The merger rate of primordial-black-hole binaries (1709.06576v2)

Abstract: Primordial black holes (PBHs) have long been a candidate for the elusive dark matter (DM), and remain poorly constrained in the ~20-100 Msun mass range. PBH binaries were recently suggested as the possible source of LIGO's first detections. In this paper, we thoroughly revisit existing estimates of the merger rate of PBH binaries. We compute the probability distribution of orbital parameters for PBH binaries formed in the early Universe, accounting for tidal torquing by all other PBHs, as well as standard large-scale adiabatic perturbations. We then check whether the orbital parameters of PBH binaries formed in the early Universe can be significantly affected between formation and merger. Our analytic estimates indicate that the tidal field of halos and interactions with other PBHs, as well as dynamical friction by unbound standard DM particles, do not do significant work on nor torque PBH binaries. We estimate the torque due to baryon accretion to be much weaker than previous calculations, albeit possibly large enough to significantly affect the eccentricity of typical PBH binaries. We also revisit the PBH-binary merger rate resulting from gravitational capture in present-day halos, accounting for Poisson fluctuations. If binaries formed in the early Universe survive to the present time, as suggested by our analytic estimates, they dominate the total PBH merger rate. Moreover, this merger rate would be orders of magnitude larger than LIGO's current upper limits if PBHs make a significant fraction of the dark matter. As a consequence, LIGO would constrain ~10-300 Msun PBHs to constitute no more than ~1% of the dark matter. To make this conclusion fully robust, though, numerical study of several complex astrophysical processes - such as the formation of the first PBH halos and how they may affect PBH binaries, as well as the accretion of gas onto an extremely eccentric binary - is needed.

• The paper analytically derives the initial orbital parameter distribution of PBH binaries through tidal torque effects and high eccentricity analysis.
• It demonstrates that early-formed PBH binaries likely dominate merger rates, influencing gravitational wave signals if PBHs are a significant dark matter fraction.
• The study sets tight constraints on PBH mass contributions to dark matter and paves the way for future numerical simulations in cosmology.

An Analytical Exploration of Primordial Black Hole Binary Merger Rates

In the paper of astrophysics and cosmology, the exploration of dark matter's nature remains one of science's foremost enigmas. Primordial black holes (PBHs) are once again at the forefront of dark matter candidates, reinvigorated by the detection of gravitational waves by LIGO, which may potentially be attributed to PBH binaries. The paper "The merger rate of primordial-black-hole binaries" by Ali-Haïmoud, Kovetz, and Kamionkowski offers a detailed examination of the merger rates for PBH binaries. This analysis leverages their early cosmic formation probabilities and scrutinizes conventional assumptions about their subsequent survival and merging.

The authors apply the foundational work of Nakamura et al. [NSTT], which posits that some PBHs form binaries shortly after creation due to proximity and gravitational attraction, settling into highly eccentric orbits. The paper provides a crucial update by analytically deriving the distribution of these binary systems' initial orbital parameters and reevaluating their survival as bound systems up to the present epoch. The principal focus is on understanding these binaries' dynamical interactions within the cosmological structure from formation until merger and assessing if these interactions might disrupt their early stability.

Fundamental Approaches and Considerations

The paper systematically revisits earlier calculations, emphasizing the role of tidal torques from surrounding structures such as other PBHs and adiabatic perturbations in the early Universe. Accounting for these factors, the authors derive a probability distribution for the initial semi-major axes and eccentricities of PBH binaries. They determine that these PBHs do indeed form extremely tight binaries due to their initial high eccentricity. The characteristic parameter estimations suggest that a significant merger rate persists, potentially contributing detectable gravitational wave signatures given a significant PBH component in dark matter.

Moreover, one of the critical findings is their conclusion about the dominance of PBH binaries formed in the early Universe, over those possibly formed in present-day halos through dynamic capture processes. Such binaries bear the bulk of the observed merger rate if they endure until the current era.

Implications and Future Directions

The merger rates derived under the assumption that PBHs constitute all dark matter exceed LIGO's recent upper limits and would impose substantial constraints if directly applied. The paper provides upper-bound predictions suggesting that if PBHs are indeed a major dark matter component, their masses in the given ranges are limited to less than a few percent. The paper essentially lays a foundation for improved LIGO data analyses and sets boundaries for future observational constraints on dark matter hypotheses.

An integral future direction points towards more robust numerical simulations to rigorously validate these theoretical predictions. These should include the paper of complex phenomena such as the evolution of PBHs in their gas accretion phase, the dark matter halo's granular effects on PBH orbits, and the evolution and impact of early cosmic structures on the PBH binary systems spanning cosmic time scales.

Conclusion

The meticulous analytical paper provided by Ali-Haïmoud et al. serves an influential role in the continuing narrative of understanding dark matter and the Universe's gravitational frameworks. By probing the dynamical properties and interactions of PBHs through comprehensive analytic methods, this work aids in deciphering not only the origins and live-experiences of these cosmic entities but also furnishes the theoretical backing necessary to adjudicate the role of primordial structures within the vast cosmological context. This paper, therefore, represents a crucial intersection of theory and observation, poised to shape upcoming gravitational wave detections and dark matter research.