Hubble Constant Measurement from Three Large-Separation Quasars Strongly Lensed by Galaxy Clusters

Abstract

Tension between cosmic microwave background-based and distance ladder-based determinations of the Hubble constant ${\rm H}_{\rm 0}$ motivates pursuit of independent methods that are not subject to the same systematic effects. A promising alternative, proposed by Refsdal in 1964, relies on the inverse scaling of ${\rm H}_{\rm 0}$ with the delay between the arrival times of at least two images of a strongly-lensed variable source such as a quasar. To date, Refsdal's method has mostly been applied to quasars lensed by individual galaxies rather than by galaxy clusters. Using the three quasars strongly lensed by galaxy clusters (SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745) that have both multiband Hubble Space Telescope data and published time delay measurements, we derive ${\rm H}_{\rm 0}$, accounting for the systematic and statistical sources of uncertainty. While a single time delay measurement does not yield a well-constrained ${\rm H}_{\rm 0}$ value, analyzing the systems together tightens the constraint. Combining the six time delays measured in the three cluster-lensed quasars gives ${\rm H}_{\rm 0}$ = 74.1 $\pm$ 8.0 km s$^{-1}$ Mpc$^{-1}$. To reach 1$\%$ uncertainty in ${\rm H}_{\rm 0}$, we estimate that a sample size of order of 620 time delay measurements of similar quality as those from SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745 would be needed. Improving the lens modeling uncertainties by a factor of two and a half may reduce the needed sample size to 100 time delays, potentially reachable in the next decade.