Strong lensing robust radius for low-mass haloes equals weighted geometric mean of arc pixels

The arXiv preprint by Tajalli et al. derives the pivot radius analytically for any two-parameter spherical profile by requiring that the Fisher information matrix element between enclosed mass and local slope vanishes. This occurs at the weighted geometric mean of pixel distances, where weights incorporate the perturber deflection angle, macro magnification, and source brightness gradient. The leading-order result holds for both subhaloes and line-of-sight haloes and directly explains why earlier empirical studies found consistent mass measurements inside a characteristic scale.

The radial leverage of the arc and the signal-to-noise ratio of high-magnification pixels set the residual uncertainty on the local slope once mass is fixed at the pivot. Data sets with arcs spanning less than 0.3 dex in radius retain strong mass-slope degeneracy even at high SNR, while wider arcs decorrelate the parameters at the 10-15 percent level. This matches the information-content patterns seen in earlier analyses of SLACS and BELLS lenses.

Future surveys such as Euclid and LSST will deliver thousands of new galaxy-galaxy lenses; applying the pivot-radius formalism will allow uniform mass-function constraints across heterogeneous data qualities. The main limitation remains the assumption of spherical symmetry; triaxial or substructured perturbers will shift the effective pivot by an amount comparable to the log-width of the arc.

Validation on hydrodynamical simulations with realistic source structure is required before the method can be applied to the first statistical samples expected in 2027.