On the velocity of jets powering hot spots similar to those in Cygnus A

Abstract

Hot spots similar to those in the radio galaxy Cygnus A can be explained by the strong shock produced by a supersonic but classical jet$\left( {u_{jet}< c/\sqrt 3 } \right)$. The high integrated radio luminosity (L≃2×10⁴⁴ erg s⁻¹) and the strength of mean magnetic field (B≃2×10⁻⁴ G) suggest the hot spots are the downstream flow of a very strong shock which generates the ultrarelativistic electrons of energy ɛ≥20 MeV. The fully-developed subsonic turbulence amplifies the magnetic field of the jet up to 1.6×10⁻⁴ G by the dynamo effect. If we assume that the post-shock pressure is dominated by relativistic particles, the ratio between the magnetic energy density to the energy density in relativistic particles is found to be ≃2×10⁻², showing that the generally accepted hypothesis of equipartition is not valid for hot spots. The current analysis allows the determination of physical parameters inside hot spots. It is found that:

• (1) The velocity of the upstream flow in the frame of reference of the shock isu ₁≃0.2c. Radio observations indicate that the velocity of separation of hot spots isu _sep≃0.05c, so that the velocity of the jet isu _jet=u ₁+u _sep≃0.25c.

• (2) The density of the thermal electrons inside the hot spot isn ₂≃5×10⁻³ e ⁻ cm⁻³ and the mass ejected per year to power the hot spot is ≃4M ₀yr⁻¹.

• (3) The relativistic electron density is less than 20% of the thermal electron density inside the hot spot and the spectrum is a power law which continues to energies as low as 30 MeV.

• (4) The energy density of relativistic protons is lower than the energy density of relativistic electrons unlike the situation for cosmic rays in the Galaxy.