2009MNRAS.397..341L

In this article, we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available Advanced Camera for Surveys images. We find masses of 2.5x10¹³ and 6.1x10¹³M_☉ within a radius of 60 and 110 kpc, respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with r_s= 58⁺²¹_–13 arcsec and c_vir = 3.91±0.74. The orientation of the elliptical NFW profile closely follows the orientation of the central cluster galaxy and the overall distribution of cluster members.