Gravitational slingshots around black holes in a binary

Abstract

The speed gain of a test mass from taking a gravitational slingshot around a celestial object (scattering centre) increases with the latter's speed and compactness (stronger deflection of the mass' trajectory becomes possible without it hitting the surface of the object). The black holes (BHs) in a tight binary (consisting of two black holes; we are not considering X-ray binaries), themselves moving at relativistic speeds, represent optimal scattering centres. Therefore, a sub-population of accreting matter particles, swept up into chaotic orbits around a BH binary, might repeatedly take slingshots and become accelerated to ultra-relativistic speeds (as seen by observers on Earth), ultimately escaping from the binary, as well as the fate of being devoured by a BH. The escaped particles can plausibly be observed on Earth as ultra-high-energy cosmic rays (UHECRs). Investigating such a possibility would require general relativistic slingshot formulae due to the high speeds involved and the close encounters with BHs. We derive them in this paper, and show that the percentage gain per slingshot in a particle's Lorentz factor remains undiminished even as the particle energizes up, thus demonstrating that the slingshot mechanism can in principal accelerate particles to extreme energies.PACS. 9 8.70.Sa -9 5.85.Ry -0 4.70.Bw -0 4.90.+e IntroductionUltra-high energy cosmic rays (UHECRs) [1,2] have garnered tremendous interest since they would suffer less deflection by the galactic and intergalactic magnetic fields, so their paths point roughly back at their sources, potentially helping to identify and elucidate some undoubtedly interesting extremely energetic astrophysical processes, but the nature of which have so far remained an open question. Nevertheless, more recent observations had revealed a wealth of important features in the UHECR spectrum, composition, anisotropy and (lack of) counterparts, that can guide our modelling efforts. For example, the most straightforward top-down approach, where some type of extremely heavy beyond-the-standard-model particle decays into lighter ones whose rest masses add up to only a small fraction of the parent particle's rest mass, is now somewhat disfavoured. Firstly, such processes tend to produce copious amounts of concomitant high energy photons and neutrinos, which are absent observationally [3,4]. Also, composition studies show that there should be large amounts of intermediate mass nuclei at the very highest energies [5,6,7], which would be rather perplexing in the decay picture, as one must wonder why ultra-relativistic nucleons (as decay products) all move in the same direction and remain bound inside a nuclei, instead of simply flying off in all directions.The bottom-up alternative of accelerating initially low energy particles is no less challenging. The macroscopic high energies reaching into hundreds of EeVs means that we need to find an extremely energy-dense environment that can boost the particles to exceptionally high Lorentz factors. Thankfully though, the candidate...