1 Introduction

The Hyades cluster is the nearest, widely observed open cluster in our Galaxy. It is regarded as a fundamental object in calibrating the cosmic distance scale and in investigating the evolution of the chemical composition in the Galaxy. Therefore, the distance and the metal abundance of the Hyades have been widely discussed by many authors (references in Krolikowska [1992]). The Hyades cluster can also be used as a laboratory for the study of the internal structure of stars. The pulsational behaviour (frequency range of excited modes) of a star belonging to a cluster can give severe constraints on pulsation models. Moreover, a comparison of the pulsational behaviour of two pulsating stars in the same cluster (initial chemical composition and age etc. are equal) is an extremely powerful tool for obtaining such constraints.

The idea of investigating of a set of short period, low-amplitude $\delta$ Scuti stars in the Hyades was outlined by Géza Kovács in the late seventies at Konkoly Observatory. A Hyades member, $\theta^2$ (78) Tau, is one of the best-studied low-amplitude $\delta$ Scuti stars (Kovács & Paparó [1989]; Breger et al. [1989]). 57 Tau was, in principle, a selected target of this project but compact observations were obtained at Konkoly Observatory only from the late eighties onwards.

A frequency analysis of 57 Tau (similar to $\theta^2$ (78) Tau) has high astroseismological potential for three reasons: (i) it belongs to the Hyades, (ii) it has been suggested to be a member of a binary system, and (iii) it exhibits multi-modal pulsations. Three advantages exist when considering these two stars 1) their membership in the Hyades allows us to define a range of hydrogen and helium abundances, and age, which are fundamental properties for numerical calculations, 2) from the distance modulus to the cluster, the absolute luminosities of these stars can be determined and 3) the position of $\theta^2$ (78) Tau and 57 Tau on the Hyades colour-magnitude diagram are slightly different; $\theta^2$ (78) Tau is close to the turn-off point but 57 Tau is situated closer to the main sequence, and further from the turn-off point of the cluster.

The light variability of 57 Tau was first discovered by Millis ([1967]) and confirmed by Horan ([1979]). Its variability was disputed by Eggen ([1970]), however, the beats present in the light curve could be responsible for his claim that light from this star is constant. Finally, 57 Tau is regarded as a $\delta$ Scuti type variable, with an amplitude of $0\hbox{$.\!\!^{\rm m}$ }02$, in the catalogue of $\delta$ Scuti stars (Rodriguez et al. [1994]; Lopez de Coca et al. [1990]).

A primary analysis of the period ratio of the dominant modes in this star, based on 13 nights of Strömgren b data, has been published by McNamara ([1983]). The 0.785 period ratio suggests fundamental and first overtone radial pulsation, as is expected for a $\delta$ Scuti star situated near to the red edge of the instability strip. The amplitudes of $\Pi_0$ and $\Pi_1$ were reported to be exceptionally small being $0\hbox{$.\!\!^{\rm m}$ }003$ and $0\hbox{$.\!\!^{\rm m}$ }002$, respectively.

The Fourier analysis of two $\delta$ Scuti stars (57 Tau and 58 Tau) in the Hyades cluster is reported by Fu Jian-ning et al. ([1996]). Two frequencies (18.221 and 20.438 c/d) were obtained with similar small amplitudes (McNamara [1983]). However, the period ratio of the new analyses did not find a period ratio within the range expected for a radial pulsator.

The aim of this paper is to perform an overall analysis for all the available observation of 57 Tau. However, the quality of data, including their sparse distribution and the low signal, allowed only the investigation of a static pulsational arrangement supposed no changes in amplitudes and phases and ruled out any kind of investigation of resonance effects. If we see a search for amplitude variability as an important scientific goal, we could not achieve that level in our comprehensive analysis. Unpublished and new observations are discussed in Sect. 2. The mean light level variation is investigated in Sect. 3. The frequency analysis is considered in Sect. 4. The state of our present knowledge on 57 Tau is discussed in Sect. 5.