Ultra-High-energy Cosmic Ray Production in Binary Neutron Star Mergers

Abstract Having previously argued that binary neutron star (BNS) mergers are the principle source of ultra-high-energy cosmic rays (UHECRs), we exploit here the highly constrained initial conditions to make quantitative predictions for the cutoff energy of various nuclei. UHECRs heavier than helium are accelerated in the magnetized turbulent outflow outside the jets to a rigidity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">cut</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">cut</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>e</mml:mi> <mml:mi>Z</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>6</mml:mn> <mml:mo>−</mml:mo> <mml:mn>9</mml:mn> </mml:math> EV, consistent with the measured value <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">cut</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>6.3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> </mml:math> EV from fitting data. This agreement strengthens the case that BNS mergers are the main site of UHECR production. The jets may accelerate protons and/or helium to cutoff energies ≈11.5 and ≈35 EeV, respectively. Such a jet component and its spallation products could explain the indication of a secondary light population at higher energy found in the analysis of M. S. Muzio et al. The relative abundances of different elements and the total energy in UHECRs per merger event will become calculable, pending advances in our understanding of the mechanism of ion uptake into the acceleration process and input from nuclear physics experiments. This scenario implies that each neutrino above 1 PeV is codirectional with a gravitational wave arriving ≈1 day earlier and that the highest-energy UHECRs have masses heavier than iron.