Spectral Clustering for Optical Confirmation and Redshift Estimation of
  X-ray Selected Galaxy Cluster Candidates in the SDSS Stripe 82
  We develop a galaxy cluster finding algorithm based on spectral clustering
technique to identify optical counterparts and estimate optical redshifts for
X-ray selected cluster candidates. As an application, we run our algorithm on a
sample of X-ray cluster candidates selected from the third XMM-Newton
serendipitous source catalog (3XMM-DR5) that are located in the Stripe 82 of
the Sloan Digital Sky Survey (SDSS). Our method works on galaxies described in
the color-magnitude feature space. We begin by examining 45 galaxy clusters
with published spectroscopic redshifts in the range of 0.1 to 0.8 with a median
of 0.36. As a result, we are able to identify their optical counterparts and
estimate their photometric redshifts, which have a typical accuracy of 0.025
and agree with the published ones. Then, we investigate another 40 X-ray
cluster candidates (from the same cluster survey) with no redshift information
in the literature and found that 12 candidates are considered as galaxy
clusters in the redshift range from 0.29 to 0.76 with a median of 0.57. These
systems are newly discovered clusters in X-rays and optical data. Among them 7
clusters have spectroscopic redshifts for at least one member galaxy.
