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

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5. A jet velocity structure

We have shown that the high bulk Lorentz factors required by the emission models of BL Lacs imply that if such objects are observed at [FORMULA] the resulting spectral properties are not compatible with what is observed in the nuclei of radio galaxies. And indeed the previous comparison of the core emission of FR I and BL Lacs (see Sect. 3) led to lower values of [FORMULA]. How can these results be reconciled within the unifying scenario? A possible and plausible effect, which could account for this discrepancy, is provided by the existence of a distribution in the bulk velocity of the flow, with the emission from plasma moving at different speeds dominating the flux observed at different viewing angles.

Let us consider this hypothesis in the frame of the unification scheme and examine the simplest case, i.e. a model with two axisymmetric components having the same intrinsic luminosity and spectra. In other words, the only difference between the center and the layer of the jet is the bulk Lorentz factor which is determined for the spine ([FORMULA]) by modeling the BL Lac SED, while for the layer ([FORMULA]) by requiring that the debeamed BL Lac match the FR I distributions in the [FORMULA] and [FORMULA] planes.

The monochromatic intensity emitted by the jet is therefore calculated as


where [FORMULA] is the comoving intensity.

The predicted luminosity trails for the two specific BL Lacs are shown in Fig. 8. Values of [FORMULA] are set to 1.2 and 1.5 for Mkn 421 and PKS 0735+178 respectively, so that the point of each trail corresponding to the angle [FORMULA] falls approximatively onto the median of the FR I optical core luminosity in each [FORMULA] bin (Fig. 9).

[FIGURE] Fig. 8. Debeaming trails in the radio-optical luminosity plane, for the case of the two-velocity jet. The five curves correspond to average SED (1,2 and 3), Mkn 421 (M) and PKS 0735+178 (P). For the average SEDs [FORMULA] and [FORMULA]; for Mkn 421 [FORMULA] and [FORMULA]; for PKS 0735+178 [FORMULA] and [FORMULA]. Circles correspond to the predicted optical-radio luminosity for different angles of sight (top to bottom: [FORMULA], 10o, 30o and 60o).

[FIGURE] Fig. 9. Debeaming trails for the optical emission of Mkn 421 and PKS 0735+178 in the two-velocity jet scenario. The circles connected by the vertical lines correspond to the sources observed at angles of (top to bottom) [FORMULA], 10o, 30o, 60o (filled black circles) and 90o. The values of [FORMULA] (1.2 for and 1.5 for Mkn 421 and PKS 0735+178, respectively) are chosen in order for the luminosity at 60o to correspond to the median value for each bin of extended radio power.

By using the same value of [FORMULA] this two-velocity model satisfactorily predicts the properties of the debeamed counterparts of LBL and in particular it reproduces the FR I location in the [FORMULA] plane.

Conversely this picture can not account for the observed optical-radio properties of debeamed HBL. The luminosity of objects seen at [FORMULA] is close to the lower limit of the FR I region in the optical, but still one order of magnitude fainter in the radio. We must stress however that the extended radio powers of HBLs correspond more closely to the range covered by the B2 radio galaxies. Clearly, any firm statement on this issue must await for the analysis of the nuclear properties of the B2 sample, but the extrapolation of the 3CR radio-optical correlation does not match the debeamed predicted luminosities of HBL. This result does not depend on the specific value of [FORMULA] adopted since, as already discussed in Sect. 4, the HBL trails run almost parallel to the radio-galaxies locus.

A further modification of this model is thus required for the HBL unification. Without altering the comoving spectra of the two components, the simplest change is to assume a lower Doppler factor for spine in the radio emitting region, as might be the case if the flow slows down between the optical and the radio emitting sites. This would increase the initial slope of the debeaming trail which would rapidly reach the FR I region.

5.1. Constraints from the X-ray observations

The limited angular resolution makes the analysis of X-ray observations of FR I sources less straightforward than in the radio and optical bands. In particular it is necessary to disentangle any non thermal nuclear radiation from the often dominant emission of the hot gas associated with the galactic corona and/or galaxy cluster. Nonetheless they provide useful constraints to high energy nuclear emission of these radio-galaxies.

We can test the validity of the two-velocity jet scenario by considering also this X-ray emission. In Fig. 10 we report the debeaming trails in the [FORMULA] plane for the average SEDs assuming the same jet parameters as before: the predicted powers in both bands appear to be consistent with the observed properties of radio galaxies, supporting the presence of a less beamed plasma component (layer) dominating the emission in the parent population also in the X-ray band. Conversely, there is no need for a different amount of beaming in these two bands. This is somehow reassuring, as optical and X-ray are believed to originate co-spatially.

[FIGURE] Fig. 10. Debeaming trails in the optical-X-ray luminosity plane for the average BL Lacs SED. Two-velocity jet with [FORMULA] and [FORMULA] for all SED. Circles are FR I, squares and triangles represent X-ray and radio selected BL Lacs, respectively. Grey scales correspond to bins of extended radio luminosity, as for Fig. 1. Open triangles and squares are sources without measurement of their extended radio power. Open circles correspond to the predicted optical-X-ray luminosity for different angles of sight (top to bottom: [FORMULA], 10o, 30o and 60o).

In addition, X-ray data can be used to define the location of radio-galaxies also in the broad band spectral indices plane. The spectral characteristics of blazars are often represented in the plane defined by [FORMULA] (5GHz-5500 Å) and [FORMULA](5500 Å-1 keV). It is therefore worthwhile to determine how relativistic beaming affects the position of the objects also in this plane. While an approximated relation between the BL Lacs and FR I broad band spectral slopes is derived in A in the case of constant local spectral indices, changes in the local spectral slopes are properly taken into account.

In this plane (Fig. 11), as already well established, HBL and LBL occupy the left (i.e. flatter [FORMULA]) and the top-center (i.e. steeper [FORMULA]) regions, respectively and their different position is accounted for by their different SEDs (e.g. Fossati et al. 1998), i.e. reflects the position of the peak of the emission. The FR I region is instead well defined at the center of the diagram. The debeaming trails for Mkn 421 and PKS 0735+178 are also shown 5: the empty circles correspond to [FORMULA], [FORMULA] [FORMULA], [FORMULA] in the case of the two components model, while the two asterisks represent each source as observed at [FORMULA] in the case of a single emitting region. PKS 0735+178 falls in the radio galaxy region for [FORMULA] or less, while Mkn 421 does not intersect this area either in the single or in two component models, confirming the results of the analysis presented above.

[FIGURE] Fig. 11. Debeaming trails in the [FORMULA] plane for Mkn 421 and PKS 0735+178. The jet parameters are the same as in Fig. 8. The black filled symbols correspond to the observed BL Lac ([FORMULA]), while the empty circles represent the predicted position for different angles of sight ([FORMULA], 30o and 60o) in the frame of a two-velocity jet model. The two asterisks indicate sources observed at [FORMULA] in the case of a single emitting component.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000