Evidence for Rapidly Rotating Black Holes in Fanaroff-Riley I Radio Galaxies

We investigate the correlation between 151 MHz radio luminosity, L _{151 MHz}, and jet power, P _jet, for a sample of low-power radio galaxies, of which the jet power is estimated from X-ray cavities. The jet power for a sample of Fanaroff-Riley I radio galaxies (FR Is) is estimated with the derived empirical correlation. We find that P _jet/L _Edd is positively correlated with L_X^{2{--}10\ {keV}}/\it L_Edd for FR Is, where L _Edd is the Eddington luminosity and L ^{2-10 keV} _X is the 2-10 keV X-ray luminosity. We calculate the jet power of a hybrid model, as a variant of a Blandford-Znajek model proposed by Meier, based on the global solution of the advection-dominated accretion flow (ADAF) surrounding a Kerr black hole (BH). Our model calculations suggest that the maximal jet power is a function of the mass accretion rate and the BH spin parameter j. The hard X-ray emission is believed to be mainly from the ADAFs in FR Is, and the mass accretion rate is therefore constrained with the X-ray emission in our ADAF model calculations. We find that the dimensionless angular momentum of BH j >~ 0.9 is required in order to reproduce the observed relation of P_jet/L_Edd{--}L_X^{2{--}10\ {keV}}/\it L_Edd for FR Is. Our conclusion will be strengthened if part of the X-ray emission is contributed by the jets. Our results suggest that BHs in FR Is are rapidly spinning, which are almost not affected by the uncertainty of the BH mass estimates.