The relationship between beam power and radio power for classical double radio sources

Beam power is a fundamental parameter that describes, in part, the state of a supermassive black hole system. Determining the beam powers of powerful classical double radio sources requires substantial observing time, so it would be useful to determine the relationship between beam power and radio power so that radio power could be used as a proxy for beam power. A sample of 31 powerful classical double radio sources with previously determined beam and radio powers is studied; the sources have redshifts between about 0.056 and 1.8. It is found that the relationship between beam power, L_j, and radio power, P, is well described by logL_j≈ 0.84(±0.14)logP+ 2.15(±0.07), where both L_j and P are in units of 10⁴⁴ergs^-1. This indicates that beam power is converted to radio power with an efficiency of about 0.7per cent. The ratio of beam power to radio power is studied as a function of redshift; there is no significant evidence for redshift evolution of this ratio over the redshift range studied. The relationship is consistent with empirical results obtained by Cavagnolo et al. for radio sources in gas-rich environments, which are primarily Fanaroff-Riley type I sources, and with the theoretical predictions of Willott et al.