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We present a parametric strong lensing model of the cluster Abell 2218 basedon HST ACS data. We constrain the lens model using 8 previously known multiplyimaged systems, of which 7 have spectroscopically confirmed redshifts. Inaddition, we propose five candidate multiply imaged systems and estimate theirredshifts using our mass model. The model parameters are optimized in thesource plane by a bayesian Monte Carlo Markov Chain as implemented in the thepublicly available software Lenstool. We find rms=0."12 for the scatter of thesources in the source plane, which translates into rms=1."49 between thepredicted and measured image positions in the image plane. We find that theprojected mass distribution of Abell 2218 is bimodal, which is supported by ananalysis of the light distribution. We also find evidence for two structures invelocity space, separated by ~1000 km/s, corresponding to the two large scaledark matter clumps. We find that the lensing constraints can not be wellreproduced using only dark matter halos associated with the cluster galaxies,but that the dark matter is required to be smoothly distributed in large scalehalos. At 100" the enclosed projected mass is 3.8e14 solar masses. At thatradius, the large scale halos contribute ~85% of the mass. We find that themodel is not very sensitive to the fainter galaxy sized halos, unless theylocally perturb a given multiply imaged system. Therefore, dark galaxy sizedsubstructure can be reliably constrained only if it locally perturbs one of thesystems. In an appendix we give a self-contained description of the parametricprofile we use, the dual pseudo isothermal elliptical mass distribution (dPIE).This profile is a two component pseudo isothermal mass distribution (PIEMD)with both a core radii and a scale radii. (Abridged)

Where is the matter in the Merging Cluster Abell 2218?