Constraints on the inner regions of lensing galaxies from central images using a recent AGN offset distribution

In gravitational lensing, central images in quads can serve as a powerful probe of the inner regions of lens galaxies. The presence of an offset central supermassive black hole (SMBH) has the potential to distort the time-delay surface in a way such that three central images form: a strongly demagnified image near the SMBH, and two less demagnified (and potentially observable) images at a central maximum and saddle point. Using a quad-lens macro-model, we simulate the constraints that could be placed on various lens galaxy parameters based on their central images’ probability of detection or non-detection. Informed by a recent low-redshift distribution of off-nucleus active galactic nucleus, we utilize Bayesian inference to constrain the mean SMBH off-nucleus distance and galactic core radius for a sample of six quads. In general, we find that a detection of the central image in any quad would favour larger SMBH off-nucleus distances and galaxy core sizes. Assuming a linear relationship between core radii and velocity dispersion r_c = bσ, these results similarly imply strong constraints on b, where the likely case of a central image non-detection in each quad constrains b to 3.11^{+2. 72}_-2.26× 10⁻⁴ kpc km⁻¹ s. Our results show that tight constraints on lens galaxy parameters can be made regardless of a detection or non-detection of a central image. Therefore, we recommend observational searches for the central image, possibly using our suggested novel detection technique in ultraviolet filters, to formalize stronger constraints on lens galaxy parameters.