THE PULSATION THEORY OF VARIABLE STARS

Abstract

The thesis deals with some problems on the pulsation of composite stellar models with a view to study the effect of central condensation on the pulsation characteristics. The thesis is divided into two parts I and II comprising of eight chapters. In part I the small radial pulsations and enharmonic pulsations of four polytropic models, each having a polytropic index 1.5 in the inner part (core) and 3 in the outer part (envelope), but having different central condensations have been considered. Their anharmonic pulsations have been considered both by Rosseland's as well as Eddington1 s method. The radial pulsations of three other composite models, having polytropic indices 0.5 or 1.5 in the core and 3 or 4 in the envelope, but with the same central condensation ( ^c/o ) have been considered. It has been shown that &/p is not sensitive enough to indicate the eigen value frequencies and amplitudes of the modes effectively. It has been found that the parameter Xfcdq will be quite suited to characterise the pulsation properties of the fundamental mode of all the models considered. Also there is a more rapid decrease in the amplitudes of higher modes of the composite models as compared to those of the complete polytropes. In the anharmonic pulsations this factor affects the radial velocity curve. In part II the small radial pulsations and anharmonic pulsations of a composite model, consisting of a ii. 2 2 core with density varying as (1-r /R ) surrounded by an envelope with density varying as the inverse square of the distance r from the centre, have been considered. Besides the above work by the author, an introductory chapter on composite polytrope Is given to make the thesis self sufficient. The contents of each chapter are outlined below. ti 8iT v. iiJti i. Chapter I, The theory regarding fitting the solutions for composite polytropes has been given in brief. Chapter II. The equation for small adiabatic radial oscillations is derived and is applied to composite models each having a polytropic index 1.5 in the core and 3 in the envelope. Four different models with interfaces at r/H • 0.2094, 0.3915, 0.6160 and 0.8250 have been studied. The radial oscillations have been considered for « • 0,6, 0,5 and 0,4. The central condensation ( ?«. /p ) for these models is 37.6662, 19.9518, 10.8507 and 7.3638 respectively. The first model shows a behaviour similar to the standard model and the third model shows a behaviour similar to the polytrope n * 2 as far as the fundamental mode and the ratios of eigen value frequencies are concerned. Chapter III. The anharmonic pulsations of the above four models have been considered by Rosseland's method, taking into consideration the interaction of the first three modes for the case « * 0.6 . The radial velocity curve shows reasonable results for the first two models but iii. for the last two models it shows humps. So the last two models are quite unsuitable as far as their anharmonic pulsations are concerned. Chapter IV, The anharmonic pulsations of the above models have been considered by Eddington* s method. This has also been worked out for the standard model (for « » 0.6) . Chapter V, The small adi abatic radial pulsations for three different composite models (for <** 0,6) with polytropic indices (i) 0,5 in the inner part and 3 in the outer part (ii) 0,5 in the inner part and 4 in the outer part (iii) 1.5 in the inner part and 4 in the outer part and having the central condensation ?<Vp equal to 37,666 (i.e. equal to the first model mentioned in Chapter II) have been obtained. These models help considerably in the conclusion on 12ie effect of central condensation on overtones. Chapter VI, An overall study of the last four chapters is done and the conclusions derived are given in an explicit form. Part II. Chapter VII. The small radial pulsations of a composite model, consisting of a core with density varying 2 2 as (1-r /R ) surrounded by an envelope with density varying as the inverse square of the distance r from the centre, have been considered. iv. Chapter VIII, The anharmonic pulsations of the above model have been considered, by Rosseland's method. The work presented here, is original research by the author except sections 1.2, 2.2, 3.2, 3.3 and 4,1 which have been put infco present a connected account of the whole.