Cosmography from two-image lens systems: overcoming the lens profile slope degeneracy

TL;DR

This paper demonstrates that high-resolution imaging of extended source images in two-image gravitational lens systems can break the radial profile slope degeneracy, enabling precise measurements of cosmological distances and improving cosmological constraints.

Contribution

It introduces a method to overcome the lens profile slope degeneracy in two-image lens systems using extended source images, enhancing the utility of such systems for cosmology.

Findings

Extended source images break the radial slope degeneracy.

Two-image systems can measure the time-delay distance with a few percent accuracy.

This approach can increase the number of useful lens systems by about six times.

Abstract

The time delays between the multiple images of a strong lens system, together with a model of the lens mass distribution, allow a one-step measurement of a cosmological distance, namely, the "time-delay distance" of the lens (D_dt) that encodes cosmological information. The time-delay distance depends sensitively on the radial profile slope of the lens mass distribution; consequently, the lens slope must be accurately constrained for cosmological studies. We show that the slope cannot be constrained in two-image systems with single-component compact sources, whereas it can be constrained in systems with two-component sources provided the separation between the image components can be measured with milliarcsecond precisions, which is not feasible in most systems. In contrast, we demonstrate that spatially extended images of the source galaxy in two-image systems break the radial slope degeneracy and allow D_dt to be measured with uncertainties of a few percent. Deep and high-resolution imaging of the lens systems are needed to reveal the extended arcs, and stable point spread functions are required for our lens modelling technique. Two-image systems, no longer plagued by the radial profile slope degeneracy, would augment the sample of useful time-delay lenses by a factor of ~6, providing substantial advances for cosmological studies.