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Black Holes in Globular Clusters: A Structural and Kinematic Perspective

Alessandro Della Croce

TL;DR

The paper addresses inferring the present-day stellar-mass BH population in globular clusters and shows that a single observable can be degenerate with different BH fractions depending on dynamical history, formalized as the BH mass fraction $M_{BH}/M_{GC}$. Using 101 MOCCA simulations with two natal-kick prescriptions, they evaluate structural and kinematic proxies such as the mass-segregation indicator, luminosity density, the core-to-half-light radius indicator $R_{hl}$, dynamical age, and the inverse of the equipartition mass, and identify the need to combine indicators. They reveal that while larger BH fractions correlate with these measures, distinct BH fractions can produce similar observables, motivating the combined diagnostic of Δ and the velocity-dispersion ratio $sigma_{central}/sigma_{global}$ to break degeneracies. The results broadly agree with Galactic GC data but current observations are insufficient to tightly constrain $M_{BH}/M_{GC}$; future high-precision astrometric and photometric surveys (e.g., Roman) could tighten these constraints and inform gravitational-wave progenitor demographics.

Abstract

Black holes (BHs) play a major role in the structural and dynamical evolutions of Globular Clusters (GCs). Several recent works searched for BHs in Galactic GCs using scaling relations derived from numerical simulations. However, the conclusions drawn by such approaches are strongly dependent on the specific prescriptions adopted in numerical simulations. Therefore, we analyzed a survey of 101 Monte Carlo simulations to identify some observable parameters that allow us to probe the present-day BH population in GCs reliably. We thoroughly show that a single observable is not suited to infer the BH mass fraction in real GCs: similar values could be attained by systems with different BH mass fractions, depending on the specific dynamical evolution of the system. Finally, we present a combination of observable parameters that efficiently breaks this degeneracy. We also compare values from numerical simulations with a sample of Galactic GCs.

Black Holes in Globular Clusters: A Structural and Kinematic Perspective

TL;DR

The paper addresses inferring the present-day stellar-mass BH population in globular clusters and shows that a single observable can be degenerate with different BH fractions depending on dynamical history, formalized as the BH mass fraction . Using 101 MOCCA simulations with two natal-kick prescriptions, they evaluate structural and kinematic proxies such as the mass-segregation indicator, luminosity density, the core-to-half-light radius indicator , dynamical age, and the inverse of the equipartition mass, and identify the need to combine indicators. They reveal that while larger BH fractions correlate with these measures, distinct BH fractions can produce similar observables, motivating the combined diagnostic of Δ and the velocity-dispersion ratio to break degeneracies. The results broadly agree with Galactic GC data but current observations are insufficient to tightly constrain ; future high-precision astrometric and photometric surveys (e.g., Roman) could tighten these constraints and inform gravitational-wave progenitor demographics.

Abstract

Black holes (BHs) play a major role in the structural and dynamical evolutions of Globular Clusters (GCs). Several recent works searched for BHs in Galactic GCs using scaling relations derived from numerical simulations. However, the conclusions drawn by such approaches are strongly dependent on the specific prescriptions adopted in numerical simulations. Therefore, we analyzed a survey of 101 Monte Carlo simulations to identify some observable parameters that allow us to probe the present-day BH population in GCs reliably. We thoroughly show that a single observable is not suited to infer the BH mass fraction in real GCs: similar values could be attained by systems with different BH mass fractions, depending on the specific dynamical evolution of the system. Finally, we present a combination of observable parameters that efficiently breaks this degeneracy. We also compare values from numerical simulations with a sample of Galactic GCs.
Paper Structure (5 sections, 2 figures)

This paper contains 5 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Numerical simulations
  4. Observations
  5. Conclusions

Figures (2)

  • Figure 1: Mass segregation parameter as a function of the velocity dispersion ratio. Symbols show whether the simulation had (diamond) or did not have (upside-down triangle) the fallback prescription for BH formation. Different colors show the BH mass fraction at 13 Gyr. The figure was reproduced from dellacroce_etal2024c.
  • Figure 2: $\Delta_{\rm obs}$ within $R_{\rm hl}$ (left panel) and $0.7 R_{\rm hl}$ (right panel) as a function of the velocity dispersion ratio. Simulation values were recomputed by adopting the same magnitude and spatial selections as in the observations. In blue, we show the values (along with error bars) obtained for Galactic GCs with at least 100 stars with PM measurements. The figure was reproduced from dellacroce_etal2024c.