Heating the hot atmospheres of galaxy groups and clusters with cavities: the relationship between jet power and low-frequency radio emission

We present scaling relations between jet power and radio power measured using the Giant Metrewave Radio Telescope (GMRT), Chandra and XMM-Newton, for a sample of 9 galaxy groups combined with the Birzan et al. sample of clusters. Cavity power is used as a proxy for mechanical jet power. Radio power is measured at 235 MHz and 1.4 GHz, and the integrated 10 MHz-10 GHz radio luminosity is estimated from the GMRT 610-235 MHz spectral index. The use of consistently analysed, high resolution low-frequency radio data from a single observatory makes the radio powers for the groups more reliable than those used by previous studies, and the combined sample covers 6-7 decades in radio power and 5 decades in cavity power. We find a relation of the form Pjet proportional to Lradio^~0.7 for integrated radio luminosity, with a total scatter of sigma_Lrad=0.63 and an intrinsic scatter of sigma_i,Lrad=0.59. A similar relation is found for 235 MHz power, but a slightly flatter relation with greater scatter is found for 1.4 GHz power, suggesting that low-frequency or broad band radio measurements are superior jet power indicators. We find our low-frequency relations to be in good agreement with previous observational results. Comparison with jet models shows reasonable agreement, which may be improved if radio sources have a significant low-energy electron population. We consider possible factors which could bias our results or render them more uncertain, and find that correcting for such factors in those groups we are able to study in detail leads to a flattening of the Pjet:Lradio relation.