Among active galactic nuclei, BL Lac objects show extreme properties that have been interpreted as the effect of relativistic beaming on the emission from a plasma jet oriented close to the line of sight. The Doppler amplification of the jet emission
makes them ideal targets for studying jet physics. In particular, low-power BL Lacs (LPBL) are very interesting because they probe the jet formation and emission processes at the lowest levels of accretion. However, they are difficult to identify since their emission is swamped by the radiation from the host galaxy in most observing bands. In this paper we propose a new LPBL selection method based on the mid-infrared emission, in addition to the traditional optical indices. We considered the radio-selected sample of Best & Heckman (2012, MNRAS, 421, 1569) and cross-matched it with the WISE all-sky survey. In a new diagnostic plane including the W2-W3 color and the Dn(4000) index, LPBL are located in a region scarcely populated by other sources. By filtering objects with small emission line equivalent width, we isolated 36 LPBL candidates up to redshift 0.15. Their radio luminosity at 1.4 GHz spans the range log L_r = 39.2-41.5 [erg/s]. Considering the completeness of our sample, we analyzed the BL Lac luminosity function (RLF), finding a dramatic paucity of LPBL with respect to the extrapolation of the RLF toward low power. This requires a break in the RLF located at log L_r~40.6 [erg/s]. The consequent peak in the BL Lacs number density is possibly the manifestation of a minimum power required to launch a relativistic jet.
We constrain the behavior of the radio luminosity function (RLF) of two classes of active galactic nuclei (AGN) namely AGN of low radio power (LRP) and BL Lac objects. The extrapolation of the observed steep RLFs to low power predicts a space density
of such objects that exceeds that of the sources that can harbor them and this requires a break to a shallower slope. For LRP AGN we obtain P_br,LRP > 10^20.5 W/Hz at 1.4 GHz to limit their density to be smaller than that of elliptical galaxies with black hole masses M_BH > 10^7.5 solar masses. By combining this value with the limit derived by the observations the break must occur at P_br,LRP~10^20.5-10^21.5 W/Hz. For BL Lacs we find P_br,BLLAC > 10^23.3 W/Hz otherwise they would outnumber the density of weak-lined and compact radio sources, while the observations indicate P_br,BLLAC < 10^24.5 W/Hz. In the framework of the AGN unified model a low luminosity break in the RLF of LRP AGN must correspond to a break in the RLF of BL Lacs. The ratio between P_br,LRP and P_br,BLLAC is ~10^3, as expected for a jet Doppler factor of ~10.
