Michele Cappellari

Abstract:

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. 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 H_0. 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. 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 H_0), 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.

Abstract:

We reanalyzed spectra that were taken as part of the SL2S lens galaxy survey with the goal to obtain the stellar velocity dispersion with a precision and accuracy sufficient for time-delay cosmography. In order to achieve this goal, we imposed stringent cuts on the signal-to-noise ratio (S/N), and employed recently developed methods to mitigate and quantify residual systematic errors that are transferred from template libraries and fitting process. We also quantified the covariance across the sample. For galaxy spectra with S/N $>20/$Å, our new measurements have an average random uncertainty of 3-4%, an average systematic uncertainty of 2%, and a covariance across the sample of 1%. We find a negligible covariance between spectra taken with different instruments. The systematic uncertainty and covariance need to be included when the sample is used as an external dataset in time-delay cosmography. We revisited empirical scaling relations of lens galaxies based on the improved kinematics. We show that the SL2S sample, the TDCOSMO time-delay lens sample, and the lower-redshift SLACS sample follow the same correlation of the effective radius, stellar velocity dispersion, and lensing mass, known as the lensing-mass fundamental plane, as the previously derived correlation that assumed isothermal mass profiles for the deflectors. We also derived for the first time the lensing-mass fundamental plane assuming free power-law mass density profiles, and we show that the three samples also follow the same correlation. This is consistent with a scenario in which massive galaxies evolve by growing their radii and mass, but stay within the plane.