Measuring the Distances to Quasars at High Redshifts with Strong Lensing

Abstract

Strongly lensed quasars with time-delay measurements are well known to provide the “time-delay distances” , and the angular diameter distances to the lens galaxies D L . These two kinds of distances give stringent constraints on cosmological parameters. In this work, we explore a different use of time-delay observables: under the assumption of a flat universe, strong lensing observations can accurately measure the angular diameter distances to the sources D S . The corresponding redshifts of the quasars may be up to z S  ∼ 4 according to the forecast. The high-redshift distances would sample the Hubble diagram between SNe Ia and the cosmic microwave background, model-independently providing direct information on the evolution of the nature of our universe, for example, the dark energy equation of state parameter w ( z ). We apply our method to the existing lensing system SDSS 1206+4332 and get at z S  = 1.789. We also make a forecast for the era of Large Synoptic Survey Telescope. The uncertainty of D S depends on the redshifts of the lens and the source, the uncertainties of D Δ t and D L , and the correlation between D Δ t and D L . Larger correlation would result in tighter D S determination.