Cross-correlation of galaxies and galaxy clusters in the Sloan Digital Sky Survey and the importance of non-Poissonian shot noise

We present measurements of angular cross power spectra between galaxies and opticallyselected galaxy clusters in the final photometric sample of the Sloan Digital Sky Survey (SDSS). We measure the autocorrelations and cross correlations between galaxy and cluster samples, from which we extract the effective biases and study the shot noise properties. We model the non-Poissonian shot noise by introducing an effective number density of tracers and fit for this quantity. We find that we can only describe the cross-correlation of galaxies and galaxy clusters, as well as the autocorrelation of galaxy clusters, on the relevant scales using a non-Poissonian shot noise contribution. The values of effective bias we finally measure for a volume-limited sample are bcc= 4.09±0.47 for the cluster autocorrelation and bgc = 2.15±0.09 for the galaxy-cluster cross-correlation. We find that these results are consistent with expectations from the autocorrelations of galaxies and clusters and are in good agreement with previous studies. The main result is two-fold: first we provide a measurement of the cross-correlation of galaxies and clusters, which can be used for further cosmological analysis; and secondly we describe an effective treatment of the shot noise.