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Astron. Astrophys. 330, 79-89 (1998)

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5. Opacity in the jets

Assuming that the frequency term in (4) dominates core position offsets, the measured [FORMULA] can be used for comparing the relative opacity in different sources. To make such a comparison, the offset measures and observing frequencies must be transformed to the respective source rest frames: [FORMULA] ; [FORMULA]. We then postulate that the largest [FORMULA] corresponds to [FORMULA], [FORMULA], and use it as a reference point for calculating the [FORMULA] for the rest of the offset measurements. The results are plotted in Fig. 7. In 3C 395, the calculated [FORMULA] is very large ([FORMULA]), suggesting that the jet viewing angle may be greater than the value cited by Lara et al. (1994). The apparent increase of [FORMULA] at shorter radial distances is consistent with the self-absorption scenario described in section 2.3(the measured [FORMULA] become smaller at higher frequencies at which the opacity is larger). The linear scale in Fig. 7 serves only as an illustration, since the intrinsic properties of the sources (reflected by the [FORMULA] term) may be different. Detailed studies of each individual object are required for establishing a connection between the jet linear scale and opacity properties. A general prediction is that the position offset should be larger in flat-spectrum cores in which [FORMULA]. When [FORMULA] increases, the offsets are expected to become smaller, and the core spectrum should be inverted.

[FIGURE] Fig. 7. Relative changes of opacity in the ultracompact jets. Reference point is the 1.5-2.3 GHz offset in 3C 309.1, with [FORMULA] and [FORMULA] assigned to it. For the rest of the data, the [FORMULA] and r are calculated from the corresponding [FORMULA] measured in the respective source rest frames. Dashed line is a model similar to that described in section 2.3, but with [FORMULA].

A reasonably good agreement found in Fig. 7 between the derived and model [FORMULA] indicates that synchrotron self-absorption may be responsible for the observed properties of optically thick emission from ultracompact jets. One can expect then to find similar physical conditions in the VLBI cores of different sources, if the measurements are done at the same rest frame frequency. To illustrate this, we calculate the magnetic fields and core distances at [FORMULA] GHz, and plot them versus jet synchrotron luminosity (Fig. 8). The derived [FORMULA] increase, with increasing [FORMULA], and follow roughly the proportionality [FORMULA] resulting from (7) and (9). The corresponding magnetic field however remains nearly constant, with an average of [FORMULA] [G]. One may expect the values of magnetic field to vary stronger, and exhibit a rather large scatter, if jet emission is affected by external factors such as free-free absorption. The homogeneity of [FORMULA] seen in Fig. 8 suggests that the jet plasma is a primary factor determining the location and properties of VLBI cores, and that intrinsic physical conditions in the jets must be fairly similar. If this suggestion holds for other sources, the expected magnetic field in VLBI core should be of the order of [FORMULA] [G], for [FORMULA] measured in GHz.

[FIGURE] Fig. 8. Magnetic field (filled circles) and distance of the core (squares) with respect to the jet synchrotron luminosities. The data are shown for [FORMULA] GHz. Dot-dashed line is [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: January 8, 1998
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