  There is a significant nonlinear correlation between the Eddington ratio
(L_bol=L_Edd) and the Eddington-scaled kinetic power (L_kin=L_Edd) of jets in
low luminosity active galactic nuclei (AGNs) (Merloni & Heinz). It is believed
that these low luminosity AGNs contain advection dominated accretion flows
(ADAFs). We adopt the ADAF model developed by Li & Cao, in which the global
dynamics of ADAFs with magnetically driven outflows is derived numerically, to
explore the relation between bolometric luminosity and kinetic power of jets.
We find that the observed relation, L_kin/L_Edd ~ (L_bol=L_Edd)^0.49, can be
well reproduced by the model calculations with reasonable parameters for ADAFs
with magnetically driven outflows. Our model calculations is always consistent
with the slope of the correlation independent of the values of the parameters
adopted. Compared with the observations, our results show that over 60% of the
accreted gas at the outer radius escapes from the accretion disc in a wind
before the gas falls into the black holes. The observed correlation between
Eddington-scaled kinetic power and Bondi power can also be qualitatively
reproduced by our model calculations. Our results show that the mechanical
efficiency varies from 10^-2 ~ 10^-3, which is roughly consistent with that
required in AGN feedback simulations.
