# X-ray Galaxy Clusters in NoSOCS: Substructure and the Correlation of Optical and X-ray Properties

### Abstract

We present a comparison of optical and X-ray properties of galaxy clusters in the northern sky. We determine the recovery rate of X-ray detected clusters in the optical as a function of richness, redshift and X-ray luminosity, showing that the missed clusters are typically low contrast systems when observed optically. We employ four different statistical tests to test for the presence of substructure using optical two-dimensional data, finding that approximately 35% of the clusters show strong signs of substructure. However, the results are test-dependent, with variations also due to the magnitude range and radius utilized.We have also performed a comparison of X-ray luminosity and temperature with optical galaxy counts (richness). We find that the slope and scatter of the relations between richness and the X-ray properties are heavily dependent on the density contrast of the clusters. The selection of substructure-free systems does not improve the correlation between X-ray luminosity and richness, but this comparison also shows much larger scatter than one obtained using the X-ray temperature. In the latter case, the sample is significantly reduced because temperature measurements are available only for the most massive (and thus high contrast) systems. However, the comparison between temperature and richness is very sensitive to the exclusion of clusters showing signs of substructure. The correlation of X-ray luminosity and richness is based on the largest sample to date ($sim$ 750 clusters), while tests involving temperature use a similar number of objects as previous works ($lsim$100). The results presented here are in good agreement with existing literature.

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