Constraints on Primordial Black Holes from $N$-body simulations of the Eridanus II Stellar Cluster

TL;DR

This study uses both semi-analytic diffusion modeling and non-cosmological N-body simulations to constrain primordial black holes (PBH) as dark matter via dynamical heating of Eridanus II’s central star cluster. The analytic framework yields a diffusion-based heating term $D[(\Delta v)^2]$ and a half-radius evolution equation $\frac{d r_\mathrm{h}}{dt}$, while the simulations implement a three-component system (stars, PBH, and background DM) in a fixed NFW halo to track $r_\mathrm{h}$ over $13.5\ \text{Gyr}$. They find that PBH must be lighter than about $1\ M_\odot$ if they constitute all the DM, and derive $f_\mathrm{PBH}$-versus-$m_\mathrm{PBH}$ constraints that are generally stronger than semi-analytic expectations, particularly for centrally concentrated DM halos and lower PBH velocity dispersions. The results provide robust, model-informed limits on macroscopic DM scenarios and guide future high-precision dynamical probes using ultra-faint dwarf galaxies.

Abstract

The evolution of old, compact stellar structures provides strong constraints on macroscopic dark matter candidates such as primordial black holes. In view of recent observational data for the Eridanus II dwarf galaxy, we perform the first $N$-body simulations of its central stellar cluster to model dynamical heating by PBHs. We find evidence that such candidates must be lighter than about one solar mass if they constitute the totality of the dark matter. We additionally derive constraints on the fraction of the dark matter in macroscopic objects as a function of mass, by modeling the remainder of the dark matter as standard, fluid-like cold dark matter.

Figures (6)

• Figure 1: Evolution of the half-light radius over a time span of $14 ~ \text{Gyr}$. The radius expands due to dynamical heating of the star cluster caused by PBH with masses $m_{\text{PBH}} = 30 ~ M_{\odot}$, PBH dispersion $\sigma_\text{PBH} = 5 ~ \mathrm{km\,s}^{-1}$ and cluster velocity dispersion $\sigma_{\rm{cluster}} = 2 ~ \mathrm{km\,s}^{-1}$. The star cluster has an initial half-light radius of $r_{\textrm{h}} = 1 ~ \mathrm{pc}$. We show the evolution for different DM densities and star cluster masses, as indicated in the legend. Each curve is obtained by solving Eq. (\ref{['eq:half_light_radius']}) for a PBH abundance of $f_{\text{PBH}} = 1.0$.
• Figure 2: Semi-analytical constraints on PBH based on the survival of the star cluster in Eri II assuming a star cluster age of $13.5 ~ \text{Gyr}$. Four different scenarios are represented with PBH densities $[0.02, 1.0] ~ M_{\odot}\,\text{pc}^{-3}$, PBH dispersion $[5.0, 10.0] ~ \mathrm{km\,s}^{-1}$ and stellar velocity of $2 ~ \mathrm{km\,s}^{-1}$. These scenarios involve PBH masses $m_{\text{PBH}}$ ranging from $1$ to $10^4 ~ M_{\odot}$. The constraints are derived by requiring that the time it takes the star cluster to grow from $r_{\text{h,initial}} = 2 ~ \text{pc}$ to its current observed size of $r_{\text{h,final}} = 13 ~ \text{pc}$ does not exceed $13.5 ~ \text{Gyr}$.
• Figure 3: Snapshots of the initial condition state of the Eridanus II galaxy for $f_{\textrm{PBH}} = 0.1$ and $m_{\rm PBH} = 10^4 ~ M_{\odot}$. Snapshot in the $xy$-plane. Background DM particles are indicated in purple, PBH in black, and stars in yellow. Upper right panel: Zoom-in snapshot of the simulation in the $xy$-plane. Both snapshots are at $t=0.0 ~ \text{Gyr}$.
• Figure 4: Evolution of the half-mass radius over $13.5 ~ \textrm{Gyr}$ for different PBH masses. At each timestep and for each value of $f_\textrm{PBH}$, the curves show the median half-mass radius over 50 simulations, with error bars corresponding to the 16th–84th percentile interval.
• Figure 5: Constraints on $f_{\text{PBH}}$ as a function of $m_{\text{PBH}}$. Limits are derived using the median $r_{\rm h}$ over $50$ simulations for each mass. Also shown is a conservative case using $r_{\rm h}$ one standard deviation below the median. The red and brown lines are the semi-analytically derived constraints.