Measuring the Stellar-to-Halo Mass Relation at $\sim10^{10}$ Solar masses, using forthcoming space-based imaging of galaxy-galaxy strong lenses

TL;DR

This work tackles constraining the SHMR at the dwarf-galaxy scale ($\sim 10^{10}\,\mathrm{M}_\odot$ halos) using strong gravitational lensing in the era of Euclid. The authors perform end-to-end simulations of galaxy–galaxy lenses with a fiducial subhalo mass $M_{200}=3\times10^{10}\,\mathrm{M}_\odot$, exploring how concentration, subhalo position, and hosted satellite light affect mass inferences, and they implement a multi-stage PyAutoLens modelling pipeline to assess detection significance via Bayesian evidence. They find Euclid-like imaging cannot fully break the mass–concentration degeneracy nor deblend satellite light, leading to biased halo masses unless high-resolution follow-up (e.g., HST) is used; with such follow-up, halo masses, concentrations, and satellite magnitudes can be recovered, enabling a statistical sample of ~$\sim100$ systems to constrain the SHMR at this mass scale to $\sim0.05$ dex in $M_h$ and $\sim0.03$ dex in $M_*$. The paper also outlines a hierarchical Bayesian framework to infer SHMR parameters, emphasizing the need for high-resolution imaging to achieve robust detections and accurate population inferences. Overall, the results underscore the necessity of combining wide-field survey discoveries with targeted, high-resolution follow-up to leverage strong lensing as a precision probe of the galaxy–halo connection at the low-mass frontier.

Abstract

The stellar-to-halo mass relation (SHMR) is central to understanding the co-evolution of galaxies and their host dark matter haloes, yet it remains weakly constrained for dwarf galaxies owing to their faintness, especially beyond the Local Group. Strong gravitational lensing offers a unique probe of the SHMR at sub-galactic scales and cosmological distances, as the masses of subhalos within the main lens can be inferred from the perturbations they imprint on lensed images. Anticipating the discovery of $\sim10^5$ galaxy--galaxy strong lenses by forthcoming facilities such as \textit{Euclid}, we perform an end-to-end simulation to forecast \textit{Euclid}'s constraints on the SHMR at the halo mass scale of $\sim10^{10}\,\mathrm{M}_\odot$. We generate mock \textit{Euclid} VIS images of lens systems hosting a fiducial $3\times10^{10}\,\mathrm{M}_\odot$ subhalo and vary its properties to assess the robustness of mass inference. We find that \textit{Euclid}'s angular resolution cannot break the intrinsic mass--concentration degeneracy of subhaloes, nor deblend the light of satellite galaxies (when present) associated with them, leading to biased inferred halo masses. These limitations are overcome with high-resolution follow-up imaging from facilities such as the \textit{Hubble Space Telescope}, enabling accurate halo-mass measurements. We forecast that a statistical sample of $\sim100$ such systems, combining lensing-derived halo masses with stellar masses from photometric SED fitting, can constrain the SHMR at dwarf-galaxy scales with a precision of $\sim0.05$~dex in halo mass and $\sim0.03$~dex in stellar mass, enabling powerful tests of galaxy formation theories.

Figures (9)

• Figure 1: The simulated mock image based on the macro model. The parameter values used for this simulation are listed in Table \ref{['tab:param']}. The image has a pixel size of $0.1\arcsec$ and is convolved with a Gaussian PSF with a FWHM of $0.18\arcsec$.
• Figure 2: Evidence--increase maps for two mock lens systems illustrating the subhalo grid-search strategy. The colour bar shows the increase in logarithmic evidence, $\Delta\ln E$, obtained when a subhalo is included in the lens model with its position restricted to each $0.5\arcsec \times 0.5\arcsec$ grid cell. Left: A system with no subhalo. No grid cell shows a significant evidence increase ($\Delta\ln E < 5$), demonstrating that the method does not produce false positives. Right: A system with an injected subhalo. The grid cell with the maximum evidence increase of $\Delta\ln E = 19.55$ correctly identifies the most probable location of the subhalo.
• Figure 3: Accuracy of subhalo mass measurements for a suite of mock lenses at various input positions. The background image displays the lensing morphology generated from the macro model. Triangles indicate the locations of successfully detected subhalos, with their colour representing the mass error coefficient $\mathcal{B}$. This coefficient reflects the difference between the inferred posterior and the true value, defined following equation \ref{['eq:bias']}. Grey crosses mark locations where the input subhalo was not detected by our pipeline.
• Figure 4: Relation between the mass error coefficient $\mathcal{B}$ and the logarithmic evidence increase $\Delta \ln E$. Blue crosses represent significant detections with $\Delta \ln E > 5$. Grey crosses represent tentative detections with only $\Delta \ln L > 10$. Under the current detection threshold (red dashed line), no apparent correlation is observed between $\mathcal{B}$ and $\Delta \ln E$. This suggests that a logarithmic evidence increase of $\Delta \ln E > 5$ is sufficient to obtain unbiased individual subhalo measurements using Euclid strong lensing data.
• Figure 5: Posterior distributions of model parameters for a simulated subhalo derived from lensing data with different angular resolutions: Euclid (left) and HST (right). The true subhalo concentration is $2\sigma$ above the median mcr_Ludlow relation. True parameter values are indicated by red lines. The 2D contours denote the $68\%$, $95\%$, $99\%$ credible regions. In the 1D marginalised histograms, the $68\%$ credible interval is shown by grey dashed lines. We treat the subhalo concentration as a free parameter by sampling its normalised offset from the mcr_Ludlow relation, $s_{\rm c}\equiv \delta\log c / \sigma_{\log c}$, where $\sigma_{\log c}=0.15$.