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In order to use strong gravitational lens time delays to measure precise and accurate cosmological parameters the effects of mass along the line of sight must be taken into account. We present a method to achieve this by constraining the probability distribution function of the effective line-of-sight convergence κext. The method is based on matching the observed overdensity in the weighted number of galaxies to that found in mock catalogs with κext obtained by ray-tracing through structure formation simulations. We explore weighting schemes based on projected distance, mass, luminosity, and redshift. This additional information reduces the uncertainty of κext from σκ ~ 0.06 to ~0.04 for very overdense LOSs like that of the system B1608+656. For more common LOSs, σκ is reduced to lsim0.03, corresponding to an uncertainty of is reduced to lsim0.03, corresponding to an uncertainty of ext almost as well as with spectroscopic redshifts. As an illustration, we apply our method to the system B1608+656. Our most reliable κext estimator gives σκ = 0.047 down from 0.065 using only galaxy counts. Although deeper multiband observations of the field of B1608+656 are necessary to obtain a more precise estimate, we conclude that griK photometry, in addition to spectroscopy to characterize the immediate environment, is an effective way to increase the precision of time-delay cosmography.
Greene et al. (Fri,) studied this question.