Multiple shocks in hot spots as the source of the spectral index-radio luminosity correlation in extended extragalactic radio sources

Abstract

The following recently established observations can be understood in terms of a simple model: the radio spectral indices of the lobes of powerful extended double radio galaxies are steeper for more powerful sources; also, high resolution maps, with high dynamic range, have revealed 'hot spots' with multiple structure. We expands on the basic idea that the multi-peaked hot spots are due to a jet passing through a sequence of shocks within the lobe, and proposes that more powerful jets pass through more and/or stronger shocks before terminating subsonically. While passing through an oblique shock, both the plasma and the magnetic field are compressed, leading to an increase in synchrotron emissivity. During the periods between successive shocks, the highest energy electrons lose their energy fastest, thereby steepening the spectral index. Reasonable combinations of our model parameters: shock strength (compressions by factors of 2-3); times between shock (≈ 10⁵ yr); and intial magnetic fields (≈ 10^-5 G), can reproduce the observed spectral index-power relation if stronger jets pass through 3-5shocks.