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Register a new userOn the collective curvature radiation
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Added by
Alexander Philippov
Publication date
2011
fields
Physics
and research's language is
English
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The paper deals with the one possible mechanism of the pulsar radio emission, i.e., with the collective curvature radiation of the relativistic particle stream moving along the curved magnetospheric magnetic field lines. It is shown that the electromagnetic wave containing one cylindrical harmonic exp{is{phi}} can not be radiated by the curvature radiation mechanism, that corresponds to radiation of a charged particle moving along curved magnetic field lines. The point is that the particle in vacuum radiates the triplex of harmonics (s, s pm 1), so for the collective curvature radiation the wave polarization is very important and cannot be fixed a priori. For this reason the polarization of real unstable waves must be determined directly from the solution of wave equations for the media. Its electromagnetic properties should be described by the dielectric permittivity tensor ^{epsilon}({omega},k,r), that contains the information on the reaction on all possible types of radiation.
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When treating the absorption of light, one focuses on the absorption coefficient, related to the probability of photons to survive while traversing a layer of material. From the point of view of particles doing the absorption, however, the elementary interaction of the particle with the photon is best described by the corresponding cross section. We revisit curvature radiation in order to find the absorption cross section for this process, making use of the Einstein coefficients and their relations with spontaneous and stimulated emission and true absorption. We derive the cross section as a function of the emission angle psi (i.e. the angle between the instantaneous velocity vector and the direction of the photon), and the cross section integrated over angles. Both are positive, contrary to the synchrotron case for which the cross section can be negative for large psi. Therefore, it is impossible to have curvature radiation masers. This has important consequences on sources of very large brightness temperatures that require a coherent emission process, such as pulsars and Fast Radio Bursts.
Fast radio bursts are extragalactic radio transient events lasting a few milliseconds with a ~Jy flux at ~1 GHz. We propose that these properties suggest a neutron star progenitor, and focus on coherent curvature radiation as the radiation mechanism. We study for which sets of parameters the emission can fulfil the observational constraints. Even if the emission is coherent, we find that self-absorption can limit the produced luminosities at low radio frequencies and that an efficient re-acceleration process is needed to balance the dramatic energy losses of the emitting particles. Self-absorption limits the luminosities at low radio frequency, while coherence favours steep optically thin spectra. Furthermore, the magnetic geometry must have a high degree of order to obtain coherent curvature emission. Particles emit photons along their velocity vectors, thereby greatly reducing the inverse Compton mechanism. In this case we predict that fast radio bursts emit most of their luminosities in the radio band and have no strong counterpart in any other frequency bands.
We consider the fundamental problem of charged particles moving along and around a curved magnetic field line, revising the synchro-curvature radiation formulae introduced by Cheng and Zhang (1996). We provide more compact expressions to evaluate the spectrum emitted by a single particle, identifying the key parameter that controls the transition between the curvature-dominated and the synchrotron-dominated regime. This parameter depends on the local radius of curvature of the magnetic field line, the gyration radius, and the pitch angle. We numerically solve the equations of motion for the emitting particle by considering self-consistently the radiative losses, and provide the radiated spectrum produced by a particle when an electric acceleration is balanced by its radiative losses, as it is assumed to happen in the outer gaps of pulsars magnetospheres. We compute the average spectrum radiated throughout the particle trajectory finding that the slope of the spectrum before the peak depends on the location and size of the emission region. We show how this effect could then lead to a variety of synchro-curvature spectra. Our results reinforce the idea that the purely synchrotron or curvature losses are, in general, inadequate to describe the radiative reaction on the particle motion, and the spectrum of emitted photons. Finally, we discuss the applicability of these calculations to different astrophysical scenarios.
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