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New classification method for the dynamical state of galaxy clusters with a Gaussian mixture model

Hyowon Kim, Marco Canducci, Rory Smith, Peter Tino, Yara Jaffe, Ho Seong Hwang, Jihye Shin, Kyungwon Chun

Abstract

Galaxy clusters are the largest gravitationally bound systems, and they continue their growth through mergers in a hierarchical ΛCDM Universe. Therefore, we can describe the merger stage of a cluster as the dynamical state of clusters. Previous studies have investigated this phenomenon, but several limitations remain, including reliance on dichotomous classifications, constraints on the number of indicators used, absence of reliability, and incompatibility of methods between observation and simulation studies. To overcome this, we developed an enhanced and observation-applicable cluster dynamical state classification method using the Bayesian classifier with the class-conditional Gaussian mixture distribution model using the N-cluster Run simulation data. The Bayesian classifier was designed for two merger stages (merger and relaxed) as well as three merger stages (recent merger, ancient merger, and relaxed) to provide a more detailed interpretation of the merger processes. In the results, using a larger number of indicators yields better results, with their order of importance being: magnitude difference, center offset, sparsity, Kuiper V statistic, and mirror asymmetry. Additionally, our analyses show that a projected classifier (built on the 6D space, but evaluated on lower dimensional projections) consistently produces better outcomes than non-projected classifiers (i.e., classifiers built directly on the corresponding low dimensional spaces), which means limited observation data can be used to classify with enhanced performance. Furthermore, the new classification method outperforms our previous research. This new method can suggest a way of overcoming previous limitations and provides new insights by providing the reliability of dynamical state classification results.

New classification method for the dynamical state of galaxy clusters with a Gaussian mixture model

Abstract

Galaxy clusters are the largest gravitationally bound systems, and they continue their growth through mergers in a hierarchical ΛCDM Universe. Therefore, we can describe the merger stage of a cluster as the dynamical state of clusters. Previous studies have investigated this phenomenon, but several limitations remain, including reliance on dichotomous classifications, constraints on the number of indicators used, absence of reliability, and incompatibility of methods between observation and simulation studies. To overcome this, we developed an enhanced and observation-applicable cluster dynamical state classification method using the Bayesian classifier with the class-conditional Gaussian mixture distribution model using the N-cluster Run simulation data. The Bayesian classifier was designed for two merger stages (merger and relaxed) as well as three merger stages (recent merger, ancient merger, and relaxed) to provide a more detailed interpretation of the merger processes. In the results, using a larger number of indicators yields better results, with their order of importance being: magnitude difference, center offset, sparsity, Kuiper V statistic, and mirror asymmetry. Additionally, our analyses show that a projected classifier (built on the 6D space, but evaluated on lower dimensional projections) consistently produces better outcomes than non-projected classifiers (i.e., classifiers built directly on the corresponding low dimensional spaces), which means limited observation data can be used to classify with enhanced performance. Furthermore, the new classification method outperforms our previous research. This new method can suggest a way of overcoming previous limitations and provides new insights by providing the reliability of dynamical state classification results.
Paper Structure (25 sections, 15 equations, 12 figures, 9 tables)

This paper contains 25 sections, 15 equations, 12 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Data
  3. N-cluster Run simulation
  4. Definition of the dynamical states for the classification class
  5. Observation data
  6. Methods
  7. Dynamical indicators
  8. Bayesian classifier and class conditional distributions with a GMM
  9. Bayesian classifier
  10. Class-conditional distributions
  11. Confusion matrix and classification report
  12. Analysis and result
  13. Best model analysis
  14. Application on observation data
  15. Model projection and number of indicator effects
  16. ...and 10 more sections

Figures (12)

  • Figure 1: Top: Halo mass function of N-cluster Run simulation. Bottom: Comparison with stellar mass function of the N-cluster Run simulation and other studies. The Orange solid and cyan dashed lines represent the simulation function from the N-cluster Run and the Illustris-TNG 100 simulation 2018MNRAS.475..648P. Gray circles and blue triangles are observational function from SDSS 2013MNRAS.436..697B and DESI Y1 data 2024ApJ...971..119W.
  • Figure 2: Top: Mass versus redshift distribution of simulation data and observation data. Dots show median values, and the shaded area shows standard deviation values within redshift bins. Middle: Histogram of redshift for both observation and simulation data. Bottom: Histogram of Mass for both observation and simulation data.
  • Figure 3: Histograms of six dynamical state indicators on (Top) N-cluster Run simulation and (Bottom) HeCS observation data. Top: Black empty, red, green, and blue colored histograms exhibit the number of galaxy clusters for total, recent merger, ancient merger, and relaxed dynamical state, respectively. The overlap of the merger and relaxed sample histogram distribution shows the projection effects on each dynamical state indicator. Bottom: Same indicator histograms as the top panels with different colors. Even though there are slight parameter range differences, the overall parameter distribution seems similar to each other.
  • Figure 4: 2D Correlation plots for each indicator distribution by merger sample. The bottom-left corner and top-right corners give the scatter plots of the indicator against the other. The diagonal shows the histogram of individual indicators. In the bottom-left panels, we overplot probability contours (varying probability value in each panel). In the top-right panels, we overplot ellipses indicating the shape of the Gaussian for all components with a weight concentration prior > 0.1. We note that ellipses match the location of the high probability contours.
  • Figure 5: 2D Correlation plots for each indicator distribution by relaxed state sample. Instructions are the same as Figure\ref{['fig:modeling']}.
  • ...and 7 more figures