Is there an upper limit to black hole masses?

Abstract: We make a case for the existence for ultra-massive black holes (UMBHs) in the Universe, but argue that there exists a likely upper limit to black hole masses of the order of $M \sim 10^{10} \msun$. We show that there are three strong lines of argument that predicate the existence of UMBHs: (i) expected as a natural extension of the observed black hole mass bulge luminosity relation, when extrapolated to the bulge luminosities of bright central galaxies in clusters; (ii) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger-induced accretion inevitably leads to the existence of rare UMBHs at late times; (iii) the local mass function of black holes computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at $z = 0$. Consistency between the optical and X-ray census of the local black hole mass function requires an upper limit to black hole masses. This consistent picture also predicts that the slope of the $M_{\rm bh}$-$\sigma$ relation will evolve with redshift at the high mass end. Models of self-regulation that explain the co-evolution of the stellar component and nuclear black holes naturally provide such an upper limit. The combination of multi-wavelength constraints predicts the existence of UMBHs and simultaneously provides an upper limit to their masses. The typical hosts for these local UMBHs are likely the bright, central cluster galaxies in the nearby Universe.

• The paper demonstrates that extrapolating the black hole mass–bulge luminosity relation predicts ultra-massive black holes with an upper limit of approximately 10^10 M☉.
• It employs high-redshift seed mass functions and local AGN observations to argue that self-regulation mechanisms impose a natural cap on black hole growth.
• The study highlights the need for high-resolution spectroscopy to overcome observational challenges and confirm the existence of these extreme black hole candidates.

On the Existence and Upper Limit of Ultra-Massive Black Holes

The paper by Natarajan and Treister explores the intriguing question of whether there is an upper bound to the masses of black holes (BHs) in the universe, particularly focusing on ultra-massive black holes (UMBHs). The authors argue for the presence of a likely upper mass limit of approximately $10^{10} M_{\odot}$. Their investigation is grounded on several theoretical and observational considerations.

Basis for UMBH Existence

The existence of UMBHs is substantiated through three primary arguments:

1. Extrapolation of the Black Hole Mass-Bulge Luminosity Relation: The observed relation between black hole masses and the luminosity of their host galaxy bulges, when extended to the bright central galaxies in clusters, predicts the existence of UMBHs.
2. High-Redshift Seed Mass Functions: Theoretical predictions suggest that black holes originating from massive seeds at high redshifts have had sufficient time to grow into UMBHs through accretion and mergers as they evolve to lower redshifts.
3. Local Mass Function Observations: The mass distribution of active galactic nucleus (AGN) black holes implies a high-mass tail at redshifts close to zero, indicative of UMBH presence.

These arguments underscore the necessity of UMBH existence while also supporting the presence of a natural mass cap to ensure consistency across observational data.

Implications and Predictions

In assessing the implications of these findings, the paper highlights several salient points:

• Theoretical Self-Regulation Models: The limitations on BH growth theorized by self-regulation mechanisms play a crucial role in defining the upper limits of BH masses. These mechanisms propose that the energy output of active black holes can inhibit the infall of surrounding matter, effectively capping growth beyond a certain mass threshold.
• Evolution of Scaling Relations: The relationship between black hole mass and the velocity dispersion of the host galactic bulge, i.e., the $M_{\rm bh}-\sigma$ relation, is anticipated to evolve at higher mass ranges with redshift. This evolution may be a result of the complex feedback processes governing both star formation and black hole accretion.

Observational Challenges and Future Directions

The authors address the observational challenges involved in detecting these extremely rare UMBHs, primarily located in the cores of brightest cluster galaxies. While the Sloan Digital Sky Survey (SDSS) hints at potential candidates with large velocity dispersions, confirmatory observations are necessary to solidify these approximations. Further observational campaigns, particularly using instruments capable of high-resolution spectroscopy and spatially resolved kinematics, are essential for identifying and characterizing these elusive objects.

Conclusion

This paper provides a comprehensive theoretical and observational framework for understanding the conditions under which UMBHs might exist and the mechanisms that could impose an upper limit on their masses. Future developments in both numerical simulations and observational astrophysics will be crucial for testing these hypotheses and enhancing our understanding of black hole demographics across cosmic time.