Reconstructing the lensing mass in the Universe from photometric catalogue data

High precision cosmological distance measurements towards individual objects such as time delay gravitational lenses or Type Ia supernovae are affected by weak lensing perturbations by galaxies and groups along the line of sight. In time delay gravitational lenses, 'external convergence', κ_ext, can dominate the uncertainty in the inferred distances and hence cosmological parameters. In this paper we attempt to reconstruct κ_ext, due to line of sight structure, using a simple halo model. We use mock catalogues from the Millennium Simulation, and calibrate and compare our reconstructed P(κ_ext) to ray-traced κ_ext 'truth' values; taking into account realistic uncertainties on redshift and stellar masses. We find that the reconstruction of κ_ext provides an improvement in precision of ~50 per cent over galaxy number counts. We find that the lowest κ_ext lines of sight have the best constrained P(κ_ext). In anticipation of future samples with thousands of lenses, we find that selecting the third of the systems with the highest precision κ_ext estimates gives a subsample of unbiased time delay distance measurements with (on average) just 1 per cent uncertainty due to line of sight external convergence effects. Photometric data alone are sufficient to pre-select the best-constrained lines of sight, and can be done before investment in light-curve monitoring. Conversely, we show that selecting lines of sight with high external shear could, with the reconstruction model presented here, induce biases of up to 1 per cent in time delay distance. We find that a major potential source of systematic error is uncertainty in the high-mass end of the stellar mass-halo mass relation; this could introduce ~2 per cent biases on the time delay distance if completely ignored. We suggest areas for the improvement of this general analysis framework (including more sophisticated treatment of high-mass structures) that should allow yet more accurate cosmological inferences to be made.