Joint semi-analytic multipole priors from galaxy isophotes and constraints from lensed arcs

Abstract Flux-ratio anomalies in quadruply imaged quasars provide a sensitive probe of low-mass dark-matter haloes, but their interpretation requires a robust smooth lens model. Massive early-type galaxies exhibit small deviations from perfect ellipticity, described by m = 3 and m = 4 multipoles. We construct a five-dimensional joint population prior for these multipole amplitudes and orientations, conditioned on the axis ratio q and calibrated on 840 SDSS E/S0 galaxies. We then test its impact on mock lenses resembling HST-quality data under two multipole strength scenarios and four inference setups: point sources only with flat and joint multipole priors and point sources with arcs with flat and joint multipole priors. When only quasar point images are available, the joint prior reduces degeneracies and tightens the 68% credible intervals of a 3 / a and a 4 / a by factors of ∼9 and ∼6, and improves the predicted flux — ratio precision by factors of ∼2–6. Adding extended arcs yields a much larger gain — uncertainties shrink by ∼20× for flat priors and ∼8× for joint priors — while there is additional boost from the joint multipole prior (∼10%). The trends are consistent across both mild and strong multipole scenarios. These results show that arcs dominate the constraining power when available, but that a realistic joint multipole prior remains crucial for lenses without arcs. This regime will be common in upcoming wide-field surveys such as the Nancy Grace Roman Space Telescope and Rubin LSST, which will discover ≳ 10 5 new strong lenses, many lacking resolved arcs. Our framework provides a scalable path toward accurate macromodels for these survey discoveries.