Binary Coalescences as Sources of Ultrahigh-Energy Cosmic Rays

Binary coalescences are known sources of gravitational waves (GWs) and they encompass combinations of black holes (BHs) and neutron stars (NSs). Here we show that when BHs are embedded in magnetic fields ($B$’s) larger than approximately ${10}^{10}\mathrm{G}$, charged particles colliding around their event horizons can easily have center-of-mass energies in the range of ultrahigh energies ($\gtrsim {10}^{18}\mathrm{eV}$) and become more likely to escape. Such $B$-embedding and high-energy particles can take place in BH-NS binaries, or even in BH-BH binaries with one of the BHs being charged (with charge-to-mass ratios as small as ${10}^{-5}$, which do not change GW waveforms) and having a residual accretion disk. Ultrahigh center-of-mass energies for particle collisions arise for basically any rotation parameter of the BH when $B\gtrsim {10}^{10}\mathrm{G}$, meaning that it should be a common aspect in binaries, especially in BH-NS ones given the natural presence of a $B$ onto the BH and charged particles due to the magnetosphere of the NS. We estimate that the number of ultrahigh center-of-mass collisions ranges from a few up to millions before the merger of binary compact systems. Thus, binary coalescences may also be efficient sources of ultrahigh energy cosmic rays (UHECRs) and constraints to NS/BH parameters would be possible if UHECRs are detected along with GWs.

Figure 1

Energy of a proton ($E_p=E_{\max }$) as a function of the rotation parameter $a/M$ for values of the magnetic field of normal pulsars. The points correspond to the BH rotation parameters and masses present in the LIGO-Virgo-KAGRA catalogs (summarized in the Supplemental Material [79]). Each marker or colored zone corresponds to a given value of $B$. We have chosen for all figures of this Letter $L_1=2.63245M{m}_p$, $L_2=2.08944M{m}_p$, and ${\mathcal{E}}_1/m_p={\mathcal{E}}_2/m_p=1$. The borders of a colored zone (for a given $B$) are obtained from the largest and smallest BH masses. An overlap between two colored zones arises because of $E_p\propto M$ and the broad range of observed BH masses.

Figure 2

Energy of a proton as a function of the rotation parameter for low values of the magnetic field. The points in the plot have the same meaning as in Fig. 1.

Figure 3

Energy of a proton as a function of the GW mass and spin for different values of the magnetic field. For each value of $B$, the points correspond to the BH masses in the LIGO-Virgo-KAGRA catalogs.

Figure 4

Poynting flux as a function of the GW mass and spin for different values of the magnetic field $R$ is the orbital radius as the Schwarzschild radius $R_S$ [12]. The points here have the same meaning as in Fig. 3.