Helical and pinching instability of supersonic expanding jets in extragalactic radio sources

The jets that are observed in extragalactic radio sources expand as distance from the nucleus increases. This can be interpreted as a jet expanding to remain in pressure balance with the interstellar and intergalactic medium. The structure of radio sources may be determined by the stability properties of jets. In this paper we consider the stability properties of an expanding jet. We find that an expanding jet, like a jet of constant radius, is unstable to Kelvin-Helmholtz perturbations. On an expanding jet, wavelengths increase and growth rates decrease proportional to the jet radius. The practical result is that wave amplitudes increase linearly rather than exponentially along the jet. The long-wavelength perturbations which can affect the structure in observable fashion can be stabilized by convection along the expanding jet. This will allow jets to propagate farther than has been previously thought for reasonable values of jet velocity, density, and Mach number. If a jet appears distorted by a pinching or a helical wave, then jet Mach number and density relative to the external medium can be estimated from observation of the wavelength.