Direct collapse of exceptionally heavy black holes in the merger-driven scenario

Abstract

We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at red-shift z ∼ 10. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within ∼5 × 105 yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typical flux and a typical strain amplitude at Earth of ∼10−8 erg s−1 cm−2 and ∼4 × 10−21. We provide a simple fitting formula for the the resulting black hole masses, which range from a few 106 M⊙ to 108 M⊙ depending on the initial SMD configuration. Crucially, our analysis does not require any specific assumption on the thermal properties of the gas, nor on the angular momentum loss mechanisms within the SMD. Led by these findings, we argue that the merger-driven scenario provides a robust pathway for the rapid formation of supermassive black holes at z > 6. It provides an explanation for the origin of the brightest and oldest quasars without the need of a sustained growth phase from a much smaller seed. Its smoking gun signatures can be tested directly via multi-messenger observations.

Direct Formation of Massive Black Holes via Dynamical Collapse in Metal-enriched Merging Galaxies at z ∼ 10: Fully Cosmological Simulations

“…Indeed, when the SMD reaches its largest mass following the gas inflow at the final merger time, 3 × 10 8 M e , the Jeans length is as small as λ J ∼ 0.01 pc (for a mean temperature of 100 K), which clearly implies that the SMD, had we had enough resolution, should contract to a much smaller size. Because of the high density and correspondingly high optical depth, the contraction will occur adiabatically, with the temperature evolving as T ∼ 1/R (Zwick et al 2023), hence the temperature will increase to nearly 10 4 K for a 2 orders of magnitude decrease in disk size, which would be very comparable with the temperature observed in the binary merger simulations of Mayer et al (2015) with a much smaller gravitational softening. The SMD is a differential rotator, hence Jeans collapse is just a crude indication that contraction should continue.…”

“…The SMD is a differential rotator, hence Jeans collapse is just a crude indication that contraction should continue. The disk will likely become globally unstable to nonaxisymmetric instabilities and then contract as a result of the internal transport of angular momentum, as discussed in Zwick et al (2023). With a softening comparable to the characteristic radius of a system, such instabilities are suppressed (see, e.g., Kaufmann et al 2007 for a relevant numerical study in the context of bars in galactic disks).…”

“…The physical arguments just outlined suggest that the disky core should shrink in size by about an order of magnitude. Zwick et al (2023) have shown that for such a compact SMD, further dynamical or (secular) viscous transport of angular momentum will bring the system to the conditions of the global GR radial instability for a wide range of structural parameters. Therefore, we repeated the calculations in the analytical SMD evolution model of Zwick et al (2023), using the maximum central gas mass reached in the isolated simulation, 3 × 10 8 M e , which is about a factor of 3.5 smaller than the default range based on the numerical results of Mayer et al (2015).…”

“…Zwick et al (2023) have shown that for such a compact SMD, further dynamical or (secular) viscous transport of angular momentum will bring the system to the conditions of the global GR radial instability for a wide range of structural parameters. Therefore, we repeated the calculations in the analytical SMD evolution model of Zwick et al (2023), using the maximum central gas mass reached in the isolated simulation, 3 × 10 8 M e , which is about a factor of 3.5 smaller than the default range based on the numerical results of Mayer et al (2015). Figure 8 illustrates our results on the predicted BH mass following the GR instability, as a function of the initial temperature of the SMD and of the slope n of its density profile.…”

“…The possibility has also been conjectured that a fully fledged SMS never forms; rather, a proto-SMS would turn directly into a very massive BH seed of 10 7 -10 9 M e , a formation route dubbed "dark collapse" (Mayer & Bonoli 2019;Haemmerlé et al 2020Haemmerlé et al , 2021. This latter direct formation route, which essentially overrides the BH seed formation stage altogether, has been studied, and shown to be plausible, in the analytical model of Zwick et al (2023), which adopts the central SMD found in the previously published simulations as a starting condition.…”