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

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4. FR I and BL Lac in the [FORMULA] and [FORMULA] plane

Since for the first time multifrequency data are available also for the nucleus of radio galaxies, we can now directly compare the spectral properties of beamed objects and their parent population: this new approach can thus combine information from the SED of BL Lacs with those inferred from their relation with FR I. In particular in Paper I and in Chiaberge et al. 2000we showed how the location of sources in the [FORMULA] and [FORMULA] plane represents a very useful tool to discuss their nuclear properties. In Fig. 4 we show the optical vs radio core luminosity for the three samples. The dashed line represents the (almost linear) correlation found between these two quantities among the FR I sources (Paper I). Radio galaxies, HBL and LBL occupy different regions of this plane: LBLs are located only marginally above the continuation of this correlation, while HBL are [FORMULA] order of magnitude brighter in the optical with respect to other objects for a given radio luminosity.

[FIGURE] Fig. 4. BL Lacs and FR I radio galaxies in the [FORMULA] plane. Empty symbols are objects with no data on their extended radio power, filled symbols and grey scale are as in Fig. 1. The dashed line is the radio-optical core correlation (Paper I). The range of core luminosity of the B2 radio galaxies is also reported. Notice that the B2 cores could at most extend this correlation by [FORMULA] order of magnitude towards lower luminosities.

In order to determine how beaming affects the observed luminosities and thus how objects could be connected in this plane, we consider the SED of BL Lacs, observationally much better determined, and calculate the observed spectrum of the misaligned objects, by taking into account relativistic transformations.

In fact, an important point, previously neglected, is that these transformations depend on the spectral index in the band considered, which in itself might change as a function of the degree of beaming. Therefore, in order to correctly de-beam the SED of BL Lacs, a continuous representation of it and an estimate of the bulk Lorentz factor of the emitting region are needed (it is again assumed [FORMULA]). While any continuous description of the SED and typical Lorentz factors can be used, we derive both of them by adopting a homogeneous synchrotron self-Compton emission model to reproduce the observed SEDs (e.g. Chiaberge & Ghisellini 1999, Ghisellini et al. 1998, Mastichiadis & Kirk 1997). This approach has the advantage of considering both the emission and dynamical ([FORMULA]) properties self-consistently. 3 The bulk velocities obtained in this way are fully compatible with those inferred from the already mentioned constraints (Sect. 3).

Let us firstly consider single objects for which the SED is well sampled, namely Mkn 421 (a typical HBL) and PKS 0735+178 (a typical LBL). We model the observed SED as explained, derive the value of [FORMULA]([FORMULA]) for the two sources and then calculate their corresponding observed SEDs for different orientations. Clearly the net effect of debeaming is a "shift" of the SED towards lower luminosities and energies (see Fig. 5).

[FIGURE] Fig. 5. Spectral energy distributions of Mkn 421 (lower panel) and PKS 0735+178 (top panel) and debeamed SED for different viewing angles in the case of a single emitting component. The Lorentz factors inferred for the two sources are [FORMULA] and [FORMULA], respectively. For comparison, we report (empty circles) the radio, IR and optical (HST) and X-ray (ROSAT) data for 3C 264 (Capetti et al. 2000). The (non-simultaneous) data for PKS 0735+178 are taken from the literature (NED). The (quasi-simultaneous) data for Mkn 421 are from Macomb et al. (1996).

Notice that, as the model is appropriate for the optically thin part of the spectrum, in order to account for the radio emission, which necessarily has to be produced on larger scales, we linearly extrapolate the fit from the infrared-mm spectral region. However, at an angle of [FORMULA] and for the Lorentz factors derived from the model, [FORMULA], the observed (debeamed) radiation at 5 GHz corresponds to what is seen in BL Lacs at far infrared frequencies (respectively [FORMULA], see Fig. 5) and therefore the debeamed points in Fig. 6 represent the correct predicted luminosities of the BL Lac component at 5 GHz.

[FIGURE] Fig. 6. Debeaming trails in the radio-optical luminosity plane for Mkn 421 and PKS 0735+178, in the frame of a single emitting region model. The filled circles correspond to the predicted luminosities of objects at different viewing angles. Top to bottom: [FORMULA], 10o, 30o and 60o.

The resulting debeamed optical and radio luminosities are reproduced in Fig. 6. The lines represent "debeaming trails" and the filled circles the calculated debeamed luminosities for [FORMULA] (i.e. the BL Lac itself), [FORMULA], [FORMULA] and [FORMULA]. Most noticeably, for [FORMULA] - which is the mean angle of sight for the misaligned population - the BL Lac component is about four orders of magnitude below the radio galaxy region in the optical, and one/four in the radio band.

While equivalently incompatible with the FR I population, the HBL and LBL move on different trails. This is due to the different shape of their SED (see Fig. 5), and in particular to the position of the synchrotron peak frequency: if - for increasing values of [FORMULA] - in the rest frame the peak overcomes the optical band, the spectral index steepens and the optical flux drops more rapidly than the radio one.

Another remarkable result is that the debeaming trail of the HBL does not even cross the region occupied by radio galaxies in the [FORMULA] plane. As this might be a serious problem for the unified scheme, we further examine this issue. In particular we closely examine the effect of the spectral shape and its relation with the intrinsic luminosity by considering three different SED, which represent the whole family of BL Lacs, from HBLs to LBLs. 4 In Fig. 7 we plot the resulting trails: once again, as in the cases of Mkn 421 and PKS 0735+178, the expected nuclear luminosity is 10-104 times fainter than what observed in FR I and the debeaming trail for the lower luminosity object (a typical HBL) does not even cross the FR I region. Note that if the luminosity is indeed related to the shape of the SED, this discrepancy would exacerbate for even fainter BL Lacs. In fact for HBL the radio and optical spectral slopes can be considered constant as the viewing angle increases, resulting in a linear (one to one) debeaming trail, parallel to the FR I correlation.

[FIGURE] Fig. 7. Debeaming trails in the radio-optical luminosity plane for average BL Lacs SED, in the frame of a single emitting component model. The filled circles correspond to the predicted optical-radio luminosity for different angles of sight (top to bottom: [FORMULA], 10o, 30o and 60o).

Summarizing: the radio and optical luminosities of BL Lacs and FR I are not consistent with the simplest predictions of the unifying scheme, if a single emitting region is responsible for the different broad band spectral properties of the beamed and parent populations. More specifically: i) Lorentz factors [FORMULA], as derived from the high energy spectral properties, underestimate the predicted emission from the parent population; ii) the relative ratio of radio to optical luminosity of HBL is inconsistent with the observed FR I spectra. In the next section we discuss and test a possible solution to these discrepancies.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000