TDCOSMO XXII: Triaxiality and projection effects in time-delay cosmography

TL;DR

Time-delay cosmography hinges on breaking the mass-sheet degeneracy (MSD) to obtain an accurate $H_0$; this work quantifies how projection effects from triaxial mass distributions and the stellar tracer population bias both lensing and kinematic observables. By forward-modeling two populations—a triaxial TNG100 ETG sample and an axisymmetric SLACS-like set—and using Jeans Anisotropic Modeling (JAM) with axisymmetric multi-Gaussian expansions (MGE), the authors quantify projection biases in $H_0$ and demonstrate correction terms that reduce MSD-related uncertainties. They show that spherical JAM biases can reach 2–4% in the MSD and that a population-corrected axisymmetric approach reduces residual velocity-dispersion uncertainties to about 0–2.2% (0–4.4% in $H_0$), with spatially resolved kinematics further constraining intrinsic shapes. The results imply that accurate time-delay cosmography requires explicit modeling of projection and selection effects tied to intrinsic galaxy shapes, and that axisymmetric kinematic modeling is capable of robustly recovering the 3D kinematics even for moderately triaxial tracers, enhancing the precision and reliability of $H_0$ from strong lensing.

Abstract

Constraining the mass-sheet degeneracy (MSD) is crucial for improving the precision and accuracy of time-delay cosmography. Joint analyses of lensing and stellar kinematics are widely adopted to break the MSD. A 3D mass and stellar tracer population is required to accurately interpret the kinematics data. Our forward-modeling procedure aims at evaluating the projection effects of strong lensing and kinematics observables and to determine an optimal model assumption for the stellar kinematics analysis leading to an unbiased MSD and $H_0$. We numerically simulate the projection and selection effects for both a triaxial ETG sample from the IllustrisTNG 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 generate mock kinematics observables with axisymmetric Jeans Anisotropic Modeling (JAM) and assess kinematic recovery under different model assumptions. Using the triaxial sample, we quantify 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 using spatially resolved kinematic data which constrain the intrinsic shape. We also show that the random uncertainty in the velocity dispersion recovery using axisymmetric JAM for axisymmetric galaxies is at the level of < 0.24%, and the uncertainty using axisymmetric JAM for triaxial galaxies is at the level of < 0.17%.

Figures (14)

• Figure 1: Axisymmetric synthetic lens set in the $\sigma_v - R_e$ space. Black dots are the SLACS grade "A" lenses reported in 2008Bolton. The purple circles are drawn from the 2D KDE of the original data points.
• Figure 2: Distribution of the velocity dispersion on a random LoS $\sigma_\mathrm{rm}$, the effective radius $R_e$, the intrinsic axis ratios $p$ and $q$ and the triaxiality parameter $T$ for the selected ETG sample from them TNG100 simulation. Dashed line represent $T = 0.5$ in the $p-q$ space and in the 1D histogram of $T$, which we used to separate the full sample into the "oblate" subsample and the "prolate" subsample.
• Figure 3: Illustration of the projection effect in the strong lensing observables. We start with 3D density profiles of lens galaxies and project onto random directions 800 times. Dashed blue line marks the mean of $\theta_E$ under random projections. Orange solid line marks the $\theta_E$ of a spherical lens of the same mass. The projection effect in lensing is reflected by the scattering of $\theta_E$ around the spherical value.
• Figure 4: Projection effect of the TNG-100 ETG sample. Each ETG is projected 4 times onto random directions (blue and coral histograms). Each dot in the 2D histograms represents a projection. We apply a lensing cross-section weighting proportional to $\theta_E^2$, as represented with the green and purple histograms. We model the lensing selection on the projected ellipticity $e$, showing that for the oblate sample, lensing selection favors more elliptical galaxies in projection, while for the prolate sample, the lensing selection favors rounder galaxies. For the oblates, the viewing angle $\theta$ equals the inclination angle $i$ for pure oblates, and thus under lensing selection $\cos\theta$ is also inclined to the lower end, i.e., towards higher inclination angles and consequently higher ellipticities. The "bias" in the kinematics under the assumption of SIS lens models $b_\sigma = \sigma_\mathrm{SIS}/\sigma_\mathrm{rm} - 1$ is labeled with dashed lines. The mean bias $\langle b_\sigma \rangle$ for the oblate sample, indicated with blue dashed lines, is directly under the coral dashed line representing $\langle b_\sigma \rangle$ for the prolate sample and thus invisible from the plot.
• Figure 5: Corner plot of the kinematics and lensing observables for the mock data, generated by projecting the axisymmetric synthetic lens sample assuming random LoS. Each ETG is projected one time. We applied a lensing selection weighted by the cross-section area, $\propto \theta_E^2$, to illustrate the lensing selection effect on the projected ellipticity and the inclination angle.