Unifying models for X-ray selected and radio selected BL Lac objects

We discuss alternative interpretations of the differences in the spectral energy distributions (SEDs) of BL Lacs found in complete radio or X-ray surveys. A large body of observations in different bands suggests that the SEDs of BL Lac objects appearing in X-ray surveys differ from those appearing in radio surveys mainly in having a (synchrotron) spectral cut-off (or break) at much higher frequency. In order to explain the different properties of radio- and X-ray-selected BL Lacs, Giommi and Padovani proposed a model based on a common radio luminosity function. At each radio luminosity, objects with high-frequency spectral cut-offs are assumed to be a minority. Nevertheless, they dominate the X-ray-selected population due to the larger X-ray-to-radio flux ratios. An alternative model explored here (reminiscent of the orientation models previously proposed) is that the X-ray luminosity function is 'primary', and that at each X-ray luminosity a minority of objects have larger radio-to-X-ray ratios. The predictions of the two scenarios, computed via a Monte Carlo technique, are compared with the observed properties of BL Lacs in the two samples extracted, respectively, from the 1-Jy radio survey and the Einstein Slew Survey. We show that both models can explain some but not all of the observed features. We then propose a completely new approach, based on the idea that the physical parameter which governs the shape of the SEDs is (or is associated with) the bolometric luminosity. Assuming an empirical relation between spectral shape and luminosity, we show that the observational properties of the two surveys can be reproduced with at least the same accuracy as the two previous models.