Particle-in-cell simulations of electron–positron cyclotron maser forming pulsar radio zebras

¹ Department of Theoretical Physics and Astrophysics, Masaryk University, 611 37 Brno, Czech Republic
e-mail: labaj@physics.muni.cz
² Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
³ Center for Astronomy and Astrophysics, Technical University of Berlin, 10623 Berlin, Germany
⁴ Astronomical Institute, Czech Academy of Sciences, 251 65 Ondřejov, Czech Republic

Received: 5 April 2023
Accepted: 5 November 2023

Abstract

Context. The microwave radio dynamic spectra of the Crab pulsar interpulse contain fine structures represented via narrowband quasiharmonic stripes. The pattern significantly constrains any potential emission mechanism. Similar to the zebra patterns observed, for example, in type IV solar radio bursts or decameter and kilometer Jupiter radio emission, the double plasma resonance (DPR) effect of the cyclotron maser instability may allow for interpretion of observations of pulsar radio zebras.

Aims. We provide insight at kinetic microscales of the zebra structures in pulsar radio emissions originating close to or beyond the light cylinder.

Methods. We present electromagnetic relativistic particle-in-cell (PIC) simulations of the electron–positron cyclotron maser for cyclotron frequency smaller than the plasma frequency. In four distinct simulation cycles, we focused on the effects of varying the plasma parameters on the instability growth rate and saturation energy. The physical parameters were the ratio between the plasma and cyclotron frequency, the density ratio of the “hot” loss-cone to the “cold” background plasma, the loss-cone characteristic velocity, and comparison with electron–proton plasma.

Results. In contrast to the results obtained from electron–proton plasma simulations (for example, in solar system plasmas), we find that the pulsar electron–positron maser instability does not generate distinguishable X and Z modes. On the contrary, a singular electromagnetic XZ mode was generated in all studied configurations close to or above the plasma frequency. The highest instability growth rates were obtained for the simulations with integer plasma-to-cyclotron frequency ratios. The instability is most efficient for plasma with characteristic loss-cone velocity in the range v_th = 0.2 − 0.3c. For low density ratios, the highest peak of the XZ mode is at double the frequency of the highest peak of the Bernstein modes, indicating that the radio emission is produced by a coalescence of two Bernstein modes with the same frequency and opposite wave numbers. Our estimate of the radiative flux generated from the simulation is up to ∼30 mJy from an area of 100 km² for an observer at 1 kpc distance without the inclusion of relativistic beaming effects, which may account for multiple orders of magnitude.