A simultaneous maximum likelihood approach for galaxy-galaxy lensing and cluster lens reconstruction

In a previous paper we investigated means for constraining the mass distribution of cluster galaxies by weak lensing. We concluded that a comprehensive method should treat the lensing effects of individual cluster galaxies and those resulting from a general cluster component simultaneously. To this end we now develop a non-parametric maximum likelihood cluster reconstruction algorithm that can implicitly take into account the presence of cluster galaxies. The method includes an entropy-like regularization prescription and directly uses the ellipticities of individual source galaxy images as observables rather than relying on an averaged ellipticity field. The mass distribution of cluster galaxies is described by parametrized models. For each set of galaxy parameters the cluster reconstruction algorithm allows us to determine the best representation of the global underlying cluster component that is consistent with the presence of the cluster galaxies and the observed image ellipticities of background galaxies. Tests with simulations yield convincing and robust results. We apply the method to a WFPC2 image of the cluster C10939 + 4713, and obtain a detection of the lensing effects of luminous elliptical cluster galaxies. We consider this application as a successful test of our technique. However, the small size of the image we analysed does not yet allow us to draw strong conclusions regarding the mass distribution of cluster,galaxies.