Measuring angular diameter distances of strong gravitational lenses

Understand

The distance-redshift relation plays a fundamental role in constraining cosmological models.

• In this paper, we show that measurements of positions and time delays of strongly lensed images of a background galaxy, as well as those of the velocity dispersion and mass profile of a lens galaxy, can be combined to extract the angular diameter distance of the lens galaxy.
• Physically, as the velocity dispersion and the time delay give a gravitational potential ($GM/r$) and a mass ($GM$) of the lens, respectively, dividing them gives a physical size ($r$) of the lens.
• Comparing the physical size with the image positions of a lensed galaxy gives the angular diameter distance to the lens.