Pulsar electrodynamics: Relativistic kinetic theory of radiative plasmas—collective phenomena and their radiation

The classical modeling of radiation by accelerated charged particles in pulsars predicts a cutoff in photon energy at around 25 GeV. While this is broadly consistent with observations, the classical treatment is not self-consistent, and cannot be extended to explain the rare high-energy detections of photons in the 100s of GeV range. In this paper we revisit the theoretical modeling of high-energy radiation processes in very strong electromagnetic fields, in the context of both single particles and collective plasmas. There are no classical constraints on this description. We find that there is indeed a critical energy of around 50 GeV that arises naturally in this self-consistent treatment, but rather than being a cutoff, this critical energy signals a transition from radiation that is classical to a quasiquantum description, in which the particle is able to radiate almost its total energy in a single event. This new modeling therefore places pulsar radiation processes on a more secure physical basis, and admits the possibility of the production of TeV photons in a self-consistent way.

Figure 1

This figure, as in Berestetskii et al. [34], shows the representation of $P_r(\mathit{r},\mathit{p},\omega ,t)/P_{\mathrm{Dir}}$ for different values of ${\rm Y}$. When ${\rm Y}\ll 0.1$ the radiating electrons are in the classical and q-classical regimes. The q-quantum regime will happen for ${\rm Y}\gg 1$, and therefore ${\rm Y}\sim 5$ gives a good picture of the radiative spectrum for q-quantum regimes. There the peak frequency of radiation is not as sharply defined as for the ${\rm Y}\ll 0.1$ case, but is around $0.8{\omega }_c$, implying $\hslash {\omega }_{\max }\sim \gamma m{c}^2$.

Figure 2

This figure shows a sketch of the distribution function (in momentum space) at different radial positions along the acceleration, at a snapshot in time, for a singe reference frame; it may also be considered as an evolutionary sketch for the distribution function as it develops in time. At early radial positions close to the star (that is, position 0 in the diagram), the distribution function of particle momenta has an arbitrary form with a nonzero minimum momentum, and a maximum that is below the threshold for which radiation recoil may become important. At position 1, the minimum momentum has grown (since the distribution is under continuous acceleration, and we are using the same reference frame as at position 0), and the maximum momentum is now sufficiently high that radiation effects need to be taken into account. At position 2, the distribution function has been significantly altered by radiation recoil: there is an extended low-momentum (low-energy) plasma at the same time as a quenching of the high-energy tail after $p_{\max }$. Note that these sketches are not to scale, and that the high-energy tail (above $p_{\mathrm{qcl}}$) in reality is significantly longer than the lower part.