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Astron. Astrophys. 332, 102-110 (1998)

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1. Introduction

Since Martin's (1938) discovery that the periods of RR Lyrae stars in [FORMULA] Centauri are predominantly increasing, many studies have been made on period changes of a great number of RR Lyrae stars in different clusters. It was hoped that the minute changes in the periods observed would give some information on the speed and direction of evolution of horizontal branch stars and provide sensitive test of the theory of stellar evolution, as it suggests that the periods of RR Lyrae stars are increasing if they evolve from blue to red in the HR diagram or decreasing if they evolve to the opposite direction.

The complex structure of some of the phase [FORMULA] diagrams, however, suggests that some kind of "noise" could be superimposed on those secular variations of the period which we expect to exist as a result of evolutionary changes in the mean stellar radius (Balázs-Detre & Detre, 1966). This would mean that the phase diagrams are instead a convolution of stochastic processes and evolutionary changes. The source of "noise" is attributed to random fluctuations in the stellar structure (e.g. Sweigart & Renzini, 1979, Stothers, 1980). In spite of these disillusioning facts hopes have never been abandoned that a proper statistical evaluation of the parametrized values of the rate and direction of changes in the periods of a great number of RR Lyrae stars observed on a long baseline would eventually reveal the evolutionary effects.

In the determination of the average rate of period changes of RR Lyrae stars in globular clusters, in order to increase the statistical weight, both types of RR Lyrae stars, [FORMULA] and [FORMULA] stars are usually combined and treated together, in spite of the fact that there are references to different period change behaviour between the groups of [FORMULA] and [FORMULA] stars (Szeidl, 1975). In the case of [FORMULA] stars only the changes in the dominant period (first overtone frequency) have been studied. As these investigations were carried out on the traditional way (the phase of maximum of the folded light curve was derived), the double mode phenomenon manifested itself as a large error on the phase [FORMULA] diagram. The theoretical expectations suggest that the relative changes ([FORMULA]) in the period (or frequency) of the fundamental and first overtone mode should be of the same sign and about of the same rate.

Although it is obvious that the period change behaviour of an [FORMULA] star is not a simple mixture of that of [FORMULA] and [FORMULA] stars, their different period change behaviour raised the idea of a simultaneous investigation of modes in [FORMULA] stars. The globular cluster M 15 is one of the richest clusters in double mode RR Lyrae stars for which the observational baseline extends over nearly a century. In this paper we present a rigorous investigation of the changes in both the fundamental and first overtone frequencies of these stars.

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© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998
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