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Relationship Between the Kinetic Power and Bolometric Luminosity of Jets: limitation from black hole X-ray binaries, active galactic nuclei, and gamma-ray bursts

The correlation between the kinetic power $P_{\rm jet}$ and intrinsic bolometric luminosity $L_{\rm jet}$ of jets may reveal the underlying jet physics in various black hole systems. Based on the recent work by Nemmen et al. (2012), we re-investigate this correlation with additional sources of black-hole X-ray binaries (BXBs) in hard/quiescent states and low-luminosity active galactic nuclei (LLAGNs). The new sample includes 29 sets of data from 7 BXBs and 20 LLAGNs, with $P_{\rm jet}$ and $L_{\rm jet}$ being derived from spectral modeling of the quasi-simultaneous multi-band spectra under the accretion-jet scenario. Compared to previous works, the range of luminosity is now enlarged to more than $20$ decades, i.e. from $10^{31}{\rm erg/s}$ to $10^{52}{\rm erg/s}$, which allows for better constraining of the correlation. One notable result is that the jets in BXBs and LLAGNs almost follow the same $P_{\rm jet} - L_{\rm jet}$ correlation that was obtained from blazars and gamma-ray bursts (GRBs). The slope indices we derived are $1.03\pm0.01$ for the whole sample, $0.85\pm0.06$ for BXB subsample, $0.71\pm0.11$ for LLAGN subsample, and $1.01\pm0.05$ for the LLAGN-blazar subsample, respectively. The correlation index around unit implies the independence of jet efficiency on the luminosity or kinetic power. Our results may further support the hypothesis that similar physical processes exist in the jets of various black hole systems.