Some future improvements to the shock models are suggested . Show more