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Astron. Astrophys. 358, 841-844 (2000)

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3. Discussion

As mentioned above, other correlation investigations have been done for [FORMULA]-ray loud blazars. It seems that the [FORMULA]-rays are correlated with some lower energetic bands (Dondi & Ghiselini 1995; Fan 1997a; Fan et al. 1998; Xie et al. 1997, 1998; Cheng et al. 2000).

If the [FORMULA]-rays result from up-scattering of emission line photons, a correlation between the [FORMULA]-rays and the emission lines should be expected. In this paper, we found that the luminosities in the [FORMULA]-rays are correlated with those of the emission lines. The correlation is better for the average [FORMULA]-fluxes than for the maximum fluxes. Does the result favour the above argument?

When considering flux-limited samples, the use of luminosities instead of flux often introduces a redshift bias to the data, since the luminosities are strongly correlated with redshift. A correlation will be present in luminosity even there is no correlation in the corresponding flux density (Elvis et al. 1978). Feigelson & Berg (1983) show that if there is no intrinsic luminosity-luminosity correlation, no correlation will appear in the flux-flux relation even in the flux-limited samples (also see Mücke et al. 1997). Since the EGRET data certainly are flux-limited, we will discuss the luminosity relation further. First, we exclude the effect of redshift on the luminosity correlation; second, we consider the flux-flux relation.

To exclude the redshift effect, we use the method of Kendall & Stuart (1979). If [FORMULA] is the correlation coefficient between [FORMULA] and [FORMULA], in the case of three variables, the correlation between two of them, excluding the effect of the third one, is


From the data in Table 1, correlation coefficients, [FORMULA] and [FORMULA] can be obtained. The correlation coefficient between the [FORMULA]-ray and the emission line luminosities, with the effect of the redshift excluded, is then [FORMULA] and [FORMULA]. Thus there is no evidence for intrinsic correlation between the [FORMULA]-rays and the emission lines. If we only consider the flat spectrum radio quasars, a similar result is obtained.

Now we consider the flux-flux relation. When linear regression is performed on the [FORMULA] 100 MeV [FORMULA]-ray flux and the emission line flux, there is no correlation between them. But if we exclude 3C 273, there is a tendency that the [FORMULA]-ray flux increases with increasing emission line flux (see Fig. 2).

[FIGURE] Fig. 2. The maximim [FORMULA]-ray flux vs. the emission line flux. The open circles are for flat spectrum radio quasars and the filled points for BL Lacertae objects

Therefore, we can say that, with the available data, there is no evidence of correlation between the [FORMULA]-rays and the emission lines. Does that suggest that the up-scattered soft photons are not from the broad emission lines? This question will only be answered with better [FORMULA]-ray data in the future. The reasons are: 1) the [FORMULA]-ray flux densities used here are based on photon fluxes and photon spectral indices both of which have substantial errors, leading to possible significant errors in the flux densities; 2) most of the EGRET-detected blazars are detected only in a flaring state, while most of the optical spectra were taken in non-flaring states. These facts should dilute any intrinsic luminosity-luminosity correlation.

Our analysis does not conflict with the SSC model, as seen from the following discussion. Observations indicate that the [FORMULA]-rays are strongly beamed. But the X-ray emissions seem not to be strongly beamed (Fan 1997b). If the emission is boosted in the form as showed in our previous paper (Fan et al. 1993, also see Fan 1999), then the emissions in neither the X-ray nor the optical bands are so strongly beamed as the radio bands. This implies that we can not expect close correlation between [FORMULA]-ray and X-ray/optical bands for the observation data. Nevertheless, we can expect a correlation between the observed radio and the [FORMULA]-rays since they both are strongly beamed (Fan 1997a; Fan et al. 1998). If the SSC model is correct, we should expect a correlation for the corrected(intrinsic) [FORMULA]-ray and optical data when the Doppler factors (boosting factors) are known. Conversely, the Doppler factor can be estimated using the SSC model.

In AGNs, the power is generated through accretion, and then extracted from the disk/black hole rotational energy and converted into the kinetic power in the jet (e.g., Blandford & Znajek 1977). Therefore, there is a possible disk-jet symbiosis in AGNs, and some tests have been performed (e.g. Rawlings & Saunders 1991; Falcke et al. 1995; Celotti et al. 1997; Serjeant et al. 1998; Cao & Jiang 1999). In those papers, the radio luminosity is taken to represent the jet and the emission line luminosity or optical luminosity is taken to represent the disk. Correlation is found to exist between those luminosities, and regarded as evidence of the disk-jet symbiosis.

If a correlation between [FORMULA]-rays and emission lines is found to exist with more data in the future, it may support a disk-jet symbiosis. In this case, the [FORMULA]-ray emissions could be taken to represent the jet, and the correlation with the emission line could be taken as the confirmation of the disk-jet symbiosis. However, this correlation gives no signature of the [FORMULA]-ray emission mechanism. Therefore, the relation does not conflict the SSC model.

In this paper, a possible relation between the [FORMULA]-ray emission and emission lines is investigated and discussed for a 36-blazar sample. The apparent luminosity correlation between the [FORMULA]-rays and the emission lines is found to be entirely due to the effect of the redshift. There is no intrinsic correlation between the two luminosities, and thus no evidence to support the argument that the up-scattered photons are from the broad emission lines. The claimed radio and [FORMULA]-ray correlation is most likely from the fact that the both emissions are strongly beamed, and we can not expect correlation between the [FORMULA]-ray and other bands.

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Online publication: June 20, 2000