Joint Semi-Analytic Multipole Priors from Galaxy Isophotes and Constraints from Lensed Arcs

Flux-ratio anomalies in quadruply imaged quasars are sensitive to the imprint of low-mass dark-matter haloes. The reliability of detection depends on the robustness of the smooth mass model. Optical surveys show that massive early-type galaxies similar to galaxy-scale gravitational lenses depart from perfect ellipticity, exhibiting $m=3$ and $m=4$ multipole distortions. We construct the semi-analytic, five-dimensional joint population prior for the $m=3$ and $m=4$ amplitude and orientation as well as the axis ratio of the deflector, calibrated on the sample of 840 SDSS E/S0 galaxies. The parameters are fitted via hierarchical Bayesian modeling, minimizing a joint Jensen-Shannon divergence between model and data. We use this prior to model the mass distribution of mock lenses with HST quality data with different multipole amplitudes. We find that we robustly measure the true multipole amplitudes and orientations. Compared to fits that use only the four point-image positions, adding the lensed host-galaxy arcs tightens the 68 % credible regions of multipole parameters by factors of 3-12 and reduces the predicted flux-ratio uncertainties by a mean factor of ~6. This analysis does not include substructure or a complex source, and thus can be considered an upper limit on the expected improvement. The combination of arc information and realistic multipole priors therefore yields an order-of-magnitude improvement in smooth mass model precision, paving the way for more robust measurements of dark-matter substructure.