A universal scaling law of black hole activity including gamma-ray bursts

Previous works show that a correlation among radio luminosity, X-ray luminosity, and black hole (BH) mass from stellar-mass BHs in X-ray binaries to supermassive BHs in active galactic nuclei (AGNs), which leads to the so-called fundamental plane of BH activity. However, there are two competing explanations for this fundamental plane, including the jet-dominated model and the disk-jet model. Thus, the physical origin of this fundamental plane remains unknown. In this paper, we show that the X-ray luminosities, radio luminosities and BH masses of gamma-ray bursts (GRBs) and M82 X-1 also show a similar distribution. The universal scaling law among stellar-mass, intermediate and supermassive BH systems, together with the fact that radio and X-ray emission of GRBs originates from relativistic jets, reveals that the fundamental plane of BH activity is controlled by a jet, i.e., the radio and X-ray emission is mainly from the jet. Our work also suggests that the jets are scale-invariant with respect to the BH mass.