1 Introduction

The colour-magnitude diagram (CMD) of a star cluster is an important tool to obtain the information on distance and age of the cluster and interstellar extinction in the direction of cluster. Accurate deep photometric observations down to V > 20 mag are necessary for such studies and the same is presented here for NGC 7790. The northern galactic open cluster NGC 7790 = C2355+609  $(l= 116\hbox{$.\!\!^\circ$ }6, b = -1\hbox{$.\!\!^\circ$ }0)$ is near the Perseus spiral arm. It has been classified as Trumpler Class II2m by Lyngå (1987) and as an intermediate age star cluster by Mermilliod (1981). The cluster radius is 2 $\hbox {$.\mkern -4mu^\prime $ }$5 and it has the unique characteristic of containing three Cepheids namely CEa Cas, CEb Cas and CF Cas (see Kraft 1958; Sandage 1958; Schmidt 1981; Pedreros et al. 1984). UBV photoelectric photometry of 33 stars and photographic photometry of 100 stars were obtained by Sandage (1958). He estimated the distance of the cluster to be $3630\pm250$ pc. Pedreros et al. (1984) carried out UBV photographic photometry down to $V \sim$ 19 mag and derived a mean value of $E(B-V)=0.64\pm0.05$ mag and a true distance modulus of $(m-M)_0=12.3\pm0.2$ mag. Romeo et al. (1989) obtained BVRI CCD photometry and they derived the value of $E(B-V) = 0.54 \pm 0.04$ mag; $(m-M)_0 = 12.65 \pm 0.15$ mag and age of $50 \pm 15$ Myr using classical models and $100 \pm 20$ Myr adopting models with overshooting of the convective core. Iyeshima et al. (1994) obtained BVR CCD photometric observations, while Phelps & Janes (1994) obtained UBV CCD data for this cluster. Frolov (1977) determined relative proper motions of stars of the cluster region in an area of $1^{\circ} \times 1^{\circ}$ with the center at $\rm\alpha=23^h 54^m 12^s, \delta=+60^{\circ} 57'$ (1950.0) and found 60 stars to be members of NGC 7790 down to a limiting magnitude B = 16.5 mag. Membership probabilities were also computed by Zhao et al. (1984) using the proper motion measurements given by Ishmukamedov (1966). However, due to relatively large distance of the cluster combined with the limited precision of the data, these proper motion data are not very useful to separate cluster members from the field-stars. In spite of a number of photoelectric, photographic and CCD photometric studies of the cluster, its parameters are not well determined as they have a range of values, e.g. E(B-V)=0.5 to 0.7 mag and distance = 2.4 to 3.6 Kpc (see Tables 2 and 3 in Romeo et al. 1989). In this paper we present a new deep BVI CCD photometric observations of the stars in the field of NGC 7790 and use them along with existing photometric, spectroscopic, proper motion and Space Telescope Science Institute digitized sky survey (DSS) data to derive the best determinations of radius, distance, interstellar extinction and age of the cluster NGC 7790 which in turn allow a more precise determination of the fundamental parameters of the Cepheids such as the zero-point of the period luminosity/age relations. The observations, data reductions and comparison of various photometries are given in the next two sections. The field-star contamination, interstellar extinction, other photometric results and their implications for the membership of the Cepheids are described in the subsequent sections of this paper.

Figure 1: Identification map of the NGC 7790 region. The (X,Y) coordinates are in pixel units and one pixel corresponds to 0 $\hbox{$.\!\!^{\prime\prime}$ }$74 on the sky. North and East directions are marked. Filled circles of 9 sizes (each corresponding to one magnitude range in V) are used to represent brightness of the stars. Largest and smallest sizes denote stars in the brightest and faintest magnitude range of V = 11 to 12 and 19 to 20 respectively. Open circle denotes the cluster radius of 3 $\hbox {$.\mkern -4mu^\prime $ }$7 with Sandage (1958) star E at the center. The region imaged by us is shown by dotted line