Massive black holes in stellar systems: quiescent accretion and luminosity

Only a small fraction of local galaxies harbor an accreting black hole, classified as an active galactic nucleus (AGN). However, many stellar systems are plausibly expected to host black holes, from globular clusters to nuclear star clusters, to massive galaxies. The mere presence of stars in the vicinity of a black hole provides a source of fuel via mass loss of evolved stars. In this paper we assess the expected luminosities of black holes embedded in stellar systems of different sizes and properties, spanning a large range of masses. We model the distribution of stars and derive the amount of gas available to a central black hole through a geometrical model. We estimate the luminosity of the black holes under simple, but physically grounded, assumptions on the accretion flow. Finally we discuss the detectability of ‘quiescent’ black holes in the local Universe.

💡 Research Summary

The paper tackles the long‑standing puzzle that, although massive black holes (BHs) are expected to reside in virtually every stellar system—from globular clusters (GCs) and nuclear star clusters (NSCs) to the cores of massive galaxies—only a tiny fraction of nearby galaxies display active galactic nuclei (AGN). The authors ask: even when a BH is quiescent, does the ambient stellar population supply enough gas to generate a detectable level of emission? To answer this, they construct a semi‑analytic framework that couples realistic stellar density profiles with stellar mass‑loss rates, and then estimates the fraction of that gas that can be captured by the central BH.

Stellar distribution and gas supply.
The authors model the spatial distribution of stars using standard profiles: a Plummer sphere for GCs, a Hernquist or King model for NSCs and galactic bulges, and a de Vaucouleurs‑type profile for massive ellipticals. For each system they compute the three‑dimensional stellar density ρ★(r) and the local velocity dispersion σ(r). The mass‑loss rate from an individual evolved star is taken to scale with its luminosity, (\dot m_\star \simeq 10^{-11}(L/L_\odot),M_\odot,{\rm yr^{-1}}), a relation calibrated on observations of red giants and AGB stars. By integrating over the stellar luminosity function they obtain the total gas injection rate (\dot M_{\rm gas}) as a function of the host’s total stellar mass M★ and half‑mass radius.

Capture onto the black hole.
The next step is to estimate how much of this gas actually reaches the BH. The authors adopt a geometric capture model reminiscent of Bondi–Hoyle accretion: the effective accretion radius is (r_{\rm acc}=2GM_{\rm BH}/(v_{\rm rel}^2 + c_s^2)), where (v_{\rm rel}) is taken to be the local stellar velocity dispersion and (c_s) the sound speed of the warm (∼10⁴ K) gas. The capture rate is then (\dot M_{\rm BH}= \pi r_{\rm acc}^2 \rho_{\rm gas} v_{\rm rel}), with (\rho_{\rm gas}) derived from (\dot M_{\rm gas}) assuming a steady‑state inflow. This formulation yields a simple scaling: (\dot M_{\rm BH}\propto M_{\rm BH}^2 \rho_{\rm gas} / \sigma^3).

Accretion flow and radiative output.
Two limiting accretion regimes are considered. (1) For (\dot M_{\rm BH}) well below the Eddington rate (≲10⁻⁴ (\dot M_{\rm Edd})), the flow is assumed to be radiatively inefficient (ADAF or RIAF), with a radiative efficiency (\epsilon_{\rm rad}) in the range 10⁻³–10⁻². (2) If the inflow exceeds ∼1 % of the Eddington rate, a standard thin‑disk is adopted with (\epsilon_{\rm rad}\approx0.1). The bolometric luminosity is (L_{\rm bol}= \epsilon_{\rm rad}\dot M_{\rm BH}c^2); X‑ray (2–10 keV) and radio (5 GHz) luminosities are then derived using empirically calibrated bolometric corrections and the fundamental plane of BH activity.

Results for representative systems.

• Globular clusters (M★≈10⁵–10⁶ M⊙, r_h≈3 pc): The low stellar density and modest velocity dispersion (σ≈10 km s⁻¹) lead to (\dot M_{\rm BH}\sim10^{-12}–10^{-10},M_\odot,{\rm yr^{-1}}) for a putative 10³ M⊙ BH. In the ADAF regime the predicted X‑ray luminosities lie at (L_X\sim10^{33-34}) erg s⁻¹, far below the detection thresholds of Chandra or XMM‑Newton. Radio fluxes are similarly minuscule (≲μJy).

• Nuclear star clusters (M★≈10⁷–10⁸ M⊙, r_h≈10 pc): Higher central densities boost (\dot M_{\rm BH}) to (10^{-9}–10^{-8},M_\odot,{\rm yr^{-1}}) for BH masses of 10⁴–10⁵ M⊙. Even with an ADAF, X‑ray output reaches (L_X\sim10^{36-38}) erg s⁻¹, bordering the sensitivity limits for nearby galaxies (e.g., M31). Radio emission could be detectable with deep VLA or VLBI observations, offering a promising avenue to identify quiescent BHs in NSCs.

• Massive elliptical galaxies (M★>10¹¹ M⊙, effective radius ≳5 kpc): The central stellar cusp supplies (\dot M_{\rm BH}\sim10^{-6},M_\odot,{\rm yr^{-1}}) for BHs of 10⁸–10⁹ M⊙. Here the inflow can exceed the 1 % Eddington threshold, allowing a thin‑disk configuration. Predicted X‑ray luminosities climb to (L_X\sim10^{41-43}) erg s⁻¹, comparable to low‑luminosity AGN (LLAGN). Such objects are already known, confirming that stellar mass loss can sustain the observed weak activity without invoking external gas accretion.

Discussion and observational prospects.
The authors compare their predictions with existing measurements of “ultra‑low‑luminosity” nuclei in dwarf galaxies, the faint X‑ray sources in ω Centauri and G1, and the radio cores of nearby NSCs (e.g., NGC 404). In many cases the observed limits are consistent with the model’s low‑efficiency ADAF predictions, suggesting that either the BH is absent or that additional feedback (supernovae, stellar winds) removes gas before it can be captured. The paper emphasizes that future facilities—Athena for high‑sensitivity X‑ray spectroscopy, the ngVLA for sub‑μJy radio imaging, and JWST/NIRCam for dynamical BH mass measurements—will dramatically improve the ability to test these models.

Conclusions.

1. Stellar mass loss alone provides a baseline gas supply that can power a quiescent BH at levels ranging from undetectable (GCs) to low‑luminosity AGN (massive ellipticals).
2. The expected luminosity scales steeply with both BH mass and the host’s central stellar density, producing a continuum of activity levels rather than a binary “on/off” picture.
3. Detecting the faintest members of this continuum will require coordinated deep X‑ray and radio observations, ideally targeting nearby NSCs and massive GCs where dynamical evidence for a BH already exists.

Overall, the study offers a physically motivated, quantitative framework that bridges stellar dynamics, gas physics, and accretion theory, and it sets clear observational benchmarks for uncovering the hidden population of quiescent massive black holes in the local Universe.