Deriving accurate galaxy cluster masses using X-ray thermodynamic profiles and graph neural networks

TL;DR

This work takes a significant step towards establishing unbiased observable mass scaling relations by integrating X-ray, SZ, and optical datasets using deep learning techniques, thereby enhancing the role of galaxy clusters in precision cosmology.

Abstract

Precise determination of galaxy cluster masses is crucial for establishing reliable mass-observable scaling relations in cluster cosmology. We employ graph neural networks (GNNs) to estimate galaxy cluster masses from radially sampled profiles of the intra-cluster medium (ICM) inferred from X-ray observations. GNNs naturally handle inputs of variable length and resolution by representing each ICM profile as a graph, enabling accurate and flexible modeling across diverse observational conditions. We trained and tested GNN model using state-of-the-art hydrodynamical simulations of galaxy clusters from The Three Hundred Project. The mass estimates using our method exhibit no systematic bias compared to the true cluster masses in the simulations. Additionally, we achieve a scatter in recovered mass versus true mass of about 6%, which is a factor of six smaller than obtained from a standard hydrostatic equilibrium approach. Our algorithm is robust to both data quality and cluster morphology and it is capable of incorporating model uncertainties alongside observational uncertainties. Finally, we apply our technique to XMM-Newton observed galaxy cluster samples and compare the GNN derived mass estimates with those obtained with $Y_{\rm SZ}$-M$_{500}$ scaling relations. Our results provide strong evidence, at 5$σ$ level, for a mass-dependent bias in SZ derived masses, with higher mass clusters exhibiting a greater degree of deviation. Furthermore, we find the median bias to be $(1-b)=0.85_{-0.14}^{+0.34}$, albeit with significant dispersion due to its mass dependence. This work takes a significant step towards establishing unbiased observable mass scaling relations by integrating X-ray, SZ and optical datasets using deep learning techniques, thereby enhancing the role of galaxy clusters in precision cosmology.

Figures (15)

• Figure 1: Comparison of the hydrostatic mass estimates $\text{M}^{\text{HSE}}_{500}$ to the true mass $\text{M}^{\text{True}}_{500}$ for a sample of 1655 galaxy clusters in The Three Hundred Project. The blue line indicates the best-fitting linear relation, and the black line corresponds to the 1-to-1 relation. The blue line and shaded region in the lower panel show the median and 1$\sigma$ dispersion of the fractional residual distribution, respectively, considering logarithmic binning. The inset plot shows the distribution of fractional residuals and the vertical dashed lines show the median of the fractional dispersion of $-0.24$.
• Figure 2: The grey lines show the pressure profiles of the 50 clusters having the lowest (left panel) and highest (right panel) fractional dispersions. The thick red lines indicate the corresponding median profiles. The bottom panel displays the ratio of reconstructed to true pressure profiles. On the right panel, we have also plotted the median profile for the lowest dispersion set with a thick blue line for comparison. The inset plot illustrates the distribution of the relaxation parameter $\chi$ for the same clusters.
• Figure 3: The number distribution of galaxy clusters in the The Three Hundred Project, shown as a function of $\text{M}^{\text{True}}_{500}$. The magenta histogram represents the original sample (1655 clusters), while the orange and green histograms represent the augmented training sample (9305 clusters built with 1305 clusters) and testing (1950 clusters built with 350 clusters) sample, respectively.
• Figure 4: Train and test loss in the evaluation mode over epochs for one of the ensemble models. Both train and test losses indicate consistent learning, with the final loss at around 0.02 for the training and testing sets.
• Figure 5: Distribution of GNN predicted masses, $\text{M}^{\text{GNN}}_{500}$, versus true cluster masses, $\text{M}^{\text{True}}_{500}$, for the training (left) and testing (right) samples of sizes 9305 and 1950 respectively. The black line represents a 1-to-1 relation. The bottom panel in both panels shows the fractional residual distribution with a solid blue line and shaded regions representing the median and 1$\sigma$ dispersion, respectively. We find a 1$\sigma$ dispersion of about 7% and 6% for the testing and training samples respectively