Radio luminosities and classificatory criteria of BL Lacertae objects

Using the sample of radio-selected BL Lacertae objects (RBLs) and X-ray selected BL Lacertae objects (XBLs) presented by Sambruna et al. ([CITE]), we calculated the luminosities in radio, optical and X-ray of each source and made a statistical analysis among the luminosities at different wave-bands, broad-band spectral indices from radio to X-ray ($\alpha_{\rm rx}$) and peak frequencies ($\nu_{\rm p}$). Our results are as follows: (i) there is a positive correlation between radio luminosity L r and $\alpha_{\rm rx}$ and a negative correlation between L r and $\nu_{\rm p}$. High-energy peak BL Lacs (HBLs) and low-energy peak BL Lacs (LBLs) can be distinguished very well; the dividing lines are probably those of $\log {L_{\rm r}}=43.25$ (erg/s) and $\alpha_{\rm rx}>$(or $\leq $)0.75 for $\log L_{\rm r}$–$\alpha_{\rm rx}$ plot and those of $\log L_{\rm r}\leq 43.25$ (erg/s) and $\log {\nu_{\rm p}}>14.7$ for the ${\bf\log}\,L_{\rm r}$ – ${\bf\log}\,\nu_{\rm p}$ plot; (ii) there is a weak positive correlation between optical luminosity L o and $\alpha_{\rm rx}$ and a negative weak correlation between $L_{\rm o}$ and $\nu_{\rm p}$; (iii) there is no correlation between X-ray luminosity L x and $\alpha_{\rm rx}$ or between L x and $\nu_{\rm p}$. From our analysis, we find that synchrotron radiation is the main X-ray radiation mechanism for HBLs while inverse Compton scattering is dominant for LBLs.