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We present scaling relations between jet power and radio power measured usingthe Giant Metrewave Radio Telescope (GMRT), Chandra and XMM-Newton, for asample 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 ismeasured at 235 MHz and 1.4 GHz, and the integrated 10 MHz-10 GHz radioluminosity is estimated from the GMRT 610-235 MHz spectral index. The use ofconsistently analysed, high resolution low-frequency radio data from a singleobservatory makes the radio powers for the groups more reliable than those usedby previous studies, and the combined sample covers 6-7 decades in radio powerand 5 decades in cavity power. We find a relation of the form Pjet proportionalto Lradio^~0.7 for integrated radio luminosity, with a total scatter ofsigma_Lrad=0.63 and an intrinsic scatter of sigma_i,Lrad=0.59. A similarrelation is found for 235 MHz power, but a slightly flatter relation withgreater scatter is found for 1.4 GHz power, suggesting that low-frequency orbroad band radio measurements are superior jet power indicators. We find ourlow-frequency relations to be in good agreement with previous observationalresults. Comparison with jet models shows reasonable agreement, which may beimproved if radio sources have a significant low-energy electron population. Weconsider possible factors which could bias our results or render them moreuncertain, and find that correcting for such factors in those groups we areable to study in detail leads to a flattening of the Pjet:Lradio relation.

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