TDCOSMO XXVI: Uniform lens modeling of eight doubly imaged quasars

We present the first uniform gravitational lens modeling analysis of eight doubly imaged quasars from multi-band observations with the Hubble Space Telescope. Previous time-delay cosmography analyses by the TDCOSMO Collaboration have primarily relied on quadruply imaged quasars, while doubly imaged systems, despite being more abundant, remain underutilized due to their fewer geometric constraints. Using an open-source $\texttt{Lenstronomy}$ framework, we reconstruct the lensing systems with a pipeline tailored for doubles. Comparing our results to the literature, the modeled Einstein radii agree at an average of 1.5$\sigma$, which is expected given data and modeling heterogeneity, while modeled image separations differ from Gaia DR2 measurements with an r.m.s of only 3.6 mas. We find a strong correlation between Fermat potential precision and the surface brightness of the spatially extended host arcs, establishing that arc surface brightness is the primary driver of mass model precision in doubly imaged systems. To further quantify the information contributed by the lensed arcs, we performed a conjugate point analysis that uses only the quasar image positions to constrain the lens mass profiles. The resulting posteriors are substantially broader than those from full image modeling, and a strong anti-correlation between mass parameter hypervolume and arc magnitude additionally confirms that arc brightness determines the degree to which the lens mass profile can be constrained in doubles. A hierarchical cosmographic analysis incorporating time-delay measurements and stellar kinematics to infer $\text{H}_0$ will be presented in a subsequent publication. The uniform pipeline and arc surface brightness trends established here will significantly accelerate the construction of time-delay cosmography samples from the large lens populations expected from LSST, Roman, and Euclid.