6 Discussion

The large number of objects included in the HRX-BL Lac sample enabled us to study in detail a number of BL Lac properties in different wavelength regions. In the following, we will discuss these properties with special emphasis on their compatibility with the most recent models trying to unify the HBL and LBL objects.

6.1 Strength of the calcium break and luminosities

We observed a clear anti-correlation between calcium break strength and the luminosity in the radio, near infrared, optical, and X-rays bands. We explain this with a wide range of luminosities for the non-thermal source, while the host galaxies seem to have approximately constant luminosity. The higher the luminosity of the central source, the more does the core outshine the hosting galaxy, leading to decreasing break strength with increasing luminosity.

The identification of several HRX-BL Lac with $25\% < {\rm Ca{-}break} < 40\%$ and the smooth extension of the correlation between break strength and luminosities into this range, supports previous findings that BL Lacs can have $\rm Ca{-}break > 25\%$ (Marchã et al. 1996; Laurent-Muehleisen et al. 1999; Rector et al. 2000; Landt et al. 2002) in contrast to earlier suggestions (Stocke et al. 1989).

Landt et al. (2002) studied in detail the dependency of the calcium break strength on the luminosity of the blazars inside the DXRBS sample (Padovani 2001). They found the same correlation as described here for the HRX-BL Lac sample and show that the calcium break values decrease with increasing jet power, and therefore with increasing luminosity. Based on this they conclude that the break value of BL Lac objects could be an indicator of the orientation. Nevertheless different luminosities of the core component (i.e. of the jet) will also play a major role in the effect, and it seems to be difficult to disentangle the influence from different orientation and from different jet luminosity. Thus though we find for the HRX-BL Lac sample the same correlation as described by Landt et al. (2002) we conclude here only that the break strength is an indicator of different apparent luminosity, either based on different orientation, or on different jet power, or on mixture of both effects.

6.2 HBL/LBL: Evolutionary dichotomy?

Most of the results for the HRX-BL Lac core sample (Bade et al. 1998) could be confirmed by the complete sample presented here. The most significant discrepancy are the different results of the $V_{\rm e}/V_{\rm a}$ test. We found negative evolution using the complete sample, but we did not find differences in evolution, if we divide the sample by $\alpha _{\rm OX}$ (or peak frequency).

The results of Bade et al. (1998) could have been arisen from selection effects due to the "patchy'' search area used. A Monte-Carlo simulation done on the HRX-BL Lac complete sample shows however, that this is not the case. By randomly selecting a subsample of 17 BL Lac objects (which is the number of objects for which Bade et al. found different types of evolution) out of the HBLs of the complete sample there is a chance of <1% only to find a $\langle V_{\rm e}/V_{\rm a} \rangle < 0.35$.

Another reason for the different results could be related to the different treatment of the radio properties. As radio detection was not a selection criterium in Bade et al., no radio flux limit was taken into account. Applying here the $V_{\rm e}/V_{\rm a}$-test to the complete sample (cf. Sect. 5), the accessible volume $V_{\rm a}$ was determined for $\approx$10% of the objects by the radio limit. The $V_{\rm e}/V_{\rm a}$ values are correspondingly increased compared to the case where only X-ray flux limit is taken into account, resulting in a less negative evolution. There remains the fact that no BL Lac objects were found yet, with $f_{\rm R} < 2 \; \rm mJy$ radio counterparts and the question is still open whether this is a selection effect or not. It could be that our decision to apply the radio detection as selection criterium weakens the negative evolution found in pure X-ray selected samples.

The result, that the evolution of BL Lac objects of the HBL and IBL type is consistent with no evolution is in good agreement with other recent studies. Neither REX or DXRBS, nor the HRX-BL Lac sample show a difference for the more or less X-ray dominated BL Lacs. On the contrary it seems that the evolution of the IBL might even be slightly more positive than that of the HBL class. This picture clearly differs from the EMSS BL Lac result of $\langle V_{\rm e}/V_{\rm a} \rangle = 0.36 \pm 0.05$, while the sendentary survey, presented by Giommi et al. (1999) seems not be complete enough up to now to draw a firm conclusion. Caccianiga et al. (2002) argue, that the REX might miss the negative evolution of the HBL is not visible simply because the sample is not deep enough, and this argumentation then would also apply for the HRX-BL Lac sample, which X-ray flux limit is about two times higher than that of the REX BL Lacs. Their simulation result in the conclusion that even a completion of the REX survey might not lead to a highly significant negative evolution ($2 \sigma$ for the simulated sample).

Finally, the evolution found in the course of this work is in good agreement with that of FR-I galaxies ( $\langle V_{\rm e}/V_{\rm a} \rangle = 0.40 \pm 0.06$) within the 3CR sample (Laing et al. 1984). This supports the assumption that the FR-I galaxies build the parent population of BL Lac objects (see e.g. Padovani & Urry 1990).

In contrast to HBLs, the LBLs show weak or positive evolution ( $\langle V_{\rm e}/V_{\rm a} \rangle = 0.61 \pm 0.05$) as shown for the 1 Jy sample by Rector & Stocke (2001). Following the sequence of blazars, also FSRQs exhibit significant positive evolution ( $\langle V_{\rm e}/V_{\rm a} \rangle = 0.58 \pm 0.03$ for the 119 FSRQs in the DXRBS sample; Padovani 2001). Also FR-II radio galaxies and "normal'' quasars seem to be more numerous and/or luminous at cosmological distances than in the neighborhood, leaving the question for the reasons of the HBL/LBL evolutionary dichotomy of relevance also in future.

6.3 A unifying model for LBL and HBL

The different evolutionary behaviour of HBLs and LBLs is a challenge for all theories to unify both BL Lac types into one class. However, the existence of transition objects and the numerous similar properties of LBLs and HBLs make it plausible that both classes belong to the same parent population.

As described by Böttcher & Dermer (2002) one way to unify both classes would be a transformation of LBLs into HBLs as the BL Lac objects grow older. In this model, BL Lac objects start as LBLs with jets of high energy densities. Strong cooling limits the electron energies leading to cutoff frequencies for the synchrotron component at optical wavelengths and for the IC component in the GeV energy range. As shown by Beckmann et al. (2002), this results in steep X-ray spectra with strong curvature. The core outshines the host galaxy leading to a low calcium break value (Landt et al. 2002) as seen also for the HRX-BL Lac sample (cf. Fig. 2).

When by the time the source of the jet gets less powerful the energy density within the jet decreases (Tavecchio et al. 1998). The cooling efficiency decreases as well resulting in higher cutoff frequencies for HBLs. The shift of the cutoff frequencies to higher energies is therefore accompanied by decreasing bolometric luminosities, which is evident from the decrease of the luminosities in the radio, near IR and optical bands. Due to the increasing peak frequencies of the synchrotron branch more energy is released in the X-ray band and the X-ray luminosity increases quite in contrast to the luminosities at shorter frequencies (cf. Table 5). The X-ray spectra are correspondingly flatter and less curved than in the LBL state (Beckmann & Wolter 2001).

Objects which do not fit into this scenario are doubtlessly the extremely luminous HBLs, like 1ES 1517+656 (Beckmann et al. 1999b). The scenario presented here assumes the HBLs to be on average less luminous than the LBLs. Apart from the exceptionally high X-ray luminosity, this object also shows an optical luminosity typical for a Flat Spectrum Radio Quasar (FSRQ). Padovani (2001) argues that those high state BL Lacs with high peak frequency might belong to the high energy peaked FSRQ class (HFSRQ), flat-spectrum radio quasars with synchrotron peak in the UV/X-ray band. In this case 1ES 1517+656 should show strong emission lines, e.g. strong H$_{\alpha}$ and H$_{\beta}$ which would be located in the near infrared for this high-redshift BL Lac (z = 0.7) and would have been missed by previous observations.

The HRX-BL Lac sample could be the basis to study the extreme end of the HBL population, the ultra high frequency peaked BL Lac objects (UHBL). Sambruna et al. (1996) argued that objects with cutoff frequencies higher than $10^{18} ~{\rm Hz}$ would be detected only in hard X-ray surveys but should be faint at lower frequencies, which would make their discovery difficult.

Nevertheless HBLs have already been detected at TeV energies, as e.g. 1ES 1426+428 (Aharonian et al. 2002; Horan et al. 2002) and 1ES 1959+650 (Horns & Konopelko 2002). Recently Costamante & Ghisellini (2002) showed that it is possible to select candidates for TeV BL Lacs on the basis of the knowledge of the SED, i.e. strong X-ray flux and a sufficiently strong radio-through-optical flux, which results in high peak frequencies of the synchrotron branch.

Also 13 HBLs within the HRX-BL Lac sample show peak frequencies $\nu_{\rm peak} > 10^{18} ~{\rm Hz}$from the parabolic fit to the synchrotron branch and three objects even $\nu_{\rm peak} > 10^{19} ~{\rm Hz}$. 1RXS J121158.1+224236 might even be a UHBL with a peak frequency of the synchrotron branch at $\nu_{\rm peak} \simeq 10^{22} ~{\rm Hz}$ . To confirm the high peak frequencies, for this extreme source, observations with the BeppoSAX satellite have been performed and results will be presented in a forthcoming paper. Investigations in the gamma region ( ${\sim} 1 ~ {\rm MeV}$) are needed to decide whether these energies are dominated by the synchrotron emission or if already the inverse Compton branch is rising. The SPI spectrograph on-board the INTEGRAL mission (see e.g. Winkler & Hermsen 2000), which has been successfully launched in October 2002, will allow to do spectroscopy in this energy region ( $20 ~{\rm keV}{-} 8 ~ {\rm MeV}$).

Acknowledgements

We would like to thank the anonymous referee for the valuable suggestions which helped us to improve the paper. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration. We acknowledge support by the Deutsche Forschungsgemeinschaft through grants Re 353/39-1 and En 176/23-1.