In an earlier paper we presented nuclear X-ray flux densities , measured with ROSAT , for the B2 bright sample of nearby low-luminosity radio galaxies .
In this paper we construct a nuclear X-ray luminosity function for the B2 radio galaxies , and discuss the consequences of our results for models in which such radio galaxies are the parent population of BL Lac objects .
Based on our observations of the B2 sample , we use Monte Carlo techniques to simulate samples of beamed radio galaxies , and use the selection criteria of existing samples of BL Lac objects to compare our simulated results to what is observed .
We find that previous analytical results are not applicable since the BL Lac samples are selected on beamed flux density .
A simple model in which BL Lacs are the moderately beamed ( \gamma \sim 3 ) counterparts of radio galaxies , with some random dispersion ( \sim 0.4 decades ) in the intrinsic radio-X-ray relationship , can reproduce many of the features of the radio-selected and X-ray-selected BL Lac samples , including their radio and X-ray luminosity functions and the distributions of their radio-to-X-ray spectral indices .
In contrast , models in which the X-ray and radio emission have systematically different beaming parameters can not reproduce important features of the radio-galaxy and BL Lac populations , and recently proposed models in which the radio-to-X-ray spectral index is a function of source luminosity can not in themselves account for the differences in the slopes of the radio and X-ray-selected BL Lac luminosity functions .
The redshift distribution and number counts of the X-ray-selected EMSS sample are well reproduced by our best models , supporting a picture in which these objects are beamed FRI radio galaxies with intrinsic luminosities similar to those of the B2 sample .
However , we can not match the redshift distribution of the radio-selected 1-Jy sample , and it is likely that a population of FRII radio galaxies is responsible for the high-redshift objects in this sample , in agreement with previously reported results on the sample ’ s radio and optical-emission-line properties .