Searching for a signature of turnaround in galaxy clusters with convolutional neural networks

TL;DR

This study investigates whether the cluster turnaround radius $R_{ta}$ can be inferred from projected observables using convolutional neural networks trained on simulated idealized data. The authors generate mock projections from N-body simulations (MDPL2 and Virgo) across cosmologies, measuring $R_{ta}$ from 3D velocity fields and transforming projections into 25×25 pixel images with channels for mass, number, and mean LOS velocity (and optionally velocity dispersion). They find a strong correlation between $R_{ta}$ and the central halo mass, with velocity dispersion offering additional information, while data inside $R_{200}$ are not essential for velocity-based predictions; single-cluster inference is challenging, but stacking and merging datasets improve performance, indicating the potential of ML approaches to probe turnaround scales. Generalization across redshift and cosmology is limited in this feasibility study, highlighting the need for larger, more diverse training sets and realistic observational effects to translate these methods to real data. Overall, the work identifies a plausible ML pathway to constrain turnaround scales and cosmological parameters, contingent on robust statistical techniques and careful treatment of observational constraints.

Abstract

Galaxy clusters are important cosmological probes that have helped to establish the $\mathrmΛ$CDM paradigm as the standard model of cosmology. However, recent tensions between different types of high-accuracy data highlight the need for novel probes of the cosmological parameters. Such a probe is the turnaround density: the mass density on the scale where galaxies around a cluster join the Hubble flow. To measure it, one must locate the distance from the cluster center where turnaround occurs. Earlier work has shown that a turnaround radius can be readily identified in simulations by analyzing the 3D dark matter velocity field. However, measurements using realistic data face challenges due to projection effects. This study aims to assess the feasibility of measuring the turnaround radius using machine learning techniques applied to simulated idealized observations of galaxy clusters. We employed N-body simulations across various cosmologies to generate galaxy cluster projections. Utilizing convolutional neural networks, we assessed the predictability of the turnaround radius based on galaxy line-of-sight velocity, number density, and mass profiles. We find a strong correlation between the turnaround radius and the central mass of a galaxy cluster, rendering the mass distribution outside the virial radius of little relevance to the model's predictive power. The velocity dispersion among galaxies also contributes valuable information concerning the turnaround radius. Importantly, the accuracy of a line-of-sight velocity model remains robust even when the data within the $\mathrm{R_{200}}$ of the central overdensity are absent. Single-cluster turnaround radius inference from projected observables seems to be highly challenging. Future progress is likely to require statistical approaches, especially stacking, to exploit cosmological information encoded at turnaround scales.

Figures (11)

• Figure 1: Histogram of the turnaround radii $\rm R_{ta}$ values from MDPL2 (black) and Virgo $\rm \Lambda CDM$ (cyan). The difference between the two distributions reflects the difference between box sizes and resolutions. The mean ($\rm \mu$) and standard deviation ($\rm \sigma$) are shown on the top right, while, for the merged data $\rm (\mu, \sigma)=(7.8, 2.5)$. Additional distributions can be found in Fig. \ref{['fig: Rta histogram Virgo OCDM SCDM ']} of the Appendix.
• Figure 2: Performance comparison across different models. Upper panel: Comparison between low- and high-velocity-cut models' performance. The plot shows different $\rm R^2$ values for each combination of the three features considered: mass column density, number column density, and mean line-of-sight velocity (indicated as "mass," "num," and "vel" respectively). Best results are obtained for the low velocity cut (due to less contamination) and for data containing the mass. Lower panel: Comparison between models including or excluding the central halo. Both analyses are performed for the low-velocity-cut data. Without the central halo, performance drops significantly across models; all models without it predict the turnaround with a similar score.
• Figure 3: Comparison between predicted and true values of $\rm R_{ta}$ for models using the MDPL2 "mass" images from: the low-velocity-cut data (left panel); the high-velocity-cut data (middle panel); and the low-velocity-cut data after removing the central halo of each projection (right panel). The colors represent the number density of the plotted points, calculated using a Gaussian kernel density estimate. $\rm R^2$ scores and the mean absolute errors (MAEs) are shown at the bottom right of each plot. While the models in the left and middle panel show some correlation between true and predicted $\rm R_{ta}$ values, the right-panel model appears to mostly predict the mean value of the $\rm R_{ta}$ distribution, especially when comparing the MAEs with the standard deviation of the $\rm R_{ta}$ distribution ($\rm 2.2\; Mpc$) as shown in the upper panel of Fig. \ref{['fig:Rta Histograms']}.
• Figure 4: $\rm R^2$ scores of different combinations of training and testing data using the mass column density (upper panel) or velocity dispersion (lower panel) information. 80% of the simulation data were used for training-validation, and 20% was used for the testing in each case located in the diagonal. Left panel: Training and testing data from different MDPL2 redshifts (z=0, 0.49, 1.03). As expected, for each training set, the $\rm R^2$ score is the highest when evaluated on data from the same redshift. Since MDPL2 is a $\rm \Lambda CDM$ concordance cosmological simulation, the $\rm \rho_{ta}$ depends on redshift. Therefore, for different redshifts, the model cannot find an apparent correlation between $\rm M_{vir}$ and $\rm R_{ta}$ because $\rm \rho_{ta}$ varies with redshift. The velocity information plot has the same form as the mass, indicating that the model just correlates the mass with the velocity dispersion. Right panel: Training and testing data from different simulations and cosmological models (MDPL2, Virgo $\rm \Lambda CDM$, Virgo OCDM, Virgo SCDM, and the merged data from MDPL2 and Virgo $\rm \Lambda CDM$). Best models seem to be the ones containing the data from the MDPL2, possibly due to the fact of the larger number of training instances. Negative $\rm R^2$ values are a direct consequence of the fact that evaluating a model on another simulation can predict values even worse than the mean (as discussed in Sect. \ref{['sec:methods']}), since the target value distribution is an unknown.
• Figure 5: Comparison between predicted and true values of the $\rm R_{ta}$ for models using the stacked velocity-dispersion images from 3000 bins of $\rm R_{ta}$ from: the MDPL2 data (left panel); the merged MDPL2 with Virgo $\rm \Lambda CDM$ data (middle panel); the merged MDPL2 with Virgo $\rm \Lambda CDM$ data with removed information inside the $\rm R_{200}$ of the central overdensity (right panel). $\rm R^2$ scores and the mean absolute errors (MAEs) are shown at the bottom right of each plot. The colors represent the number density of the plotted points, calculated using a Gaussian kernel density estimate. It is apparent that the merging of the two datasets significantly improves the performance of the model even without the central halos' velocity information.