Black hole mass limits
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Upper Mass Limits of Black Holes
Research indicates that there is a likely upper limit to black hole masses in the universe. Several studies converge on the idea that ultra-massive black holes (UMBHs) can exist, but their masses are generally capped at around 10^10 solar masses (M☉) due to physical and observational constraints. This upper limit is supported by the relationship between black hole mass and the luminosity of their host galaxy bulges, predictions from black hole seed growth models, and the observed local black hole mass function. These findings suggest that the most massive black holes are typically found in the centers of the brightest cluster galaxies, and that self-regulation mechanisms in galaxy and black hole co-evolution naturally impose this mass ceiling .
Another study refines this upper limit, showing that black holes cannot grow beyond about 5 × 10^10 M☉ through luminous gas accretion, which is the process that powers quasars and active galactic nuclei (AGN). In extreme cases, such as black holes with maximal prograde spin, this limit could reach up to 2.7 × 10^11 M☉. However, black holes that exceed this mass through mergers cannot become luminous accretors again, meaning they would not be visible as quasars or AGN but might still be detectable through other means like gravitational lensing .
Observational Evidence and Scaling Relations
Observations of quasars and galaxies support these theoretical mass limits. The largest black hole masses found in the local universe and in quasar surveys are consistent with these upper bounds, with no evidence for black holes significantly exceeding 10^10 M☉. The Eddington luminosity, which sets a physical limit on how fast black holes can accrete matter, also aligns with the observed maximum luminosities of AGN, reinforcing the idea of a mass cap 27.
The scaling relations between black hole mass and properties of their host galaxies, such as the M_bh–σ relation (linking black hole mass to stellar velocity dispersion), continue to hold down to lower masses, but at the high-mass end, these relations suggest a natural upper boundary 17.
Limits on Primordial and Intermediate-Mass Black Holes
For primordial black holes (PBHs), which could have formed in the early universe, there are strong constraints on their possible masses and abundance. Observations of the cosmic microwave background (CMB) and quasar microlensing data rule out significant populations of PBHs in the mass range of 10^6–10^9 M☉, as their formation would have left detectable imprints in the CMB or caused observable microlensing effects. These constraints mean that PBHs in this mass range cannot play a major cosmological role or account for dark matter 59.
Intermediate-mass black holes (IMBHs), with masses between 100 and 10^5 M☉, are still being searched for, but there are few solid detections. Observational limits suggest that while some low-mass galaxies may host black holes in this range, their overall abundance is low, and they do not significantly affect the upper mass limits discussed above .
Theoretical Limits in Alternative Gravity Theories
In alternative theories of gravity, such as those involving Gauss–Bonnet terms, the small mass limit of black holes is explored, but these studies also place upper bounds on certain parameters, like the coupling constant, to avoid inconsistencies such as naked singularities. However, these theoretical considerations do not significantly alter the upper mass limits established by standard astrophysical processes .
Conclusion
Current research strongly supports the existence of an upper mass limit for black holes, generally around 10^10 M☉, with extreme cases possibly reaching a few times higher. This limit is set by a combination of physical accretion processes, galaxy-black hole co-evolution, and observational constraints. Black holes can grow larger through mergers, but such objects would not be luminous and are rare. Observational and theoretical studies together provide a consistent picture of black hole mass limits across the universe 127.
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