Galaxy-cluster associations from gravitational lensing

We investigate the associations between background galaxies and foreground clusters of galaxies due to the effect of gravitational lensing by clusters of galaxies. Similar to the well-known quasar-galaxy ones, these associations depend sensitively on the shape of galaxy number-magnitude or number-flux relation, and both positive and ``negative" associations are found to be possible, depending on the limiting magnitude and/or the flux threshold in the surveys. We calculate the enhancement factors assuming a singular isothermal sphere model for clusters of galaxies and a pointlike model for background sources selected in three different wavelengths, $B$, $K$ and radio. Our results show that $K-$ selected galaxies might constitute the best sample to test the ``negative" associations while it is unlikely that one can actually observe any association for blue galaxies. We also point out that bright radio sources ($S>1$ Jy) can provide strong positive associations, which may have been already detected in 3CR sample.