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Astron. Astrophys. 358, 104-112 (2000)

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3. Core versus extended luminosity

According to the unification models the beamed and unbeamed populations must cover the same range of extended luminosity, as this is considered to be isotropic. On the contrary, emission from the core is affected by beaming: radio galaxies should have a fainter central component, whose intensity would depend on the Doppler factor [FORMULA], where [FORMULA], [FORMULA] is the bulk velocity of the emitting plasma and [FORMULA] the angle between the direction of the jet and the line of sight. The transformation law for the specific flux density is in fact [FORMULA], where the primed quantity refers to the comoving frame, [FORMULA] is the local spectral index, [FORMULA] for a continuous jet and [FORMULA] for a moving sphere.

Therefore the comparison of the core emission of beamed objects and their parent population with similar extended emission provides a direct estimate of the Lorentz factor of the radiating plasma, if the typical observing angles are known. With this aim and similarly to what has been done in the radio band (e.g. Kollgaard et al. 1996), we plot the optical V band luminosity ([FORMULA]) vs the extended radio luminosity at 1.4 GHz ([FORMULA]) for the three samples (Fig. 1).

[FIGURE] Fig. 1. Optical core luminosity (V band) versus radio extended luminosity at 1.4 GHz for FR I (circles), HBLs (squares) and LBLs (triangles). The grey scale refers to the three bins of extended radio power. The dashed line represents the linear fit to the FR I sample, having excluded the most aligned sources, here marked with crosses (see text). The range of extended power covered by the B2 sample of radio galaxies is also indicated.

First we should note that the HBL objects do not fully share the range of extended radio power of the 3CR radio galaxies (the HBL total luminosities are in fact more similar to the objects belonging to the B2 sample of low power radio galaxies). Conversely, [FORMULA] of LBL well match those FR I of the 3CR catalog.

Also notice that the regions occupied by the two samples of BL Lacs appear to be continuously connected, the lower radio power BL Lacs (which are HBLs) and the higher radio power ones (LBLs) having an optical luminosity which weakly increases for increasing extended luminosity. Because of this trend, in order to compare sources with the same [FORMULA] we have sub-divided the samples into three bins, namely: [FORMULA] [erg s-1 Hz-1] [FORMULA], [FORMULA] between 31.5 and 32.5, and [FORMULA].

We thus calculate the median values of the observed nuclear luminosity of FR I and BL Lacs in each interval of extended power. BL Lacs are on average 4 orders of magnitude brighter than FR I cores. We can assume that BL Lacs are observed 1 at [FORMULA] and FR Is at [FORMULA]: in fact, for an isotropic distribution of objects, [FORMULA] corresponds to the median angle if, as it is in the case of FR I, the scatter in the optical luminosity is dominated by relativistic beaming. Bulk Lorentz factors [FORMULA] [FORMULA] for the case of an emitting sphere and [FORMULA] for a continuous jet are required in order to account for the different core luminosities of FR I and BL Lacs in each bin of extended power. An optical spectral index [FORMULA] is assumed for all sources (independent of beaming).

An alternative method to estimate [FORMULA] relies on the fact that, for a randomly oriented sample, the best fit regression line of a luminosity distribution corresponds to the behavior of sources observed at [FORMULA], once the most core dominated objects are excluded (Kollgaard et al. 1996). We thus determine the best fit regression of FR I in the [FORMULA] plane, after excluding from the sample the 5 objects in which optical jets are detected. These sources, in fact, have the most luminous optical cores, are among the most core dominated objects in the radio band, and their radio jets are shorter, indicating that they are pointing towards the observer (Sparks et al. 1995). Interestingly, we obtain that there is a remarkable correlation ([FORMULA]) between [FORMULA] and [FORMULA], among the remaining 20 "highly misoriented" objects, although with a slope ([FORMULA]) marginally steeper than the correlation between [FORMULA] and core radio luminosity ([FORMULA]) found by Giovannini et al. (1988) for a larger sample of radio galaxies. In Fig. 2 we show the regions in which the three samples are located in the [FORMULA] plane, and the dashed lines represent the "beamed" FR I population as observed under an angle [FORMULA] in the case of [FORMULA]. Also with this method [FORMULA] [FORMULA] ([FORMULA]) are required to displace the FR I to the regions occupied by both HBL and LBL for [FORMULA] ([FORMULA]).

[FIGURE] Fig. 2. The regions occupied by the three samples in the optical luminosity versus extended radio luminosity plane, as for Fig. 1. The dashed lines indicate the correlation found between these two quantities when shifted by beaming effects for the values of the bulk Lorentz factor marked on the left.

Let us now consider [FORMULA] (at 5 GHz) versus [FORMULA] (Fig. 3), analogously to what is shown by Kollgaard et al. (1996) for a larger sample of radio galaxies (which also includes our objects). The typical radio core luminosities of HBL and LBL are significantly different, the latter objects being on average about one order of magnitude more luminous than the former ones. Conversely, as we have already pointed out, no substantial difference between the two classes is found in the case of [FORMULA].

[FIGURE] Fig. 3. Radio core luminosity (at 5 GHz) versus radio extended luminosity at 1.4 GHz for FR I (circles), X-ray selected (squares) and radio-selected BL Lacs (triangles). The dashed line is the correlation between these two quantities found for a larger sample of galaxies by Giovannini et al. (1988) and converted to 1.4 GHz using [FORMULA].

These results have been initially attributed to a different amount of beaming for X-ray and radio-selected BL Lacs (i.e. different angle of sight and/or different jet velocities 2) while more recently a consistent picture has emerged where this diversity can be accounted for by the different shape of their intrinsic SED (e.g. Padovani 1992, Ghisellini & Maraschi 1989, Giommi & Padovani 1994, Fossati et al. 1998). The role of these two scenarios will be further explored in the next section, through the comparison of the SED of both types of BL Lacs with their parents.

We conclude that the Lorentz factors inferred from the comparison of the radio, but also optical emission of FR I and BL Lacs, are consistent with those previously estimated from the statistics of these sources within the unifying scheme. However, as already mentioned, such values are significantly and systematically lower than those required by other independent means, such as superluminal motions and high energy spectral constraints (fit to the overall SED and time-lags) in both LBLs and HBLs. (Maraschi et al. 1992, Sikora et al. 1994, Celotti et al. 1998, Tavecchio et al. 1998). These latter methods require a value of the Doppler factor [FORMULA] in the range 15-20 for the region emitting most of the radiation in both HBLs and LBLs. The need for high degrees of beaming will constitute a crucial point in the following.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000