4.4.4. The dual nature of the BLLs
Our analysis of the published results confirms the assumption made by a number of authors that the sources classified as BLLs are a mixture of two physically different populations with different parent objects. One population consists of sources which are closely aligned with our line of sight and have large Lorentz factor (< > ~ 10); they are highly variable and have high brightness temperatures; they are the extreme end of the HPQ population with the smallest viewing angles; their parent population is the strong, distant FR II radio galaxies. The other population consists of sources which are also beamed toward us, but not as closely as the ``distant BLLs''; they have smaller Lorentz factor (< > ~ 3) and consequently have smaller brightness temperatures and are less variable; they are FR I radio galaxies favorably oriented. , using various methods, obtained a slightly larger value (< > ~ 4) which may be due to the fact that his sample of BLLs was contaminated by the presence of some missclassified HPQs having larger values of .
The inclusion of a sizable number of HPQs in samples of BLLs may lead to incorrect conclusions.
Stickel et al. (1991) have used their complete sample of 34 BLLs to build their core radio luminosity function at 5 GHz.  have compared this luminosity function to that of FR Is; they found that the space densities of BLLs and FR Is are about equal above 1033 erg s-1 Hz-1, the space density of BLLs being about 30 times smaller than that of FR Is below 1032 erg s-1 Hz-1. However, the BLL radio luminosity function was built assuming that the 34 objects in the sample were genuine BLLs; but we have reclassified as HPQs 16 of these objects and 10 more could be HPQs.
Stickel et al. (1991) sample contains 10 objects with no measured redshift or with z > 0.4 (table 5). Most objects with no measured redshift probably have a relatively high z (>0.5) since, in general, it has not been possible to detect the host galaxy (). We have computed the extended radio luminosity of these 10 objects assuming that the redshift is z=0.5 when it was not known. It seems very likely that at least eigth of them are extreme cases of HPQs. Indeed, most have a rather high extended radio luminosity; PKS0048-09, PKS0735+17 and PKS1519-27 have a high (> 5); PKS0426-380, S50716+71 and PKS1749+70 have a high index of rapid optical variability (I > 7.7%); PKS0735+17 and PKS1749+70 show high superluminal velocities (a > 6c). The status of two objects (S50454+84 and B21147+24) is rather uncertain due to the lack of data; they could possibly be genuine BLLs.
We are then probably left with only 8 to 10 genuine BLLs; their luminosity function is therefore very poorly determined, especially for luminosities larger than 1032 erg s-1 Hz-1; in fact, we cannot exclude that the space density of BLLs is 30 times smaller that of FR Is for any value of the radio luminosity.  expected to find 3 BLLs out of 18 observed FR Is with radio luminosities > 1032 erg s-1 Hz-1; they found none. This result is not in contradiction with the corrected BLL luminosity function.
Urry et al. (1999) have observed the host galaxies of nine BLLs with the HST; one has no reliable measured redshift and three have been reclassified as HPQs. The host galaxy has been detected in each of the five remaining BLLs ; they are E galaxies with smooth morphology; their average k-corrected absolute magnitute is -23.6 (rather than -24.6 as given by Urry et al. for the seven detected objects). This again stresses the need of a good classification of all objects in a sample to get reliable results.