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 Bîrzan 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 P _ { jet } \propto L _ { radio } ^ { \sim 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 P _ { jet } : L _ { radio } relation .