Compact stellar systems hosting an intermediate-mass black hole: Magnetohydrodynamic study of inflow-outflow dynamics

Context. Intermediate-mass black holes (IMBHs) have remained elusive in observations; there have been only a handful of tentative detections. One promising location for the existence of IMBHs is in dense stellar clusters such as IRS 13E in the Galactic center. Such systems are thought to be fed by stellar winds from massive Wolf–Rayet (WR) stars. Understanding the accretion dynamics in wind-fed IMBHs in such clusters is important for predicting observational signatures. These systems are, however, relatively unexplored theoretically. Understanding the interplay between IMBHs and the surrounding stars, especially through the high-velocity, dense stellar winds of WR stars, is essential for clarifying IMBH dynamics within such environments and explaining why these objects continue to evade unambiguous detection. Aims. Inspired by the IRS 13E stellar association near the Galactic center, we examined how high wind velocities, magnetic fields, and metallicity-dependent radiative cooling influence the fraction of stellar wind material captured by the black hole, the formation and survival of dense clumps, and the resulting high-energy emission. We also compared isotropic and disk-like stellar distributions to see how the flow structure and IMBH detectability may vary. Methods. We conducted three-dimensional magnetohydrodynamic and hydrodynamic simulations in which each WR star represents a source term in mass, momentum, energy, and magnetic field. A metallicity-dependent cooling function accounts for radiative energy losses. By varying the cluster’s geometry, magnetization, and chemical abundance, we characterized the resulting flow structures, accretion rates, and X-ray luminosity corresponding to the cluster and the IMBH. Results. In all configurations, the accretion rate onto the IMBH is up to five orders of magnitude lower than the total mass-loss rate from the cluster’s WR stars. High-velocity wind-wind collisions generate turbulent, shock-heated outflows that expel most injected gas. While enhanced cooling in high-metallicity runs fosters dense clump formation, these clumps typically do not reach the black hole. The integrated X-ray emission is dominated by colliding stellar winds, rendering the IMBH radiative signature elusive. Intermittent, quasi-periodic variations in inflow rates are driven by close stellar passages, leading to short-lived accretion enhancements or flares that nonetheless remain difficult to detect against the dominant wind emission. Conclusions. Despite continuous mass injection from dense stellar winds, these compact systems exhibit outflow-dominated flows and weak, though strongly variable black hole accretion, naturally explaining the low detectability of IMBHs in such settings. The observed quasi-periodic or flaring accretion episodes are overwhelmed by the luminous shock-heated winds, making unambiguous observational identification of the IMBH challenging with the current X-ray instruments. Nevertheless, our results provide a framework for interpreting current data and developing future observational strategies to unveil IMBHs in dense stellar systems.