Neural posterior estimation of the line-of-sight and subhalo populations in galaxy-scale strong lensing systems

TL;DR

This study examines whether a neural posterior estimator can extract anisotropic line-of-sight signatures and subhalo populations from galaxy-scale strong lensing images by modeling the two-point function multipoles of the effective convergence. Using a simulation-based inference pipeline with an $x$ResNet-34 CNN trained on 400k mock HST-like images that incorporate subhalos, LOS halos, and realistic noise, the authors infer both dark-matter substructure parameters and multipole statistics, as well as macrolens properties. They find strong predictive power for certain substructure parameters but significant degeneracies (notably between LOS and subhalo amplitudes) and biases introduced by skewed training priors, and they observe only modest constraints on the two-point function multipoles due to noise and model simplifications. The work highlights the potential and current limitations of SBI for DM microphysics studies in strong lensing and suggests directions such as normalizing flows and lens-light-removal strategies to improve inference in future analyses.

Abstract

Strong gravitational lensing is a powerful probe for studying the fundamental properties of dark matter on sub-galactic scales. Detailed analyses of galaxy-scale lenses have revealed localized gravitational perturbations beyond the smooth mass distribution of the main lens galaxy, largely attributed to dark matter subhalos and intervening line-of-sight halos. Recent studies suggest that, in contrast to subhalos, line-of-sight halos imprint distinct anisotropic features on the two-point correlation function of the effective lensing deflection field. These anisotropies are particularly sensitive to the collisional nature of dark matter, offering a potential means to test alternatives to the cold dark matter paradigm. In this study, we explore whether a neural density estimator can directly identify such anisotropic signatures from galaxy-galaxy strong lens images. We model the multipoles of the two-point function using a power-law parameterization and train a neural density estimator to predict the corresponding posterior distribution of lensing parameters, alongside parameter distributions for dark matter substructure. Our results show that recovering the dark matter substructure mass functions and mass-concentration parameters remains challenging, owing to difficulties in generating uniform training data set while using physically motivated priors. We also unveil an important degeneracy between the line-of-sight halo mass-function amplitude and the subhalo mass-function normalization. Furthermore, the network exhibits limited accuracy in predicting the two-point function multipole parameters, suggesting that both the training data and the adopted power-law fitting function may inadequately represent the true underlying structure of the anisotropic signal.

Figures (11)

• Figure 1: Effective multi-plane convergence maps ($\kappa_{\rm div}$) for the same CDM halo realization, shown for three different values of the rescaling factor $\beta$ controlling the amplitude of the mass–concentration relationship.
• Figure 2: Comparison of the predicted and true mean values for three parameters describing dark matter halo properties ($\delta_{\rm LOS}, \,\Sigma_{\rm sub},$ and $\beta$) across 1,000 test lenses. Each point represents a single lens, with the Pearson correlation coefficient ($\rho$) displayed in the bottom-right corner of each plot, quantifying the correlation between the neural density estimator’s predictions and the true values. The color of each point corresponds to the predicted standard deviation. Black lines indicate where the predicted values align with the true values.
• Figure 3: Posterior distributions estimated by the trained neural network for parameters describing dark matter substructure from four different test images, shown in the upper-right corner of each panel. This figure illustrates the neural posterior density estimator's ability to predict substructure abundances and concentrations under different conditions of low/high subhalo and line-of-sight halo abundances, as well as low/high halo concentrations. Blue contours represent the neural network's predictions, while beige contours indicate the prior distributions used in the training data. Dark and light contours correspond to the 68% and 95% confidence intervals, respectively. The true parameter values used to generate the strong lens images are marked by black points.
• Figure 4: Histograms illustrating the distributions of the parameters $\Sigma_{\rm sub}$, $\beta$, $A_0$, $n_0$, $A_2$, and $n_2$ within the training dataset. The pronounced skewness in these distributions may introduce biases in the neural posterior density estimator, potentially leading it to favor outputs that mirror the underlying training set distribution.
• Figure 5: In the top and middle rows, the left panels highlight points with overpredictions and underpredictions using color coding, while the right panels show the corresponding locations of these points in the other parameter space. These panels illustrate an inverse relationship between the predicted line-of-sight dark matter contribution ($\delta_{\rm LOS}$) and the subhalo mass function normalization ($\Sigma_{\rm sub}$): underestimating one tends to coincide with overestimating the other. At higher values, both parameters deviate from the one-to-one relation, indicating systematic underpredictions. In the bottom row, points that show significant deviations are color-coded, and their locations are displayed in the complementary parameter space.This highlights the consistency of the trend across lens systems and further supports the degeneracy between $\delta_{\rm LOS}$ and $\Sigma_{\rm sub}$.