XXII. Triaxiality and projection effects in time-delay cosmography

Context. Constraining the mass-sheet degeneracy (MSD) is crucial for improving the precision and accuracy of time-delay cosmography. Joint analyses based on lensing and stellar kinematics have been widely adopted to break the MSD. A three-dimensional (3D) mass and stellar tracer population is required to accurately interpret the kinematics data. Aims. Our forward-modeling procedure is aimed at evaluating the projection effects using strong lensing and kinematics observables and to determine an optimal model assumption for the stellar kinematics analysis leading to an unbiased interpretation of the MSD and H₀. Methods. We numerically simulated the projection and selection effects for both a triaxial early-type galaxy (ETG) sample from the TNG100 simulation and an axisymmetric sample that matches the properties of slow-rotator galaxies representative of the strong lens galaxy population. Using the axisymmetric sample, we generated mock kinematics observables with spherically aligned axisymmetric Jeans anisotropic modeling (JAM) and assessed the kinematic recovery under different model assumptions. Using the triaxial sample, we quantified the random uncertainty introduced by modeling triaxial galaxies with axisymmetric JAM. Results. We show that spherical JAM analysis of spatially unresolved kinematic data introduces a bias of up to 2–4% (depending on the intrinsic shape of the lens) in the inferred MSD. Our model largely corrects this bias, resulting in a residual random uncertainty in the range of 0–2.2% in the stellar velocity dispersion (0–4.4% in H₀), depending on the projected ellipticity and the anisotropy of the stellar orbits. This residual uncertainty can be further mitigated by the use of spatially resolved kinematic data, which constrain the intrinsic axis ratio. We also show that the random uncertainty in the kinematics recovery using axisymmetric JAM for axisymmetric galaxies is at the level of 0.24% in the velocity dispersion, and the uncertainty using axisymmetric JAM for triaxial galaxies is at the level of 0.17% in the velocity dispersion.