The Spark‐associated Soliton Model for Pulsar Radio Emission

Abstract

We propose a new, self-consistent theory of coherent pulsar radio emission based on the nonstationary sparking model of Ruderman & Sutherland, modified by Gil & Sendyk. The polar cap is populated by a number of sparks with a characteristic perpendicular dimension D approximately equal to the polar gap height scale h, separated from each other also by about D ≈ h. Each spark reappears in approximately the same place on the polar cap for a timescale much longer than its 10 μs lifetime and delivers to the open magnetosphere a sequence of e-e+ clouds that flow orderly along a flux tube of dipolar magnetic field lines. The overlapping of particles with different momenta from consecutive clouds leads to effective two-stream instability, which triggers electrostatic Langmuir waves at the altitudes of about 50 stellar radii. The electrostatic oscillations are modulationally unstable, and their nonlinear evolution results in formation of plasma solitons. Because of relative streaming of electrons and positrons and the corresponding difference in relativistic masses, the pondermotive Miller force acts on them at different rates, which results in the net soliton charge. A characteristic soliton length along magnetic field lines is about 30 cm, so they are capable of emitting coherent curvature radiation at radio wavelengths. A perpendicular cross section of each soliton at radiation altitudes follows from a dipolar spread of a plasma cloud with a characteristic dimension near the star surface of about D ≈ h ≈ 50 m. If Δγ = |γ+ - γ-| ~ 100, then the net soliton charge is about 1021 fundamental charges contained within a volume of about 1014 cm3. For a typical pulsar, there are about 105 solitons associated with each of about 25 sparks operating on the polar cap at any instant. One soliton moving relativistically along dipolar field lines with a Lorentz factor of the order of 100 generates a power of about 1021 ergs s-1 by means of curvature radiation. Then the total power of a typical radio pulsar can be estimated as being about 1027-1028 ergs s-1. The energy of the soliton curvature radiation is supported by kinetic energy of secondary electron-positron plasma created by the primary beam produced by the accelerating potential drop within the polar gap. A significant fraction of kinetic energy generated by sparks is radiated away in the form of the observed coherent radio emission.