Anisotropy and tracer-profile assumptions in aperture-based strong-lens dynamics: Conditional inference from supernova distance ratios and unresolved stellar kinematics

Abstract

Single-aperture stellar kinematics jointly constrain the mass distribution, tracer light profile, and velocity anisotropy. Their coupling affects the interpretation of an inferred anisotropy. We quantify how tracer-profile assumptions and data treatment affect common-anisotropy comparisons and inferred mass-density slopes in a compiled galaxy-scale lens sample. We analyse 107 lenses using distinct \pantheon\ supernova counterparts, spatial flatness, distance duality, and the full supernova covariance. We compare the individual-slope power-law tracer with Hernquist and Sérsic profiles using measured effective radii. Numerical Jeans solutions, likelihood comparisons, posterior distributions, and controlled recovery experiments quantify the effects of tracer representation. The power-law fixed-minus-free Bayesian information criterion differences are 6.74 for isotropy and 41.51 for fixed $\beta =0.18$, compared with $-3.89$ and $-2.26$ for Hernquist and $-4.67$ and $-4.30$ for Sérsic $n=4$. The preference also changes with Sérsic index. Removing 12 systems with linearised distance-ratio uncertainty above 20\% reduces the power-law isotropy comparison to 2.51. In isotropic Sérsic $n=4$ and Hernquist simulations, power-law fits yield $\Delta {\mathrm{BIC}}_0>6$ in 60.0\% and 50.0\% of realisations, respectively, compared with 0.5\% and 1.0\% for matched-tracer fits.} {The preference for a common free anisotropy parameter depends on the tracer representation and sample composition. Controlled recovery identifies tracer mismatch as one mechanism that can generate this preference within the adopted aperture models. Physical interpretation requires joint treatment of photometry, distance uncertainties, and kinematic weighting.

arXiv comment18 pages, 13 figures; revised version submitted to ApJ