7 Discussions and conclusions

Using all available photoelectric and CCD multi-colour UBVRI photometric data including the present deep CCD BVI photometry, the best set of magnitudes and colours are calculated for the stars of NGC 7790 region. In the absence of kinematical data for most of stars fainter than $V \sim 13$, it is difficult to separate unambiguously cluster members from the field-stars only on the basis of available photometric observations. The radial stellar density profile indicates that the cluster radius is $3\hbox{$.\mkern-4mu^\prime$ }7 \pm 0.2$. Using stars located well within a cluster radius, we determine the most reliable values of E(B-V) and the true distance modulus as $0.51\pm0.03$ and $12.6\pm0.15$ mag respectively. This value of distance agrees very well with that determined from Cepheids using the PLR given by Sandage et al. (1999). The interstellar reddening across the cluster region is uniform and normal. The cluster contains a well defined MS with a gap on the evolving part of the MS. It also contains two blue stragglers, a few bright red giants and three Cepheids, all having proper motion membership. The upper MS of the cluster shows evolutionary effects. The spectroscopic data of a few stars on the brighter part of the MS indicate that they are of B spectral type and of IV luminosity class. Their location in the M_v, (B-V)₀ diagram also indicates that they are in the sub-giant phase of stars, just evolving off the MS. Both the bright MS stars and the Cepheid variables are fitted well with the Z=0.008metallicity isochrone, rather than the solar metallicity isochrones. An age of 120$\,\pm\,$20 Myr has been derived in this way for the NGC 7790. Both age and distance estimates for the Cepheid variables are consistent with the present determination of reddening, distance and age to the cluster NGC 7790. This supports the cluster membership of the Cepheids.

Acknowledgements

We gratefully acknowledge the useful comments given by the referees F. Fusi Pecci and J.C. Mermilliod, which improved the paper significantly. This research has made use of the cluster database prepared by J.C. Mermilliod.