On the maximum energy of non-thermal particles in the primary hotspot of Cygnus A

TL;DR

This paper investigates particle acceleration limits in Cygnus A's hotspot, showing that magnetic turbulence and cosmic ray instabilities can explain observed electron energies without traditional synchrotron loss constraints.

Contribution

It demonstrates that non-resonant hybrid instabilities can amplify magnetic fields and accelerate particles to observed energies, challenging previous assumptions about synchrotron loss limits.

Findings

Maximum electron energy is about 0.8 TeV in 100 μG magnetic field.

Magnetic field amplification up to 50-400 μG is feasible via cosmic-ray streaming instabilities.

Synchrotron losses are not the primary constraint on maximum particle energy.

Abstract

We study particle acceleration and magnetic field amplification in the primary hotspot in the northwest jet of radiogalaxy Cygnus A. By using the observed flux density at 43 GHz in a well resolved region of this hotspot, we determine the minimum value of the jet density and constrain the magnitude of the magnetic field. We find that a jet with density greater than $5\times 10^{-5}$ cm$^{-3}$ and hotspot magnetic field in the range 50-400 $\mu$G are required to explain the synchrotron emission at 43 GHz. The upper-energy cut-off in the hotspot synchrotron spectrum is at a frequency < $5\times 10^{14}$ Hz, indicating that the maximum energy of non-thermal electrons accelerated at the jet reverse shock is $E_{e, \rm max} \sim 0.8$ TeV in a magnetic field of 100 $\mu$G. Based on the condition that the magnetic-turbulence scale length has to be larger than the plasma skin depth, and that the energy density in non-thermal particles cannot violate the limit imposed by the jet kinetic luminosity, we show that $E_{e,\rm max}$ cannot be constrained by synchrotron losses as traditionally assumed. In addition to that, and assuming that the shock is quasi-perpendicular, we show that non-resonant hybrid instabilities generated by the streaming of cosmic rays with energy $E_{e, \rm max}$ can grow fast enough to amplify the jet magnetic field up to 50-400 $\mu$G and accelerate particles up to the maximum energy $E_{e, \rm max}$ observed in the Cygnus A primary hotspot.