4 Results

Theoretical models that explain the nature of the observed behaviors of blazars predict a continuity between the various subclasses. To check if this is true for the objects belonging to our catalogue, we computed the distributions of redshifts, X-ray and broad band spectral indices and luminosities.

Moreover, another goal of this work is to compare the blazar characteristics observed in the soft and in the hard X-ray band. We divided our sources into two groups, one with the data obtained with ROSAT (0.1-2.4 keV) and another one with the data obtained with EXOSAT, ASCA, and BeppoSAX (2-10 keV). As anticipated (see Table 2) the first group of sources contains 227 objects, while the second one contains 88 sources (38 HBL, 19 LBL and 31 FSRQ). In addition, since the two sources 2344+514 and 1652+398 are very variable and we have data both for a quiescent and a flaring state, in the latter group we put the data of two observations (one for the high and one for the low state) for each of them.

 

 

Table 3: Average values of X-ray spectral indices, redshifts, $\nu L_\nu$ luminosities in different bands and broad band spectral indices. The listed errors are weighted errors.

	HBL	LBL	FSRQ
$\alpha _{\rm x}$[2-10 keV]	$1.34\pm0.05$	$0.84\pm0.07$	$0.65\pm0.04$
$\alpha _{\rm x}$[0.1-2.4 keV]	$1.28\pm0.04$	$1.39\pm0.08$	$0.76\pm0.06$
z	$0.25\pm0.02$	$0.46\pm0.05$	$1.27\pm0.12$
Log $\nu_{\rm r}L_{\nu_{\rm r}}$	$41.51\pm0.07$	$43.65\pm0.16$	$44.93\pm0.13$
Log $\nu_{\rm o}L_{\nu_{\rm o}}$	$44.66\pm0.06$	$45.49\pm0.12$	$46.35\pm0.11$
Log $\nu_{\rm x}L_{\nu_{\rm x}}$	$44.62\pm0.08$	$44.52\pm0.15$	$45.89\pm0.11$
$\alpha_{\rm ro}$	$0.36\pm0.01$	$0.56\pm0.02$	$0.66\pm0.01$
$\alpha_{\rm ox}$	$1.03\pm0.02$	$1.38\pm0.02$	$1.21\pm0.02$
$\alpha_{\rm rx}$	$0.59\pm0.01$	$0.84\pm0.01$	$0.85\pm0.01$

Figure 1: Distribution of the energy spectral index $\alpha _{\rm x}$ in the 2-10 keV hard X-ray energy band. Note the difference between the HBL and the other two subclasses of blazars. The KS test gives a probability $P=8\times 10^{-6}$ that the HBL and the LBL values are drawn from the same distribution ( $P=2\times 10^{-12}$ for HBL-FSRQ and P=0.03 for LBL-FSRQ).

Figure 2: Distribution of the energy spectral index $\alpha _{\rm x}$ in the 0.1-2.4 keV soft X-ray energy band. In this case LBL are more similar to HBL than to FSRQ. KS test results: P=0.20 for HBL-LBL; 10-8 for HBL-FSRQ; $5\times 10^{-8}$ for LBL-FSRQ.

   
4.1 Histograms

The distribution of spectral indices, redshifts and luminosities are shown by the histograms in Figs. 1-9. In the figure captions we give the probability, according to the Kolmogorov-Smirnov (KS) test, that two distributions are drawn from the same parent population, comparing HBLs and LBLs, HBLs and FSRQs, LBLs and FSRQs.

The mean values of the plotted quantities are listed in Table 3.

4.1.1 Spectral indices

The distributions of the energy spectral indices (Figs. 1 and 2) show that for FSRQ we have an average value less than unity in both energy ranges. This suggests that for this subclass of blazars we are observing only the inverse Compton component in the entire X-ray band, from 0.1 to 10 keV. For HBL, instead, the average energy spectral index is greater than unity, indicating that we are observing the synchrotron component after its peak. On average, LBL show a flattening going from the soft to the hard X-ray bands.

These results suggest that both the soft and the hard X-ray bands are dominated by the inverse Compton process in FSRQs and by the synchrotron process in HBL, while in LBL we have the synchrotron flux dominating in the soft band and the flatter Compton component emerging at higher X-ray energies.

Figure 3: Redshift distribution for the three subclasses. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $P=2 \times 10^{-3}$ for HBL-LBL; $9\times 10^{-17}$ for HBL-FSRQ; $5\times 10^{-5}$ for LBL-FSRQ.

Figure 4: Distribution of the radio luminosity for the three subclasses. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $7 \times 10^{-19}$ for HBL-LBL; $7 \times 10^{-33}$ for HBL-FSRQ; 10-6 for LBL-FSRQ.

Figure 5: Distribution of the optical luminosity for the three subclasses. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $P=2 \times 10^{-7}$ for HBL-LBL; 10-22 for HBL-FSRQ; $3 \times 10^{-5}$ for LBL-FSRQ.

Figure 6: Distribution of the X-ray luminosity for the three subclasses. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): P=0.6 for HBL-LBL; $3 \times 10^{-13}$ for HBL-FSRQ; $2 \times 10^{-8}$ for LBL-FSRQ.

Figure 7: Distribution of the broad band radio-optical spectral index for the three subclasses. Fluxes have been K-corrected as explained in the text. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $P=4 \times 10^{-18}$ for HBL-LBL; $2\times 10^{-35}$ for HBL-FSRQ; $4\times 10^{-4}$ for LBL-FSRQ.

Figure 8: Distribution of the broad band optical-X-ray spectral index for the three subclasses. Fluxes have been K-corrected as explained in the text. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $P=5 \times 10^{-17}$ for HBL-LBL; 10-5 for HBL-FSRQ; 10-8 for LBL-FSRQ.

Figure 9: Distribution of the broad band radio-X-ray spectral index for the three subclasses. Fluxes have been K-corrected as explained in the text. Thick solid lines refer to the entire sample, while thin solid lines refer to sources with only ROSAT data. KS test results (for the entire sample): $P=8 \times 10^{-39}$ for HBL-LBL; $5 \times 10^{-40}$ for HBL-FSRQ; 0.7 for LBL-FSRQ.

4.1.2 Redshift

While the redshifts of FSRQs are quite uniformly distributed up to a value of $\simeq$3, BL Lacs have redshifts lower than 1 (and HBL have lower redshifts than LBL, see Fig. 3). There is no significant difference between the redshift distributions of sources observed in the hard and in the soft X-ray bands. Of the sources in our sample, about 25% have no measured redshift (38 HBL and 17 LBL). This incompletness, even if not severe, could bias the shown redshift distribution of HBLs towards the lower part (since larger redshifts are more difficult to measure).

4.1.3 Luminosities

From the radio, optical and 1 keV monochromatic fluxes we have calculated the "$\nu L_\nu$'' luminosities in the corresponding bands. The distributions of radio and optical luminosities (Figs. 4 and 5) show a continue variation in the three subclasses of blazar: HBLs are the least powerful sources, and FSRQs are the most luminous objects. this is more pronounced in the radio than in the optical band. The X-ray luminosities of HBLs and LBLs are very similar (Fig. 6), while FSRQs are more luminous by a factor of 10.

4.1.4 Broad band indices

Also the broad band spectral index $\alpha_{\rm ro}$ changes smoothly between the subclasses of blazar (Fig. 7). On average, it becomes steeper going from HBL to FSRQs. The optical to X-ray broad band index distribution (Fig. 8) is broader for HBL, with an average value smaller than for LBL and FSRQs. The spectral index $\alpha_{\rm rx}$ (Fig. 9) is on average the same for FSRQs and LBLs, and obviously flatter (by definition) for HBLs.