  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 disk 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) disk 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}~M^{17/12}. The 7-9 orders of magnitude difference in black hole
mass between microquasars and 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 mdot and F_{nu} for different accretion disk models. For
radiatively inefficient accretion modes we find that the flat spectrum emission
follows F_{nu}~(mdot*M)^{17/12}.

Astrophysics