Lens Model Accuracy in the Expected LSST Lensed AGN Sample

TL;DR

The paper tackles scalable lens-modeling for LSST-scale samples of lensed AGN to enable time-delay cosmography constraints on $H_0$ using a pipeline based on Neural Posterior Estimation (NPE) and Bayesian Hierarchical Inference (HBI). It builds a realistic mock catalog (~1344 LAGN) by painting OM10 lenses onto cosmoDC2 host galaxies and simulating 5-year LSST $i$-band coadds, then recovers key lens parameters with NPE and aggregates population-level properties with HBI. The mass-models (PEMD) yield Einstein radii $θ_E$ with bias $<1\\%$ and precision 6.5\% per lens, and density slopes $γ_{lens}$ with bias $<3\%$ and precision 8\% per lens; lens-light subtraction helps only if data are drawn from the training prior, while deconvolution before modeling improves precision by roughly a factor of 2. Population inferences achieve bias $<1\%$, enabling robust cosmological inferences from LSST’s LAGN population. These results demonstrate the viability of automated, scalable lens modeling for large LSST datasets and highlight the conditions under which pre-processing steps enhance parameter recovery.

Abstract

Strong gravitational lensing of active galactic nuclei (AGN) enables measurements of cosmological parameters through time-delay cosmography (TDC). With data from the upcoming LSST survey, we anticipate using a sample of O(1000) lensed AGN for TDC. To prepare for this dataset and enable this measurement, we construct and analyze a realistic mock sample of 1300 systems drawn from the OM10 (Oguri & Marshall 2010) catalog of simulated lenses with AGN sources at $z<3.1$ in order to test a key aspect of the analysis pipeline, that of the lens modeling. We realize the lenses as power law elliptical mass distributions and simulate 5-year LSST i-band coadd images. From every image, we infer the lens mass model parameters using neural posterior estimation (NPE). Focusing on the key model parameters, $θ_E$ (the Einstein Radius) and $γ_{lens}$ (the projected mass density profile slope), with consistent mass-light ellipticity correlations in test and training data, we recover $θ_E$ with less than 1% bias per lens, 6.5% precision per lens and $γ_{lens}$ with less than 3% bias per lens, 8% precision per lens. We find that lens light subtraction prior to modeling is only useful when applied to data sampled from the training prior. If emulated deconvolution is applied to the data prior to modeling, precision improves across all parameters by a factor of 2. Finally, we combine the inferred lens mass models using Bayesian Hierarchical Inference to recover the global properties of the lens sample with less than 1% bias.

Figures (4)

• Figure 1: Probabilistic Graphical Model (PGM) depicting the levels of inference in this project. We assert broad priors on lensing parameters $\rm \nu_{int}$ (shown in gray) and sample $\rm N=500k$ lens systems with model parameters $\xi_N$. This is used to optimize model weights that we apply to the test image ($d_k$) for each of the $k$ LAGN systems. From the data, we recover lens model parameters $\rm p(\xi_k|d_k, \nu_{int})$ (shown in purple contours), and infer the lens population model $\rm p(\nu|\{d\})$ (shown as overlaid green contours).
• Figure 2: OM10-cosmoDC2 mapping. We "paint on" host galaxies from cosmoDC2 to systems in the OM10 catalog. Nearest neighbor mapping: To obtain a mapping between the two catalogs, we map AGN in OM10 to AGN in cosmoDC2 using their redshift and absolute magnitude and use their corresponding host galaxy. First panel: The red OM10 systems are mapped to the blue cosmoDC2 systems. The blue points are a subset of the gray points. Second panel: We demonstrate the scatter of the OM10-cosmoDC2 system mapping along AGN redshift axis. Third panel: We demonstrate the scatter of the OM10-cosmoDC2 system mapping along AGN $i$-band absolute brightness (AB mag) axis.
• Figure 3: Deflector Galaxy and AGN Host Galaxy Selection. We display the following four galaxy properties: Redshift ($z$), stellar mass ($\log(M_*/M_{\odot})$), effective size ($\log(R_{\rm eff}/\rm kpc)$) and absolute brightness ($M_{i}$). Left -- In gray we show properties of a sample of randomly selected galaxies from a cone. In red we show massive elliptical galaxies that constitute the lenses in our sample. The selection of galaxies is intrinsic: i.e more massive galaxies act as lenses. Right -- In gray, we show the population of galaxies that contain an AGN. In blue, we show the AGN containing galaxies in our sample that are lensed by a massive foreground galaxy. The selection on AGN host galaxies in this case arises from cuts placed to ensure that these systems are detectable in LSST. Thus, this selection of AGN host galaxies in blue is observationally imposed, rather than intrinsic.
• Figure 4: 5 simulated LSST lensed quasar systems in the $i$-band. We test our inference pipeline on 3 different preparations of the data. Subtraction of different light components have been shown to improve the performance of the modeling pipeline in lens parameter recovery. We discuss this further in Section \ref{['sec:3_preps']}. In the first column (to the left of the black line), we show the deconvolved version of the second column of images (to the right of the black line). Deconvolution also helps in the lens modeling, detailed also in Section \ref{['sec:3_preps']}. Top row: include lens light, AGN light and host galaxy light. Middle row: Lens light subtracted. Poisson noise due to lens light remains. Bottom row: Lens light and AGN light subtracted. Poisson noise due to all light remains. The background Gaussian noise also remains constant across 3 different preparations.