New parameters for star cluster dynamics: observational results

TL;DR

This study validates new empirical nCRD parameters $A_5$ and $P_5$ (and $S_{2.5}$ in simulations) as robust tracers of globular cluster dynamical aging by applying them to a homogeneous set of 40 Galactic GCs with HST UV photometry. The observed $A_5$ and $P_5$ follow the trends predicted by MOCCA simulations, showing steeper inner cumulative radial distributions for more dynamically evolved clusters and anti-correlations with the central relaxation time $t_{rc}$. A revised separation between pre- and post-core-collapse states is proposed ($A_5>0.008$, $P_5>0.47$), and strong correlations with $A^+_{rh}$ further support the utility of these metrics for dynamical-age assessments and for flagging clusters that may host intermediate-mass or stellar-mass black holes. While powerful, the method requires high-resolution, complete UV photometry to 0.5 $r_h$ and careful handling of $r_h$ in PCC clusters, motivating future refinements and joint usage with kinematic data for BH searches within the GENESIS project.

Abstract

We recently used a large set of Monte Carlo simulations of globular clusters (GCs) to define new fully empirical parameters (named A5, P5, and S2.5) able to trace the internal dynamical evolution of dense stellar systems. These parameters are specifically designed to quantify the steepness of the cumulative radial distribution of stars in the innermost region of the host system, which tends to progressively increase with dynamical aging due to core contraction. Following the original definitions, here we measure A5 and P5 in a sample of 40 Galactic GCs homogeneously surveyed through HST photometric observations. In agreement with the predictions of our simulations, the largest values of A5 and P5 are found for the most dynamically evolved GCs, i.e., those previously classified as post-core collapse systems based on the shape of their density profile, and those characterized by the shortest central relaxation times. Moreover, the new dynamical parameters here measured strongly correlate with A+rh, another fully empirical, independent parameter that traces the dynamical age of star clusters through the level of central segregation of blue straggler stars.

Figures (6)

• Figure 1: Projected density profile corrected for Galactic field contamination (black circles) for the PCC clusters NGC 6624, NGC 6681, and NGC 7099 (left, central and right panels, respectively). In each case, the values of the best-fit king66 model parameters are labeled, and the bottom panel shows the residuals between the model and the observations.
• Figure 2: Observed nCRDs of the 40 GCs analyzed in this work. The red lines refer to the four PCC systems in the sample, the blue lines to the other GCs. The right panel shows a zoom in the innermost region (out to $0.05 \times r_h$), where the nCRD parameters are measured. In both panels, the gray shaded areas correspond to the region occupied by the nCRDs of the B24 simulated clusters.
• Figure 3: $P_5$ parameter plotted as a function of $A_5$ for the 40 surveyed GCs, with the blue circles referring to pre-CC systems, and the red squares marking PCC clusters. The gray circles show the results from the Monte Carlo simulations of B24. The dashed lines mark the limits in $A_5$ and $P_5$ proposed by B24 as boundaries to separate pre-CC from PCC clusters. The solid lines mark the revised limits proposed here.
• Figure 4: $A_5$ parameter as a function of the best-fit King model concentration $c$ for the observed clusters (colored symbols, as in Fig. \ref{['a5p5']}) and for the B24 simulations (gray circles). The solid horizontal line marks the proposed $A_5$ boundary separating pre-CC from PCC systems. The thick black curve traces the values of $A_5$ calculated from the integration of King density profiles of varying concentration parameters $c$.
• Figure 5: $A_5$ and $P_5$ parameters (right and left panels, respectively) as a function of the central relaxation time, in logarithmic units. The meaning of the symbols and horizontal line is as in Fig. \ref{['conc']}. The gray symbols encircled in green and orange correspond, respectively, to the simulated clusters that, at an age of 13 Gyr, host a central IMBH (green) and at least 30 stellar-mass BHs (orange).