The scientific world is constantly working to unravel the various mysteries of the universe. Among these, understanding the nature of dark matter (DM) is one of the most intriguing complexities in fundamental physics.
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While the exploration of DM originates in astrophysics and cosmology, efforts to unveil its mysteries have extended to particle physics experiments, including those conducted at colliders and in DM detection experiments.1
One remarkable prediction of general relativity is that when a mass (M) collapses within its Schwarzschild radius, it forms a black hole—a region where the gravitational field is so intense that even light cannot escape.
Black holes may exist across various mass scales, including those termed "primordial," which could have formed in the early Universe.2
Primordial Black Holes (PBHs) emerged in the early moments of the Universe, preceding the formation of the first stars. Studying PBHs could offer valuable insights into the physical processes occurring during this relatively unexplored period.
DM plays a crucial role in the identification of PBHs, as its presence affects their interactions—the presence of DM spikes influences whether PBHs collide rapidly or undergo a slower merging process, depending upon specific conditions.3
Primordial Black Holes: An Overview
Understanding the formation of stars and galaxies toward the conclusion of the cosmic dark ages—a period occurring a few hundred million years after the Big Bang—stands as a pivotal objective in modern cosmology.
The formation of PBHs is a fundamental aspect of studying galaxy formation. It is well-established that the nuclei of most galaxies contain black holes. Remarkably, numerous quasars hosting black holes with masses of 109 M⊙ have been observed at redshifts higher than six, indicating their presence when the Universe was less than a billion years old.4
PBHs are believed to originate from substantial curvature fluctuations in the early universe, leading to direct gravitational collapse and the formation of black holes. Regardless of the specific formation mechanism, PBHs become dynamically linked to cosmic expansion, resulting in negligible peculiar velocities.
PBHs typically become gravitationally bound to one another when their local density matches that of the surrounding radiation, a process that typically occurs after matter-radiation equality.5
Scientists also hypothesize that primordial black holes may have formed within the first second of the universe’s formation.
During this time, pockets of dense hot material could have condensed to form black holes, with potential masses ranging from 100,000 times less than a paperclip to 100,000 times more than the Sun's mass. As the universe rapidly expanded and cooled, the conditions conducive to the formation of black holes in this manner ceased.6
Now, 13.8 billion years later, the search for definitive evidence of PBHs continues. One plausible theory suggests that some PBHs have gradually evaporated over time as the cosmos aged, owing to quantum mechanical processes occurring at the edges of their event horizons.
Exploring the Relationship Between DM Spikes and PBHs
The formation possibility of PBHs, as predicted by Zeldovich and Novikov in 1967 and further explored by Hawking in 1971, provides valuable insights into early universe processes.
If formed in significant quantities, PBHs can themselves constitute DM, or they can act as seeds for the formation of DM clumps. Secondary accretion in cold DM onto a PBH—where DM flows toward the PBH and forms a halo upon virialization at a certain radius—is a key focus in studies of DM clumps surrounding PBHs.7
The density of DM around PBHs can significantly exceed that of secondary accretion. This is because, within the thermal velocity distribution, DM particles exist with sufficiently low velocities that maintain finite orbits around PBHs unaffected by cosmological expansion. The accumulation of these particles around PBHs leads to the formation of density spikes.7
During the radiation-dominated epoch, primordial curvature perturbations (ζ) at a given scale wavenumber (k) facilitate the growth of linear-order DM density perturbations (δ). This growth occurs due to un-accelerated particle drift, with particles traversing comoving distances that scale logarithmically with the scale factor (a).
Initially, these particles are propelled by the transient peculiar potential as they enter the horizon before being homogenized by radiation pressure. Given the negligible impact of peculiar gravitational forces, analyzing ellipsoidal collapse becomes relatively straightforward, allowing for independent drift along each axis.8
DM clumps can arise from several mechanisms, including cosmological density perturbations within the DM itself or around compact seed masses, such as cosmic strings or primordial black holes.
While secondary accretion has been traditionally viewed as the primary method of DM accumulation around PBHs, recent findings suggest an alternative mechanism that results in denser DM clumps than those predicted by secondary accretion models.9
During the radiation-dominated stage, the density of DM around PBHs increases due to the presence of slow DM particles in their thermal velocity distribution.
Following their kinetic decoupling, these relatively slow particles orbit PBHs in finite orbits, resulting in the formation of high-density DM clumps. The density profile of these clumps can be determined by considering the kinematics of particles around PBHs.
While DM particles in the clumps' central regions may have already annihilated, the surrounding halos remain densely packed, fostering intense annihilation within them—an aspect of considerable interest for experiments aimed at the indirect detection of DM particles through their annihilation products.9
In scenarios where non-relativistic DM decouples from radiation (as large-amplitude initial density variations enter the horizon), ultradense DM spikes and minihaloes are expected to vastly outnumber PBHs.
This DM could manifest as particle DM or smaller PBHs, leading to two potential scenarios: either PBHs constitute a minor portion of the DM with ultra-dense haloes forming from particles, or PBHs account for all DM but with a mass distribution that spans many orders of magnitude, resulting in ultradense haloes comprised of clusters of smaller PBHs.8
The Influence of DM Spikes on PBH Merger Rates
Observations made by the LIGO-Virgo-Kagra (LVK) collaboration, using gravitational wave detection, could be enhanced by the mergers of PBHs.
Recent studies have examined the dynamics of PBH binaries enveloped by DM spikes, particularly for PBHs characterized by extended mass functions. These studies have explored PBH binary systems with DM spikes spanning a wide range of masses and have provided estimates for their merger rates.
Recent calculations have confirmed that the mass of the DM spike accumulated around an isolated PBH is directly correlated with the mass of the PBH itself.
Novel research has shown, for the first time, that the influence of DM spikes on the formation of PBH binaries is consistent, regardless of the PBHs' individual masses.
The impact of DM spikes on the orbital parameters escalates with the scale factor at which the binary formation occurs, allowing more time for the DM spike to expand.10
The merger rates of PBH binaries, particularly within extended mass functions, demonstrate complex behavior. Studies have revealed that, in scenarios involving evaporated DM spikes, the merger rates can fluctuate by approximately a factor of two. This is because DM spikes can expedite the merging process of PBH binaries.
Looking ahead, it is crucial to develop a method that accounts for the feedback from DM spikes in highly eccentric systems. Such a prescription would enable the creation of a more comprehensive and generalized approach, allowing for a deeper exploration of the actual merger dynamics of PBH binaries surrounded by DM spikes.
Such advancement would contribute significantly to our understanding of these systems and their behavior.
Quantifying DM Spikes Surrounding PBHs
Upcoming ground-based gravitational wave observatories are poised to detect binary black hole mergers across remarkable distances. While most observed events will likely be close-to-equal mass mergers, the improved sensitivity and expanded frequency range of the newly suggested Einstein Telescope and Cosmic Explorer observatories will also facilitate the observation of intermediate-mass ratio mergers.11
The planned frequency ranges for Cosmic Explorer, f ∼ [5, 5000] Hz, and Einstein Telescope, f ∼ [1, 5000] Hz, indicate that these observatories will be capable of detecting long-duration signals from light systems. The identification of such systems is expected to have significant implications for gravitational wave astronomy and fundamental physics.
Employing a suitable model for parameter estimation—one that incorporates the influence of the DM spike on the waveform—it will be possible to reconstruct and precisely calculate the mass ratio and various parameters of the spike, including its density normalization and the power law governing the DM density profile, with just a week's worth of data.
The Einstein Telescope is also projected to measure the parameters of DM spikes with greater precision than the Cosmic Explorer. This is attributed to its lower frequency reach, which allows for the observation of more cycles and, thus, the accumulation of more dephasing.12
The Future of PBHs
Support for the hypothesis that PBHs exist comes from various sectors, including DM physics, astrophysics, gravitational microlensing, and quantum cosmology. Distinct from their astrophysical counterparts, PBHs are primarily differentiated by their unique redshift and mass distributions, presenting two key characteristics that set them apart.13
PBHs exhibit a range of potentially interesting direct gamma-ray signals associated with Hawking evaporation. Exploding PBHs, which represent the late-time limit of Hawking evaporation for small PBHs, offer intriguing candidates for future very high-energy gamma-ray telescopes. These telescopes may investigate transient phenomena, particularly related to the new frontier of PBHs of ultralow masses.
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References and Further Reading
[1] Arbey, A., et al. (2021). Dark matter and the early Universe: a review. Progress in Particle and Nuclear Physics. doi.org/10.1016/j.ppnp.2021.103865
[2] Carr, B., et al. (2022). Primordial black holes as dark matter candidates. SciPost Physics Lecture Notes. doi.org/10.21468/SciPostPhysLectNotes.48
[3] Feldman, A. (2024). Astronomers might have a shot at imaging primordial black holes. [Online] Advanced Science News. Available at: https://www.advancedsciencenews.com/astronomers-might-have-a-shot-at-imaging-primordial-black-holes/ (Accessed on 29 March 2024).
[4] Latif, M. et al. (2013). Black hole formation in the early Universe. Monthly Notices of the Royal Astronomical Society, 433(2). doi.org/10.48550/arXiv.1304.0962
[5] Raidal, M., et al. (2019). Formation and evolution of primordial black hole binaries in the early universe. Journal of Cosmology and Astroparticle Physics. doi.org/10.1088/1475-7516/2019/02/018
[6] NASA. (2024). Black Holes Types. [Online] Nasa. Available at: https://science.nasa.gov/universe/black-holes/types/ (Accessed on 31 March 2024).
[7] Eroshenko, Y., et al. (2016). Dark matter density spikes around primordial black holes. Astron. Lett. doi.org/10.1134/S1063773716060013
[8] Delos, M., et al. (2023). Ultradense dark matter haloes accompany primordial black holes. Monthly Notices of the Royal Astronomical Society. doi.org/10.1093/mnras/stad356
[9] Eroshenko, Y. (2024). Dark Matter Density Spikes around Primordial Black Holes. [Online] Institute for Nuclear Research. Available at: https://ar5iv.labs.arxiv.org/html/1607.00612 (Accessed on 2 March 2024).
[10] Jangra, P., et al. (2023). Impact of dark matter spikes on the merger rates of Primordial Black Holes. Journal of Cosmology and Astroparticle Physics. doi.org/10.1088/1475-7516/2023/11/069
[11] Evans, M., et al. (2021). A horizon study for cosmic explorer: science, observatories, and community. arXiv preprint arXiv:2109.09882. doi.org/10.48550/arXiv.2109.09882
[12] Cole, P., et al. (2022). Measuring dark matter spikes around primordial black holes with Einstein Telescope and Cosmic Explorer. arXiv preprint arXiv:2207.07576. doi.org/10.1103/PhysRevD.107.083006
[13] Riotto, A., Silk, J. (2024). The Future of Primordial Black Holes: Open Questions and Roadmap. arXiv preprint arXiv:2403.02907. doi.org/10.48550/arXiv.2403.0290
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