The Stellar IMF and Dark Matter Halo of ESO0286: Constraints from Strong Lensing and Dynamics

Abstract

The internal mass structure of elliptical galaxies offers critical insights into galaxy formation, yet disentangling stellar mass from dark matter and determining the stellar initial mass function (IMF) remains challenging. We present a detailed analysis of ESO0286-G022 ($z=0.0312$), a rare nearby strong-lens system with a fast-rotating elliptical galaxy, combining high-resolution Hubble Space Telescope (HST) imaging with VLT/MUSE integral-field stellar kinematics. We construct axisymmetric and triaxial Schwarzschild orbit-superposition models to reconstruct its intrinsic shape and mass distribution. Despite being a fast rotator, ESO0286 exhibits clear kinematic signatures of intrinsic triaxiality, characterized by rotation along both the major and minor axes, making it only the second such confirmed case. By incorporating the mass enclosed within the Einstein radius from strong lensing as a complementary constraint, we tightly anchor the total mass at large radii. This significantly reduces the uncertainty on the outer mass profile and orbital structure, demonstrating that only models with strong radial anisotropy beyond the IFU field of view are compatible with the data. In the inner regions, we robustly constrain an upper limit for the stellar mass around $r \sim 0.7$ kpc, ruling out an IMF more bottom-heavy than Kroupa, though a gentle gradient toward a slightly heavier central IMF is permitted. This aligns with recent dynamical studies of local massive early-type galaxies but contrasts with heavier IMFs reported for lenses at $z>0.1$. Our work demonstrates the power of combining lensing and dynamical modeling to resolve the detailed inner structure of massive galaxies.

Figures (15)

• Figure 1: Photometric and kinematic constraints for the lens ESO0286. Left: HST/F814W image of the lens overlaid with the MUSE WFM FoV (white rectangle). The coordinate system ($x, y$) aligns with the galaxy's photometric major and minor axes, respectively. The upper inset provides a zoom-in of the central region to highlight the dust structure, while dashed circles mark lensed images A and B (shown in the bottom insets). Right: Predicted $M_{\rm Ein}$ in units of $10^{10}~\rm M_\odot$, derived from lensing and dynamical modeling. The more transparent green and orange regions show the probability density distribution of $M_{\rm Ein}^{\rm lens}$ constrained only by image positions and flux ratios, while the less transparent regions correspond to models constrained by the extended images in the F814W and F336W bands. The vertical black line and gray shaded region indicate the inferred value, $\overline{M_{\rm Ein}^{\rm lens}} = (8.85 \pm 0.38) \times 10^{10}~\rm M_\odot$, based on the best-fit EPL-ESR and PIEMD-ESR models. The gray dashed line marks the lens mass derived by 2018Collier.
• Figure 2: Setup for the mass distribution in the dynamical modeling, illustrating the implementation of the stellar mass-to-light ratio gradient. The inner radius $r_i$ is fixed at 0.1 kpc. The mass-to-light ratios $\Upsilon_{\ast,i}$ and $\Upsilon_{\ast,f}$, as well as the outer radius $r_f$, are allowed to vary during the dynamical modeling. As indicated by the shaded region and dotted lines, the variation range for $r_f$ is restricted to between $r_{f,\rm min} = 0.45$ kpc and $r_{f,\rm max} = 1.2$ kpc.
• Figure 3: Kinematic data and modeling. The top row shows the observed MUSE rotation-velocity field (left) and the HST-derived isophotal position angle (right), with the red region corresponding to the dust-affected region. The bottom row displays velocity residuals for the best-fit axisymmetric model (left), revealing a systematic structure along the $y$-axis, and the triaxial model (right).
• Figure 4: Statistical robustness check using bootstrapping. Top panel: The distribution of absolute AIC values for the global best-fit model (red line) and the second-best model (blue line) across 100 Monte Carlo noise realizations. The x-axis represents the individual Monte Carlo runs, and the y-axis shows the resulting AIC value for each fit. Bottom panel: The difference in AIC values ($\Delta \mathrm{AIC} = \mathrm{AIC}_{\mathrm{best}} - \mathrm{AIC}_{\mathrm{2nd}}$) calculated for each corresponding realization in the top panel. The grey points indicate the specific $\Delta \mathrm{AIC}$ value obtained for each noise iteration.
• Figure 5: AIC envelopes for $\Upsilon_{*,i}$ and $M_{\rm Ein}^{\rm kin}$ based on all triaxial mass models. The thin colored lines show the AIC envelopes for individual model classes, with solid points marking the global best-fit value for each specific model family (in the corresponding color of Model ID in Tab. \ref{['tab:model_summary']}). The thick dashed blue and thick solid red lines represent the overall combined envelopes for the kinematics-only (K) and kinematics+lensing (K$\&$L) categories, respectively. Shaded horizontal regions denote the $2\sigma$ statistical uncertainty threshold derived from bootstrapping for the K (light blue) and K$\&$L (light red) models. The vertical orange line and its corresponding shaded region in the $M_{\rm Ein}^{\rm kin}$ panel represent the independent mass measurement and uncertainty from the lensing-only model.