Hubble Space Telescope observations of the gravitationally lensed Cloverleaf broad absorption line QSO H1413+1143: Modeling the lens

We investigate gravitational lens models for the quadruply lensed Cloverlea f broad absorption line QSO H1413+1143 based on the Hubble Space Telescope (HST) WFPC/WFPC2 astrometric and photometric data of the system by Turnshek et al, and the HST NICMOS-2 data by Falco et al. The accurate image positi ons and the dust-extinction-corrected relative amplifications, along with a possible detection of the lensing galaxy in the infrared, permit more accu rate lens models than were previously possible. While more recent models ar e qualitatively consistent with the HST data, none of the previous models c onsidered the dust-extinction-corrected relative amplifications of the imag e components. We use the power-law elliptical mass model to fit the HST dat a. We find that a single elliptical galaxy perturbed by an external shear c an fit the image positions within the observational uncertainties; however, the predicted relative magnifications are only roughly consistent with the observational relative amplifications. We find that a primary galaxy combi ned with a secondary galaxy in the vicinity of the Cloverleaf or a cluster centered (south-) west of the Cloverleaf can fit both the image positions a nd relative amplifications within the observational uncertainties. We discu ss future observations that could be used to test and/or further constrain lens models of the Cloverleaf.