TOOLS FOR COMPUTING THE AGN FEEDBACK: RADIO-LOUDNESS DISTRIBUTION AND THE KINETIC LUMINOSITY FUNCTION

We studied the active galactic nucleus (AGN) radio emission from a compilation of hard X-ray-selected samples, all observed in the 1.4 GHz band. A total of more than 1600 AGNs with 2-10 keV de-absorbed luminosities higher than 10(42) erg s(-1) cm(-2) were used. For a sub-sample of about fifty z less than or similar to 0.1 AGNs, it was possible to reach similar to 80% of radio detections and therefore, for the first time, it was possible to almost completely measure the probability distribution function of the ratio between the radio and the X-ray luminosity R(X) = log(L(1.4)/L(X)), where L(1.4)/L(X) = nu L(nu) (1.4 GHz)/L(X)(2-10 keV). The probability distribution function of R(X) was functionally fitted as dependent on the X-ray luminosity and redshift, P(R(X)vertical bar L(X), z). It roughly spans over six decades (-7 < R(X) < -1) and does not show any sign of bi-modality. The result is that the probability of finding large values of the R(X) ratio increases with decreasing X-ray luminosities and (possibly) with increasing redshift. No statistically significant difference was found between the radio properties of the X-ray absorbed (N(H) > 10(22) cm(-2)) and un-absorbed AGNs. Measurement of the probability distribution function of R(X) allowed us to compute the kinetic luminosity function and the kinetic energy density which, at variance with that assumed in many galaxy evolution models, is observed to decrease by about a factor of 5 at redshift below 0.5. About half of the kinetic energy density results in being produced by the more radio quiet (R(X)< -4) AGNs. In agreement with previous estimates, the AGN efficiency epsilon(kin) in converting the accreted mass energy into kinetic power (L(K) = epsilon(kin)(m) over dot c(2)) is, on average, epsilon(kin) similar or equal to 5 x 10(-3). The data suggest a possible increase of epsilon(kin) at low redshifts.