Testing an entropy estimator related to the dynamical state of galaxy clusters

Abstract

We propose the entropy estimator $H_Z$, calculated from global dynamical parameters, in an attempt to capture the degree of evolution of galaxy systems. We assume that the observed (spatial and velocity) distributions of member galaxies in these systems evolve over time towards states of higher dynamical relaxation (higher entropy), becoming more random and homogeneous in virial equilibrium. Thus, the $H_Z$-entropy should correspond to the gravitacional assembly state of the systems. This was tested in a sample of 70 well sampled clusters in the Local Universe whose gravitational assembly state, classified from optical and X-ray analysis of substructures, shows clear statistical correlation with $H_Z$. This estimator was also tested on a sample of clusters (halos) from the IllustrisTNG simulations, obtaining results in agreement with the observational ones.

Figures (9)

• Figure 1: Two examples of sampled TNG300 halos. Left: subhalo distribution for a high entropy halo (TNG-halo-34). Right: subhalo distribution for a low entropy halo (TNG-halo-87). Each dot represents a member subhalo: the small dots are subhalos with masses less than $2.0\times 10^{10} \mathcal{M}_\odot$ while the big dots are the subhalos taken for our analysis.
• Figure 2: Boxplots of $H_Z$-entropy for the five assembly classifications of clusters. The lower and upper extremes of each box are the 25th and 75th percentiles, respectively, while the central red line marks the median. Whiskers extend to the most extreme non-outlier data, while outliers are represented by red '+' symbols.
• Figure 3: Sample of galaxies for A2199 cluster in ca2021. Color bars represent the redshift ($z$) distribution. Left panel: the cylinder along the line-of-sight direction. Right panel: projected distribution in the sky plane with RA and Dec coordinates transported to the origin (the FRG, see the text).
• Figure 4: Probability density functions for the radial-$r$, azimuthal-$\theta$ and redshift-$z$ distributions of member galaxies in the A2199 cluster. The red solid lines represent the observed PDFs obtained by smoothing (normal kernel) from observational data histograms, while dashed blue lines represent the relaxed PDFs of equilibrium distributions. The error bars represent the difference between the height of the smoothed curve and the height of the corresponding bin in each 1D-histogram.
• Figure 5: Scatter plot of $H_Z$vs.$H_S$ made with the entropy values estimated for the Top70 clusters. The symbols and color scale of the points represents the U-P-S-M-L assembly level classification of clusters performed by ca2021. The dashed line represents the best ---power law--- fit with $\mathcal{R}^2=0.886$.