Ultra High Energy Electrons Powered by Pulsar Rotation

Abstract

A new mechanism of particle acceleration, driven by the rotational slow down of the Crab pulsar, is explored. The rotation, through the time dependent centrifugal force, can efficiently excite unstable Langmuir waves in the electron-positron (hereafter e±) plasma of the star magnetosphere. These waves, then, Landau damp on electrons accelerating them in the process. The net transfer of energy is optimal when the wave growth and the Landau damping times are comparable and are both very short compared to the star rotation time. We show, by detailed calculations, that these are precisely the conditions for the parameters of the Crab pulsar. This highly efficient route for energy transfer allows the electrons in the primary beam to be catapulted to multiple TeV (~ 100 TeV) and even PeV energy domain. It is expected that the proposed mechanism may, unravel the puzzle of the origin of ultra high energy cosmic ray electrons.

ON THE SPECTRUM OF THE PULSED GAMMA-RAY EMISSION OF THE CRAB PULSAR FROM 10 MeV TO 400 GeV

“…The highest Lorentz factor of the primary electron obtained at the stellar surface due to acceleration in the gap region for a typical pulsar is ∼10 7 (Usov & Shabad 1985). The existence of more energetic particles in the pulsar magnetosphere can be explained by re-acceleration of the fastest beam electrons via Landau damping of L waves that are excited in the magnetospheric plasma through the parametric instability (Mahajan et al 2013). The L waves are efficiently damped on the most energetic primary beam electrons, as the damping takes place only for particles with velocities close to the speed of light.…”

“…As only a small fraction of the beam particles with the highest Lorentz factors can participate in the Landau damping process, the process will result in the elongation of the distribution function toward higher energies (Figure 2). This process was studied in detail by Machabeli et al (2005) and Mahajan et al (2013). In the latter study, it was shown that, for the Crab pulsar magnetosphere, the beam acceleration by Landau damping of parametrically driven L waves is quite effective.…”

“…For typical parameters of pair plasmas in pulsar magnetospheres, the growth rate of the instability is quite sufficient (see Gogoberidze et al 2008) that it inevitably permits the existence of L waves in the vicinity of the light cylinder zone. Moreover, recently we have shown that the stellar rotation, through the time-dependent centrifugal force, can efficiently excite unstable L waves in the plasma of the Crab pulsar magnetosphere (Mahajan et al 2013). The periodic centrifugal force plays the role of a parameter in this process, creating the so-called parametric instability, which efficiently converts the pulsar rotational energy into L waves.…”

“…In the present work, we consider the particle acceleration plasma mechanism exciting near the light cylinder, which should provide Lorentz factors γ b 10 9 for the beam electrons. Particularly, the electrostatic Langmuir waves existing in the region of the pulsar magnetosphere close to the light cylinder (Mahajan et al 2013;Gogoberidze et al 2008) can effectively damp the fastest beam electrons. Due to the Landau damping process, the one-dimensional distribution function of the primary beam particles with an initial power-law decline will acquire a higher energy "tail," up to Lorentz factors of γ ∼ 10 9 (see Section 3).…”

New mechanism of acceleration of particles by stellar black holes

“…It has been shown that the total energy gained by the beam electrons in magnetospheres of pulsars is given by [9] ǫ ≈ n 1 F δr n GJ ,…”