Inferring the dark matter distribution of massive galaxy clusters from deep optical observations: insights from the TNG300 simulation

TL;DR

This work tests whether the dark matter distribution in massive galaxy clusters can be inferred from deep optical imaging of intracluster light by leveraging the TNG300 simulation and forward-modeled WWFI-like observations. It uncovers a universal, near-linear scaling between the central DM surface density and the masked BCG+ICL surface brightness, enabling recovery of central subhalo DM profiles and halo parameters with typical uncertainties of about 0.1 dex (roughly 20–25%) for $M_{200}$ and $c_{200}$, and similar performance for $R_{500}$-based measures, while also offering global photometric proxies. The study also quantifies the impact of numerical resolution and baryonic physics on the inferred DM properties and provides practical recommendations for applying these relations to real clusters from upcoming surveys like LSST and Euclid. Overall, the results highlight a feasible, photometry-based pathway to constrain cluster DM structure that complements lensing and X-ray techniques in the era of wide, deep optical surveys.

Abstract

Extragalactic stars within galaxy clusters contribute to the intracluster light (ICL), which is thought to be a promising tracer of the underlying dark matter (DM) distribution. In this study, we employ the TNG300 simulation to investigate the prospect of recovering the dark matter distribution of galaxy clusters from deep, wide-field optical images. For this, we generate mock observations of 40 massive clusters ($M_{200}\gtrsim 10^{14.5}\,{\rm M}_\odot$) at $z=0.06$ for the $g'$ band of the Wendelstein Wide-Field Imager (WWFI), and isolate the emission from the brightest cluster galaxy (BCG) and the ICL by masking the satellite galaxies, following observational procedures. By comparing $Σ_{\rm BCG+ICL}$ profiles from these images against $Σ_{\rm DM}$ profiles for the central subhaloes, we find that $Σ_{\rm cen-DM}/Σ_{\rm BCG+ICL}$ exhibits a quasi-linear scaling relation in log space with the normalised distance $r/R_Δ$, for both $R_Δ=R_{200}$ and $R_{500}$. The scatter in the scaling is predominantly stochastic, showing a weak dependence on formation time and dynamical state. We recover the DM concentration and mass within $\approx 23$ and $\approx 15$ per cent of their true values (for $R_{200}$), respectively, and with $\approx 3$ per cent larger uncertainties for $R_{500}$. Alternatively, we find that the concentration can be estimated using the BCG+ICL fraction, the central's DM mass using the BCG+ICL flux, and the total DM mass using the bolometric flux. These results demonstrate the feasibility of deriving dark matter characteristics of galaxy clusters to be observed with facilities like the Vera C. Rubin Observatory in the near future.

Figures (14)

• Figure 1: An illustration of the synthetic WWFI-like images generated for the TNG300 clusters (see Section \ref{['imagegen']} for details). The images shown here correspond to the cluster with the subfind ID 94882. The idealised image (without incorporating observational factors) for the $g'$-band is shown in the left panel. The middle panel shows the realistic image obtained after simulating the impact of the PSF, background noise, and shot noise. The right panel shows the realistic image with masked satellite galaxies used to characterise the BCG+ICL component.
• Figure 2: The scaling relation between the intrinsic central subhalo's DM surface density profile and the 'masked' BCG+ICL surface brightness profile for TNG300 clusters. The left and right panels show $\Sigma_{\rm cen-DM}/\Sigma_{\rm BCG+ICL}$ against cluster-centric radii normalised by $R_{200}$ and $R_{500}$, respectively. The $\Sigma_{\rm BCG+ICL}$ profile is derived from the optical image after masking the emission from satellite galaxies, and the DM profile is calculated from the DM map for the central subhalo. Each colour denotes a specific cluster (Section \ref{['analysis']}). The grey shaded region in the left shows the regime where the profiles are unreliable due to numerical heating driven by two-body scattering of particles (see the text). The yellow curve shows the median relation, and the corresponding yellow shaded region spans 16th to 84th percentiles. The solid black line is the maximum-likelihood linear fit to the profiles beyond the shaded region, and the dashed lines show 1-$\sigma$ scatter from the fit along $y$-axis. The slope ($\alpha$), intercept ($\beta$), and the $\sigma$ are mentioned in the bottom-right corner of each panel.
• Figure 3: Comparison of $\Sigma_{\rm cen-DM}$ profiles recovered from the median $\Sigma_{\rm cen-DM}$--$\Sigma_{\rm BCG+ICL}$ scaling relation for $R_{\Delta}=R_{200}$ (top panel) and the linear fit to this relation (bottom panel). Each panel shows the ratios of the recovered $\Sigma_{\rm cen-DM}$'s to the true values, where the solid curve shows the median ratios and the shaded region shows the 16th to 84th percentiles. The vertical shaded region in the left spans the radii where the profiles are rendered unreliable due to two-body scattering between collisionless elements. The profiles recovered via the median scaling generally match the true ones, whereas those recovered with the linear scaling show systematic deviations, particularly at $r\gtrsim 0.5R_{200}$.
• Figure 4: Comparisons of DM characteristics derived from the $\Sigma_{\rm cen-DM}$ profiles reconstructed from the BCG+ICL profiles (based on the masked optical images) against those derived from the $\rho_{\rm cen-DM}$ profiles. All the DM properties correspond to the best-fit NFW profiles (Section \ref{['dmrec']}), where the top row shows the results for the concentrations and halo masses assuming $R_{\Delta}=R_{200}$, and the bottom row shows similar results for $R_{\Delta}=R_{500}$. Each panel shows the values for two approaches of reconstructing $\Sigma_{\rm cen-DM}$ from $\Sigma_{\rm BCG+ICL}$: a) using the raw median relation in Fig. \ref{['scaling']} (shown in blue), and b) using the linear fit to the data in equation (\ref{['fit']}) (orange). The solid orange/blue line corresponds to the best-fit for the data with the same colour, and the corresponding dashed lines encapsulate the 1-$\sigma$ scatter about the line. The black dash-dotted lines show the 1:1 relations.
• Figure 5: Correlation matrices displaying the Spearman rank correlations of various halo and photometric quantities with the offset ($\mathcal{R}-\mathcal{R}_{\rm med}$; see the text) from one of the two median $\Sigma_{\rm cen-DM}$--$\Sigma_{\rm BCG+ICL}$ scaling relations in Fig. \ref{['scaling']}, along with correlations among the quantities themselves. The top matrix shows the results for profiles extending out to $R_{200}$ (corresponding to the left panel in Fig. \ref{['scaling']}), and the bottom matrix shows them for $R_{500}$. Each cell in a given matrix shows the correlation coefficient ($\rho_{\rm sp}$) for the associated pair of quantities, and corresponds to the colour indicated by the colour bar on the right. Trends with $<3$-$\sigma$ significance are marked with grey boundaries around the respective cells. The offset is significantly correlated with the magnitude gaps, but at weak strengths ($\rho_{\rm sp} < 0.2$). The central subhalo's DM concentration correlates strongly ($\rho_{\rm sp}\gtrsim 0.68$) with the BCG+ICL fraction, $F_{\rm \Delta,\,BCG+ICL}$ (i.e. the fraction of total luminosity contributed by BCG+ICL). The central subhalo's DM mass exhibits the strongest trend (at $\rho_{\rm sp}\gtrsim 0.74$) with the BCG+ICL flux, $I_{\rm \Delta,\,{\rm BCG+ICL}}$.