6 Correlations

In order to see if the proposed parameterization of the average SED of blazars (constructed on the basis of a subsample of the sources in our catalogue) can account for the general properties of all the blazars in our catalogue, we have investigated the correlations between the X-ray spectral index (both hard and soft) with the radio and X-ray luminosities and with the broad band spectral indices. We have then considered the correlations between broad band indices. The results are shown in Figs. 12-18 (solid line), where we have superposed the relations predicted by the new parameterization.

In Figs. 11 and 12 we show the hard and soft X-ray indices as a function of the radio and X-ray luminosity for all sources, and compare these data with the model expectations. Note that the latter have been constructed to describe the average properties of blazars, whatever the scatter around it. Bearing this in mind, we can consider the description of the model quite satisfactorily.

Figure 11: Soft and hard X-ray spectral index vs. the radio luminosity. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 12: Soft and hard X-ray spectral index vs. the X-ray luminosity. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 13: Soft and hard X-ray spectral index vs. the broad band radio to X-ray index. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 14: Soft and hard X-ray spectral index vs. the broad band radio to optical index. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 15: Soft and hard X-ray spectral index vs. the broad band optical to X-ray index. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 16: Radio to optical vs. optical to X-ray broad band indices. Circles: HBL, Squares: LBL, Triangles: FSRQs.

In Fig. 13 we show the hard and soft X-ray indices as a function of the broad band index $\alpha_{\rm rx}$. The model well describes the small $\alpha_{\rm rx}$ part (corresponding to HBLs), but fails to describe the X-ray flattest sources with the steeper value of $\alpha_{\rm rx}$. This is due to two reasons: i) the slope of the power law of the Compton component is assumed to be $\alpha=0.7$, so that flatter indices are not possible; ii) the ratio between the radio and the 1 keV Compton luminosity is fixed for all sources. This results in a saturated value of $\alpha_{\rm rx}\sim 0.85$, occurring when the Compton component dominates at 1 keV (i.e. for powerful sources).

In Figs. 14 and 15 we show $\alpha_{\rm X}$ as a function of $\alpha_{\rm ro}$ and $\alpha_{\rm ox}$: the average properties are well described by the model.

In Fig. 16, we show the "classic'' $\alpha_{\rm ro}$- $\alpha_{\rm ox}$ diagram for the two subsamples of sources. Note that the model well describes all the data but those sources with the largest values of $\alpha_{\rm ox}$, corresponding to "transition'' sources between the LBLs and FSRQ.

 

 

Table 6: References used in Table 5. TW means This Work.

Ba94:	Bade et al. (1994)	Gh99:	Ghisellini et al. (1999)	Pa95:	Padovani et al. (1995)
Ba98:	Bade et al. (1998)	BSGh:	Ghisellini in BeppoSAX Archive	Pa99:	Padovani et al. (1999)
Br85:	Bregman et al. (1985)	Gi98:	Giommi et al. (1998)	Pe96:	Perlman et al. (1996)
Br94:	Brinkmann et al. (1994)	Gi99:	Giommi et al. (1999)	Sa94:	Sambruna et al. (1994)
Br97:	Brinkmann et al. (1997)	Go95:	Ghosh et al. (1995)	Sa97a:	Sambruna et al. (1997)
Ca97:	Cappi et al. (1997)	Gr96:	Greiner et al. (1996)	Sa97b:	Sambruna et al. (1997)
Co95:	Comastri et al. (1995)	Kh81:	Khuer et al. (1981)	Sa99:	Sambruna et al. (1999)
Co97:	Comastri et al. (1997)	Ku98:	Kubo et al. (1998)	Sb96:	Siebert et al. (1996)
Cs00:	Costamante et al. (2000)	IT90:	Impey et al. (1990)	Sb99:	Siebert et al. (1999)
El99:	Elvis et al. (1999)	IT91:	Impey et al. (1991)	Sn97:	Sing et al. (1997)
Fa97:	Fabian et al. (1997)	La96:	Lamer et al. (1996)	Ta00:	Tagliaferri et al. (2000)
Fa98:	Fabian et al. (1998)	Le97:	Leighly et al. (1997)	Tv99:	Tavecchio et al. (2000)
Fo98:	Fossati et al. (1998)	LM99:	Laurent-Muehleisen et al. (1999)	VV93:	Veron-Cetty et al. (1993)
Fo98b:	Fossati et al. (1998)	Ma98b:	Maraschi et al. (1998)	Xu99:	Xue et al. (1999)
Ge96:	George et al. (1996)	BSMc:	Maccacaro in BeppoSAX Archive	Ya98:	Yaqoob et al. (1998)
Gh93:	Ghisellini et al. (1993)	Na96:	Nass et al. (1996)	Wa99:	Watson et al. (1999)
Gh98:	Ghisellini (1998)	NED:	NASA-IPAC Extragalactic Database	Wo98:	Wolter et al. (1998)
Gh98b:	Ghisellini et al. (1998)	Or98:	Orr et al. (1998)	Wo90:	Worrall et al. (1990)

Figure 17: Optical to X-ray vs. radio to X-ray broad band indices. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figure 18: Radio to optical vs. radio to X-ray broad band indices. Circles: HBL, Squares: LBL, Triangles: FSRQs.

Figures 17, and 18: note that HBL are well separated from the other classes of blazars. Note also that the model, by construction, has an asymptotic limit for $\alpha_{\rm rx}$, whose value therefore saturates at $\alpha_{\rm rx} \simeq 0.85$.