5 The average SED

In Fig. 10 we show the sequence of average SEDs as published by F98, but including the [2-10 keV] averages spectral indices and fluxes. The latter have been constructed considering only the same samples considered by F98.

Figure 10: The average SED of the blazars studied by Fossati et al. (1998), including the average values of the hard X-ray spectra. The thin solid lines are the spectra constructed following the parameterization proposed in this paper.

It can be seen that in general the 2-10 keV fluxes and spectral indices connect smoothly on the softer ROSAT data even if they are, on average, flatter than the latter. This is due to the emergence, in the hard X-ray band, of the inverse Compton component which is progressively more dominant as the luminosity increases.

For the average SED corresponding to the second lowest luminosity bin, there is a mismatch between the soft and hard X-ray data. By comparing the data of each source in common, we found that all 5 sources were brighter when observed by ASCA or BeppoSAX than at the time of the ROSAT observations. We therefore believe that the mismatch is due to the variable nature of the objects and the small number of sources in this luminosity bin.

The average spectral indices of the objects in common with F98 are listed in Table 4, which also lists the average luminosities at 4.47 keV (the logarithmic mid point between 2 and 10 keV).

 

 

Table 4: Average values of the X-ray luminosity at 4.47 keV ($\nu L_\nu$values) and average 2-10 keV spectral indices, for the sources in common with Fossati et al. (1998), for each radio luminosity bin.

$<\log\nu_{\rm r} L_{\nu_{\rm r}}>$	$<\log\nu_{\rm x}L_{\nu_{\rm x}}>$	$N_{\rm sources}$	$\alpha _{\rm x}$
	@4.47 keV		2-10 keV
<42	44.2	12	$1.39\pm0.21$
42-43	44.5	5	$1.19\pm0.21$
43-44	44.9	6	$0.95\pm0.11$
44-45	45.8	6	$0.68\pm0.02$
>45	47.0	11	$0.58\pm0.06$

The continuous lines in Fig. 10 correspond to a simple parametric model derived by the one introduced by Fossati et al. (1998). We introduce minor modifications, adopted both to better represent our data at small luminosities and to follow a more physical scenario, in which the low power HBLs can be described by a pure synchrotron-self Compton model (see e.g. Ghisellini et al. 1998). We remind the reader here of the key assumptions of the F98 parametric model:

$\bullet$

The observed radio luminosity $L_{\rm R}=(\nu L_\nu)\vert _{\rm 5~GHz}$ is assumed to be linearly proportional to the bolometric luminosity, and related to the location of the synchrotron peak through:

$$\nu_{\rm s} \, \propto L_{\rm R}^{-\eta}$$ (1)

where $\eta=1.8$ for $L_{\rm R}<3\times 10^{42}$ erg s^-1 and $\eta= 0.6$ for $L_{\rm R}>3\times 10^{42}$ erg s^-1.

$\bullet$

The ratio between the Compton and the synchrotron peak frequencies is constant: $\nu_{\rm c}/\nu_{\rm s} = 5\times 10^8$ for all luminosities.

$\bullet$

The ratio between the power of the inverse Compton and the radio powers is constant: $L_{\rm c}/L_{\rm R} = 3\times 10^3$ for all luminosities;

$\bullet$

The ratio between the radio and X-ray (at 1 keV) Compton luminosity is fixed.

The SED is then constructed assuming for the synchrotron component a flat ( $\propto \nu^{-0.2}$) radio spectrum connecting to a parabola (in log-log space) peaking at $\nu_{\rm s}$. The junctions between the power law and the parabola is continuous. For the inverse Compton spectrum it is assumed that an initial power law of index $\alpha = 0.6$ ends in another parabola peaking at $\nu_{\rm c}$.

We modified the Fossati et al. (1998) description in the following way:

$\bullet$

We changed the values of $\eta$, assuming $\eta=1.2$ and 0.4 for $L_{\rm R}$ smaller and greater than 10⁴³ erg s^-1;

$\bullet$

The ratio $\nu_{\rm c}/\nu_{\rm s}$ is assumed to be constant with the same value as before for $L_{\rm R}>10^{43}$ erg s^-1, but for smaller radio luminosity we set:

$$% {\nu_{\rm c} \over \nu_{\rm s}} \, = \, 5\times 10^8 L_{\rm R,43}^{-0.4};$$ (2)

$\bullet$

Below $L_{\rm R}<10^{43}$ erg s^-1 we assume that the synchrotron and Compton peaks have the same luminosities. For greater $L_{\rm R}$ we assumed, as before, $L_{\rm c}/L_{\rm R} = 3\times 10^3$.

The spectra predicted by this new parameterization are shown in Fig. 10 as thin solid lines. As anticipated, the assumptions described above have a physical motivation. In fact, for low luminosity sources, we have evidences that the seed photons producing the Compton spectrum are the locally produced synchrotron ones, with no or negligible contributions from seed photons produced externally to the jet (e.g. from the Broad Line Region). In this case:

i)

The ratio $\nu_{\rm c}/\nu_{\rm s}$ increases with $\nu_{\rm s}$ as long as the scattering process is in the Thomson regime, and decreases with $\nu_{\rm s}$ in the Klein Nishina regime;

ii)

On average, the BL Lacertae objects detected by EGRET with $L_{\rm R}<10^{43}$ erg s^-1 have roughly the same power in the synchrotron and Compton components;

iii)

The radio luminosity $L_{\rm R}=10^{43}$ erg s^-1may corresponds to the power for which emission lines and/or external seed photons becomes important for the formation of the inverse Compton spectrum (see e.g. Ghisellini et al. 1998).