The final parsec problem presents a significant challenge in astrophysics, particularly in the study of the coalescence of binary black hole systems. This problem arises from the inefficiency of gravitational wave emission in driving the black holes together once ... 1/

... they reach a separation of approximately one parsec. Various mechanisms have been proposed to address this issue, including stellar dynamical processes, gas dynamics, and the role of massive perturbers. 2/

Binary black hole systems, composed of two black holes orbiting a common center of mass, are of great interest in astrophysics due to their role in the generation of gravitational waves and their potential impact on galactic evolution. 3/

As these systems evolve, they emit gravitational radiation that gradually reduces their separation. However, when the distance between the black holes reduces to about one parsec, the emission of gravitational waves alone becomes insufficient to further decrease ... 4/

... their separation, leading to what is known as the final parsec problem. The final parsec problem occurs because the rate of gravitational wave emission declines sharply as the black holes approach a separation of one parsec. At this stage, the gravitational radiation ... 5/

... mechanism is inefficient, and other processes must facilitate further coalescence. Without an additional mechanism, the black holes may stall at this distance, preventing their merger within a Hubble time. 6/

At separations greater than one parsec, dynamical friction against the surrounding stars and gas effectively reduces the orbital separation of the binary black holes. However, as the separation decreases, the influence of dynamical friction wanes, ... 7/

... and the binary's orbital decay stalls. This stalling point is critical because it challenges our understanding of how binary black holes can merge within a reasonable cosmic timeframe. 8/

One proposed solution involves stellar dynamical processes, particularly the interaction of the binary with nearby stars. The presence of a dense stellar environment can lead to close encounters that extract energy and angular momentum from the binary system, promoting ... 9/

... further orbital decay. Processes such as the ejection of stars from the core of the host galaxy (loss cone theory) can replenish the reservoir of stars interacting with the binary, aiding in their eventual coalescence. 10/

Gas dynamics present another potential mechanism for overcoming the final parsec barrier. In gas-rich environments, interactions with a circumbinary disk can facilitate angular momentum transfer from the binary to the surrounding gas. 11/

This interaction can drive the black holes closer together. The efficiency of this process depends on the gas density, viscosity, and the presence of instabilities within the disk. 12/

Massive perturbers, such as other massive black holes or giant molecular clouds, can induce perturbations in the orbits of the binary black holes. These perturbations can lead to variations in the binary's orbital eccentricity, enhancing the rate of gravitational wave ... 13/

... emission during pericentric passages. Such interactions can help the binary system to bridge the gap from one parsec to the regime where gravitational radiation becomes dominant again. 14/

Recent numerical simulations and observational data have provided insights into the plausibility of these mechanisms. For example, studies of galactic centers with high-resolution simulations have shown that stellar interactions can indeed drive binary black holes closer ... 15/

... than one parsec under certain conditions. Observations of active galactic nuclei (AGNs) have suggested that gas dynamics in such environments can significantly influence binary evolution. 16/

Furthermore, the detection of gravitational waves by observatories such as @LIGO and @ego_virgo has provided empirical evidence for the existence of merging binary black holes, indirectly supporting the idea that mechanisms must exist to overcome the final parsec problem. 17/

These observations have spurred theoretical advancements and more refined models of binary black hole evolution. 18/18

Thank you for the correction.

This new paper proposes that dynamical friction from a DM (dark matter) spike surrounding the SMBHs (supermassive black hole) can solve the final parsec problem, especially if the DM has a self-interaction cross section of around 1 cm²/g. In such a scenario, self-interacting dark matter (SIDM) can create an isothermal core that acts as an energy reservoir, facilitating the inspiral of SMBHs and leading to a softening of the GW spectrum at low frequencies, aligning with current data. For collisionless cold dark matter, the energy deposited by the black holes can disrupt the spike, making it unable to bridge the final parsec. However, SIDM, with a realistic velocity dependence like that produced by a massive mediator such as a dark photon, can maintain the DM spike and ensure efficient hardening of the binary. This mechanism not only addresses the final parsec problem but also fits within models addressing small-scale structure issues in cosmology. The preferred cross sections for SIDM, matching the observed GW spectrum and small-scale structure constraints, support a scenario where SIDM facilitates SMBH mergers more effectively than CDM. 👉