Improving the precision of time-delay cosmography with observations of galaxies along the line of sight

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 κ_ext. The method is based on matching the observed overdensity in the weighted number of galaxies to that found in mock catalogs with κ_ext 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 κ_ext from σ_κ ∼ 0.06 to ∼0.04 for very overdense LOSs like that of the system B1608+656. For more common LOSs, σ_κ is reduced to ≲0.03, corresponding to an uncertainty of ≲ 3% on distance. This uncertainty has comparable effects on cosmological parameters to that arising from the mass model of the deflector and its immediate environment. Photometric redshifts based on g, r, i and K photometries are sufficient to constrain κ_ext almost as well as with spectroscopic redshifts. As an illustration, we apply our method to the system B1608+656. Our most reliable κ_ext estimator gives σ_κ = 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.