Hot gaseous coronae of early-type galaxies and their radio luminosity function

Abstract

Recent X-ray observations have revealed that early-type galaxies (which usually produce extended double radio sources) generally have hot gaseous haloes extending up to ∼10²kpc^1,2. Moreover, much of the cosmic X-ray background radiation is probably due to a hotter, but extremely tenuous, intergalactic medium (IGM)³. We have presented^4–7 an analytical model for the propagation of relativistic beams from galactic nuclei, in which the beams' crossing of the pressure-matched interface between the IGM and the gaseous halo, plays an important role. The hotspots at the ends of the beams fade quickly when their advance becomes subsonic with respect to the IGM. This model has successfully predicted (for typical double radio sources) the observed⁸ current mean linear-size (∼2D≃350 kpc)^4,5, the observed^8–11 decrease in linear-size with cosmological redshift^4–6 and the slope of the linear-size versus radio luminosity^10,12–14 relation⁶. We have also been able to predict the redshift-dependence of observed numbers and radio luminosities of giant radio galaxies^7,15. Here, we extend this model to include the propagation of somewhat weaker beams. We show that the observed flattening of the local radio luminosity function (LRLF)^16–20 for radio luminosity P≈ 10²⁴ W Hz⁻¹ at 1 GHz can be explained without invoking ad hoc a corresponding break in the beam power function Φ(L_b), because the heads of the beams with L^b < 10²⁵ W Hz⁻¹ are decelerated to sonic velocity within the halo itself, which leads to a rapid decay of radio luminosity and a reduced contribution of these intrinsically weaker sources to the observed LRLF.