Acceleration of Ultrahigh Energy Particles from Fast Radio Bursts

Abstract

Two extreme events in the universe, fast radio bursts (FRBs) and cosmic rays (CRs), could be corelated, where FRBs with extreme field strength near their sources may contribute to CRs. This study investigates localized particle acceleration driven by FRB-like ultra-relativistic electromagnetic pulses. It is found ultra-high energy neutral plasma sheets form constantly via the front erosion of an FRB pulse. There are two ion acceleration regimes depending upon the field strength and the plasma density: the wakefield regime dominated by charge separation fields, and the piston regime driven by the $\mathbf{V}\times\mathbf{B}$ force of the pulses. The predicted energy scalings align well with particle-in-cell simulations. A power-law energy spectrum naturally arises with an index close to the CRs during FRB diffusion outward. Joint observations of FRBs and CRs may provide an opportunity to understand these extreme events and advance the development of multi-messenger astronomy.

Figures (7)

• Figure 1: Schematic of ion acceleration via FRB pulse front erosion. (a) The pulse front is eroded by the front electron sheet (FES) to form a shock-like front. (b) Ion acceleration in the wakefield regime, where the FES erodes the FRB pulse (red line) and accelerates the ion sheet (IS) until the two sheets coincide to form a quasi-neutral plasma sheet (PS). The PSs move faster than the FRB ($v_{PS} \sim c > v_{FRB}$) and continuously form at the FRB front. (c) Ion acceleration in the piston regime, where the plasma is directly compressed and accelerated as a series of PSs at the eroded front of the pulse.
• Figure 2: Two regimes of plasma wake-waves in electron – proton plasma driven by ultra-relativistic electromagnetic pulse. (a1) – (a4) are obtained for $a_0={10}^3$, (b1) – (b4) $a_0={10}^5$. (a1) and (b1) are the vector potential of the pulse. (a2) and (b2) are the normalized densities of electron and proton fluids from Eqs.$\,$(\ref{['equ:a3']}) and (\ref{['equ:a4']}), (a3) and (b3) are their Lorentz factors Eqs.$\,$(\ref{['equ:a5']}) and (\ref{['equ:a6']}) given in Appendix A. (a4) and (b4) are the normalized longitudinal electrostatic fields as $e_x = eE_x/m_ec\omega$. The red line in (a4) represents the scalar potential $\phi$ in arbitrary unit. The plasma density for both cases is $N_0=0.5$.
• Figure 3: The acceleration process in the wakefield regime obtained from 1D-PIC simulation in a frame moving with $c$ with $a_0={10}^3$, $N_0=0.5$ and $\Delta\xi_{up}=7.4\lambda_0$. (a) Spatiotemporal evolutions of the FRB pulse front, where the inset shows the field structure at the front at $t=580 \tau_0$. (b) Electrostatic field which is multiplied by a factor of 10. (c) and (d) are the electron and proton densities, respectively. (e) and (f) are their Lorentz factors.
• Figure 4: The energy spectra of the accelerated protons from PIC simulation. (a) the blue line from the same simulation in Fig.$\,$\ref{['fig:fig2']} at $2000\tau_0$, where the black dashed line at 48.8 GeV is the predicted value of Eq.$\,$(\ref{['equ:equ9']}). (b) the blue line from the same simulation in Fig.$\,$\ref{['fig:fig3']} at $5000\tau_0$, the black dashed line at 1.5 TeV is the predicted value of Eq.$\,$(\ref{['equ:equ12']}). The green dotted lines represent results from 1D simulations with radiation reaction. The red dashed lines represent results from 3D simulations.
• Figure 5: The kinetic energy of the protons inside the plasma sheets from acceleration models and PIC simulations. In (a) - (c), the blue lines come from Eq.$\,$(\ref{['equ:equ9']}), the yellow lines come from Eq.$\,$(\ref{['equ:equ12']}), the red dots represent the 1D-PIC simulation results. (d) is the proton kinetic energy scaling from acceleration models. The dashed line in (b) and white line in (d) represents the boundary with $\Delta x_0/\lambda=0.5$. The left side of the boundary line represents the wakefield regime, and the right side represents the piston regime. Radiation reaction need to be consider at the right side of the dashed line in (d).