A Fundamental Line of Black Hole Activity

Black hole systems with outflows are characterized by intrinsic physical quantities such as the outflow beam power, $L_j$, the bolometric accretion disk luminosity, $L_{bol}$, and black hole mass or Eddington luminosity, $L_{Edd}$. When these systems produce compact radio emission and X-ray emission, they can be placed on the fundamental plane (FP), an empirical relationship between compact radio luminosity, X-ray luminosity, and black hole mass. We consider a fundamental line (FL) of black hole activity written in terms of dimensionless intrinsic physical quantities: $\rm{log} (L_j/L_{Edd}) = A ~\rm{log}(L_{bol}/L_{Edd}) +B$ or equivalently $\rm{log} (L_j/L_{bol}) = (A-1) ~\rm{log}(L_{bol}/L_{Edd}) +B$, and show that the FP may be written in the form of the FL. The FL has a smaller dispersion than the FP suggesting the FP derives from the FL. Disk-dominated and jet-dominated systems have consistent best fit FL parameters suggesting they are governed by the same physics. There are sharp cutoffs at $L_{bol}/L_{Edd} \simeq 1$ and $L_j/L_{Edd} \simeq 0.2$, and no indication of a strong break as $L_{bol}/L_{Edd} \rightarrow 1$. Consistent values of $A$ are obtained for numerous samples including FRII sources, LINERS, AGNs with compact radio emission, and Galactic black holes, which indicate a weighted mean value of $A \simeq 0.45 \pm 0.01$. The results suggest that a common physical mechanism related to the dimensionless bolometric luminosity of the disk controls the jet power relative to the disk power. The beam power $L_j$ can be obtained by combining FP best-fit parameters and compact radio luminosity for sources that fall on the FP.