Magnetars in the Metagalaxy: An Origin for Ultra High Energy Cosmic Rays in the Nearby Universe

TL;DR

The paper argues that relativistic winds from newly formed magnetars in ordinary galaxies can serve as the metagalactic origin for ultra-high-energy cosmic rays (UHECR). By deriving a near flat injection spectrum with $dN_i/d\gamma \propto 1/\gamma$ and tracking intergalactic transport, the author shows that the observed UHECR spectrum can be reproduced, with the high-energy tail modulated by gravitational-wave spindown losses. The model requires only a small fraction (about 5–10%) of magnetars to be born with sufficiently high voltages to accelerate particles to $E \gtrsim 10^{20}$ eV, and predicts correlations with bursts of gravitational radiation and rare, observable UHECR bursts from individual magnetar events. The framework ties UHECR production to magnetar winds, Rayleigh-Taylor shredding of supernova envelopes, and magnetar wind nebula dynamics, and it makes concrete predictions for Auger and gravitational-wave observatories, offering a multimessenger avenue to test the scenario.

Abstract

I show that the relativistic winds of newly born magnetars with khz initial spin rates, occurring in all normal galaxies, can accelerate ultrarelativistic light ions with an E^{-1} injection spectrum, steepening to E^{-2} at higher energies, with an upper cutoff above 10^{21} eV. Interactions with the CMB yield a spectrum in good accord with the observed spectrum of Ultra-High Energy Cosmic Rays (UHECR), if ~ 5-10% of the magnetars are born with voltages sufficiently high to accelerate the UHECR. The form the spectrum spectrum takes depends on the gravitational wave losses during the magnetars' early spindown - pure electromagnetic spindown yields a flattening of the E^3 J(E) spectrum below 10^{20} eV, while a moderate GZK ``cutoff'' appears if gravitational wave losses are strong enough. I outline the physics such that the high energy particles escape with small energy losses from a magnetar's natal supernova, including Rayleigh-Taylor ``shredding'' of the supernova envelope, expansion of a relativistic blast wave into the interstellar medium, acceleration of the UHE ions through surf-riding in the electromgnetic fields of the wind, and escape of the UHE ions in the rotational equator with negligible radiation loss. The abundance of interstellar supershells and unusually large supernova remnants suggests that most of the initial spindown energy is radiated in khz gravitational waves for several hours after each supernova, with effective strains from sources at typical distances ~ 3 x 10^{-21}. Such bursts of gravitational radiation should correlate with bursts of ultra-high energy particles. The Auger experiment should see such bursts every few years.

Figures (2)

• Figure 1: Comparison of bare magnetar theory to UHECR data. The experimental data are from Nagano and Watson's (2000) summary except for the data from the Hi-Res (monocular) results, which are taken from Abu-Zayyad et al. (2002b). The three theoretical curves are for differing assumed equatorial ellipticities of the neutron stars: $\epsilon = 0$ ("no GR"); $\epsilon = 10^{-2}$ ("moderate GR"); $\epsilon =10^{-1}$ ("strong GR"). The theoretical curves were fit to the data by eye, by requiring the model flux at $3 \times 10^{19}$ eV to provide the whole intensity at this energy. That fit yields values for the average source strength $K_0 = W_{geom} \nu_m I n_g T_H/\mu$, which are listed for the three cases shown in Table \ref{['tab:source_strength']}. All the curves use the same upper cutoff energy $E_{max} = 3.3 \times 10^{21}$ eV, corresponding to $Z \eta_1 \mu_{33} \Omega_4^2 =1$ (a polar dipole field strength of $2 \times 10^{15}$ Gauss and an initial rotation period of 0.6 msec.) Lowering the upper cutoff to the minimum acceptable value of $3 \times 10^{20}$ eV yields qualitatively unacceptable fits to the observations - there is too much curvature in $E^3 J(E)$ below $6 \times 10^{19}$ eV. Including a "galactic" component $E^3 J_{galactic}(E) = 7 \times 10^{23} (E/ 30 \; {\rm EeV})^{-3.2}$ ev$^2$/meter$^2$-sec-ster constructed to represent the data at energies well below $E_a$ and extrapolated to all energies above $E_a$ reduces the inferred values of $K_0$ by a factor 0.65. These modified values are also shown in Table \ref{['tab:source_strength']}.
• Figure 2: Frozen-in current sheet structure of the oblique split monopole in the inner wind, from Bogovalov (1999). Left panel: Meridional cross-section of the poloidal field structure at large $r$, showing the crinkled current sheet. Right panel: Intersection of the curent sheet with the equatorial plane. The toroidal magnetic field forms stripes with opposite directions between each current layer, as indicated by the arrows between the current sheets.