The non-linear dependence of flux on black hole mass and accretion rate in core-dominated jets

We derive the non-linear relation between the core flux F (nu) of accretion-powered jets at a given frequency and the mass M of the central compact object. For scale-invariant jet models, the mathematical structure of the equations describing the synchrotron emission from jets enables us to cancel out the model-dependent complications of jet dynamics, retaining only a simple, model-independent algebraic relation between F-nu and M . This approach allows us to derive the F-nu -M relation for any accretion disc scenario that provides a set of input boundary conditions for the magnetic field and the relativistic particle pressure in the jet, such as standard and advection-dominated accretion flow (ADAF) disc solutions. Surprisingly, the mass dependence of F-nu is very similar in different accretion scenarios. For typical flat-spectrum core-dominated radio jets and standard accretion scenarios, we find F-nu similar toM (17/12). The 7-9 orders of magnitude difference in black hole mass between microquasars and active galactic nuclei (AGN) jets imply that AGN jets must be about 3-4 orders of magnitude more radio-loud than microquasars, i.e. the ratio of radio to bolometric luminosity is much smaller in microquasars than in AGN jets. Because of the generality of these results, measurements of this F-nu-M dependence are a powerful probe of jet and accretion physics. We show how our analysis can be extended to derive a similar scaling relation between the accretion rate and F-nu for different accretion disc models. For radiatively inefficient accretion modes, we find that the flat-spectrum emission follows F-v proportional to (M(m) over dot)(17/12).