5 Conclusion

We have developed an objective and automatic cluster-finding method. It is a variant of P96 method with some improvements. The method uses positions and apparent magnitudes of galaxies simultaneously, and detects clusters by fitting artificial cluster models which contain redshift and richness as free parameters by maximizing the likelihood function. Therefore redshift and richness of clusters are estimated as byproducts of detection. Good accuracies in the estimates of cluster's position, redshift, and richness are confirmed by a number of Monte Carlo simulations. For clusters at z=0.20 and as rich as the Coma cluster, errors in estimating redshift and richness are $\Delta z\sim$0.02 and $\Delta N\sim$360 (12%), respectively. Spurious detection rate of this method is also studied with Monte Carlo simulations and is shown to be less than $\sim$10% of that by conventional techniques using only surface density of galaxies. A cluster survey in the NGP region is performed as a test with real data. Despite the poor quality of the data, two known real clusters are successfully detected.

At present, it is quite difficult to make a deep X-ray survey over a wide area on the sky and to build a large catalog of, especially, distant (z>0.3) clusters though some attempts are being made such as SHARC (Collins et al. 1997; Burke et al. 1997), RDCS (Rosati et al. 1998), RIXOS (Castander et al. 1995), and WARPS (Scharf et al. 1997). Thus optical search is almost the only realistic way to find a large number of distant clusters. Objective and automated methods for finding clusters from optical data must be indispensable tools in the near future for quickly constructing large, statistically complete cluster catalogs from the data covering an extremely wide area, for example, those from SDSS (Gunn & Weinberg 1995; Okamura 1995), or for compiling catalogs of extremely distant clusters up to z>1 from deep imaging data with $\rm 8{-}10\,m$ class telescopes.

Acknowledgements

The authors would like to thank Naoki Yasuda and Masafumi Yagi for valuable comments and suggestions in the early stage of this work and Maki Sekiguchi for the Mosaic CCD camera development and help in observation. WK is grateful to Nobunari Kashikawa, Toru Yamada, and Masayuki Akiyama for their help in reducing the NGP data.