The Impact of Orbital Anisotropy Assumptions in Lensing-Dynamics Modeling

TL;DR

This study quantifies how assumptions about stellar orbital anisotropy impact joint lensing-dynamics inferences for massive early-type galaxies. By constructing self-consistent mock datasets from IllustrisTNG (TNG100) ETGs at z = 0.2, 0.5, and 0.7, and applying a logistic anisotropy profile to mirror real stellar orbits, the authors test isotropic, constant-β, and Osipkov-Merritt anisotropy models within a two-component (stars + gNFW dark matter) mass framework. They find that total stellar mass and central dark matter fraction biases are small (roughly Δ log M*/M⊙ ≈ -0.03 dex and Δf_dm ≈ a few percent), while the dark matter inner slope is modestly over-predicted (Δη_dm ≈ +0.15). The biases from anisotropy assumptions are generally smaller than those arising from radial gradients in the stellar mass-to-light ratio, and the inferred total density slope remains robust at the population level, supporting the reliability of common anisotropy prescriptions in lensing-dynamics analyses. Overall, the work clarifies that orbital anisotropy priors are a secondary source of systematic error compared to M*/L gradients in stellar-dark matter decomposition.

Abstract

We investigate potential systematic biases introduced by assumptions regarding stellar orbital anisotropy in joint lensing-dynamics modeling. Our study employs the massive early-type galaxies from the TNG100 simulation at redshifts z = 0.2, 0.5, and 0.7. Based on the simulated galaxies, we generate a self-consistent mock dataset containing both lensing and stellar kinematic observables. This is achieved through taking the potential composed of both dark matter and baryons of the simulated galaxies, plus the radial variation of the stellar orbit anisotropy depicted by a logistic function. By integrating constraints from both lensing and stellar kinematics, we separate the contributions of stars and dark matter inside the galaxies. Under three commonly adopted stellar anisotropy assumptions (isotropic orbits, constant anisotropy, and the Osipkov-Merritt profile), the model inferences suggest that the systematic biases in the total stellar mass and central dark matter fraction are not significant. Specifically, the total stellar mass on average is underestimated by less than $0.03\pm0.10$ $\rm dex$ while the dark matter fraction experiences only a statistically insignificant increase of less than $2\%\pm10\%$ at the population level. The dark matter inner density slope in our tests is over-predicted by $0.15\pm0.2$. Additionally, these lacks of significant biases are insensitive to the discrepancies between the assumed anisotropy in modeling and the ground truth orbital anisotropy of mock sample. Our results suggest that conventional assumptions regarding orbital anisotropy, such as an isotropic profile or the Osipkov-Merritt model, would not introduce a significant systematic bias when inferring galaxy mass density distribution at the population level.

Figures (10)

• Figure 1: The stacked stellar orbit anisotropy profile of the massive early-type galaxies in TNG100. The purple curve shows the mean anisotropy profile, with the shaded region indicating the $1\sigma$ level scatter across the sample. For comparison, the dashed curve in light green is the Osipkov-Merritt model with a transition radius of $1.6R_{\rm eff}$ (Shajib_2021_Lensing_NFWHalo). The stacked mock anisotropy and its $1\sigma$ scatter from the logistic fitting (see Sec. \ref{['sec:2.2.3']}) are depicted by the blue solid curve and the shaded area, respectively.
• Figure 2: The comparison of the mock stellar kinematics synthesized from smoothed mass profiles and that directly obtained from the motion of stellar particles. Left: velocity dispersion integrated along the line-of-sight within $0.5R_{\rm eff}$. Each data point represents one individual simulated galaxy. The y- and x-axis are the results extracted from the kinematics synthesized from mock mass profiles and those directly obtained from the motion of stellar particles, respectively. The dashed line is $y=x$. Mid: the comparison of averaged orbital anisotropy within effective radius $R_{\rm eff}$. Right: the comparison of the radial gradient of orbital anisotropy defined as the difference between its averaged value within $2R_{\rm eff}$ and $0.5R_{\rm eff}$. The detailed formulations for these averaged anisotropies, such as $\beta_{\rm e}^{\rm (mock)}$ can be found in Appendix \ref{['sec:mock_anisotropy']}.
• Figure 3: The biases of model parameters under the isotropic orbit assumption. The y-axes display the discrepancies between parameter values estimated by our joint lensing-dynamics model and their true values, so the horizontal dotted line indicates the unbiased results. The quantities appearing in the x-axes $\beta^{(\rm mock)}_{\rm 2e}$, $\beta^{(\rm mock)}_{\rm e}$, $\beta^{(\rm mock)}_{\rm e/2}$ are the averaged anisotropy within $2R_{\rm eff}, R_{\rm eff}, 0.5R_{\rm eff}$ of our mock stellar kinematics (see Appendix \ref{['sec:mock_anisotropy']}). The purple points denote galaxies with nearly isotropic orbits, while the blue points represent anisotropic systems. Here, the isotropic and anisotropic systems are classified according to the mock logistic anisotropy profile (see Sec. \ref{['sec:4.1']}). The dark red dashed line is the best-fit linear function depicting the dependencies of the systematic biases on the anisotropy (top panels) as well as its radial gradient (bottom panels). The shaded area shows the $1\sigma$ error of this linear fit.
• Figure 4: This is an example from the results of our joint lensing-dynamics modeling under the isotropic orbit assumption. This galaxy is drawn from the snapshot $z = 0.2$ (subfind ID: 230767). The three top panels present the combined posterior probability distributions where the contours represent $68.27\%$, $95.45\%$ and $99.73\%$ confidence levels. The dashed cross denotes the best-fit value of the parameter. And the bottom large panel shows the reconstruction for the density profile obtained from our best-fit model parameters. In the bottom panel, the pink, blue and purple points are the true total, stellar and dark matter density profile, respectively. The density profiles from our best-fit model are color-coded identically for comparison. We provide the inferred values of three model parameters followed by their true values (in bracket) directly derived from the simulation. The arrow indicates the position of the Einstein radius. We also list the Einstein radius, size, mock anisotropy as well as its gradient in the top-right corner.
• Figure 5: The statistical results of the lensing-dynamics modeling when we apply the anisotropy as a constant free parameter. Following the structure of Fig. \ref{['fig:results_iso']}, we present the bias of the individual mass distribution parameter as the y-axis in the associated panel. And the x-axis of the bottom panel is still the anisotropy gradient of our mock galaxy. But the x-axis of the top panel represents the deviation between the model-predicted anisotropy parameter $\beta^{\rm (mod)}$ and the averaged anisotropy within $2R_{\rm eff}$. The purple and blue points are the galaxy with a constant anisotropy and other systems having a significant anisotropy gradient, respectively (see Sec. \ref{['sec:4.2']}). The vertical dotted lines in the top panels denote the position of unbiased inference on the anisotropy itself.