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Astron. Astrophys. 334, 427-438 (1998)

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Appendix A


Table A1. Fluxies of 3C 275.1 at different frequencies - references

Appendix B

We derive the expressions for the velocity components and deflection angles for two above discussed cases:
i) the magnetic field is parallel to flow velocities in both upstream and downstream flows

From the boundary conditions, we obtain the following relations for the velocity components:
[FORMULA] [FORMULA] Here: [FORMULA] ; [FORMULA] and [FORMULA]. Putting [FORMULA] and [FORMULA] as the ratios of gas and of magnetic field pressures respectively, we derive:
[FORMULA]. The Lorentz factors are described by: [FORMULA]. Since [FORMULA] the normal components of upstream and downstream velocities are related to Lorentz factors by: [FORMULA]. Applying the Lorentz transformation to above expressions and putting [FORMULA] and [FORMULA], one has after the calculations:
[FORMULA] [FORMULA] Here [FORMULA] is the Lorentz factor corresponding to the y - component of velocity. The above expressions reduce to those ones given by Bicknell (1994: see also Landau and Lifshitz, 1987) for [FORMULA]. Putting the above expressions for [FORMULA] and [FORMULA], one has: [FORMULA] The above relations can be Lorentz transformed to the observer's frame. For an example:
where [FORMULA] and [FORMULA] refer to the shock; subscripts "fl,obs" and "fl,sh" refer to fluid with respect to observer and fluid with respect to shock respectively. Accordingly, the velocity components of the gas in the observer's frame for the ultra-relativistic equation of state, i.e. [FORMULA] and [FORMULA], are given by: [FORMULA] [FORMULA] ii) the magnetic field of the upstream flow is parallel to the velocity flow, while that of downstream flow is perpendicular
We derive from the above given jump (shock) conditions the expressions for the normal components of upstream and downstream flow velocities, as follows: [FORMULA] ; [FORMULA] ; [FORMULA] ; where: [FORMULA] and [FORMULA]. Accordingly, one has: [FORMULA]. Here: [FORMULA]
and the compression ratio of shock for gas is given by: [FORMULA]. Due to interaction of the magnetic field and of plasma flow there are the different Lorentz factors for normal components of velocities [FORMULA], i.e. [FORMULA], and for those of magnetic field, namely [FORMULA]. The laboratory and rest frame variables are related via the Lorentz transformation of mass density [FORMULA], of momentum density [FORMULA] and of energy density [FORMULA]. Moreover, the angle [FORMULA] between the jet direction and the observer (the line of sight), discussed in the beginning of this section, is related to the angle between normal to the shock surface and the line of sight [FORMULA] and to the angle between observer and the shock surface [FORMULA] by: [FORMULA]. Applying the Lorentz transformation to above solutions, we derive for the ultrarelativistic equation of state the expressions: [FORMULA]


[FORMULA]. Here: [FORMULA] ; [FORMULA], [FORMULA] and [FORMULA]. Thereafter, the relation between the angles of the pre- and post-shock velocities to the shock normal is described by: [FORMULA].

Appendix C

We suppose that the radio structure of 3C 275.1 is already disturbed at the parsec scale, since there are knots of forbidden line emission from OII and OIII ions in the nucleus of the host galaxy. Hence, we made high resolution observation of the core of 3C 275.1. The VLBI Mk III observation was made in November 16, 1994 at frequency 1.6 GHz with 6 EVN stations: Effelsberg, Jodrell Bank, Medicina, Noto, Onsala and Westerbork. There were significant interferences from GLONASS in this session, and in addition due to some technical problems, almost whole information from baselines with WSRT station was lost. Using the closure phase method (Jennison 1958, Rogstad 1968, Rogers et al. 1974) and CLEAN algorithm in AIPS package (Högbom 1974) to deconvolve the data, we obtained the "clean" map of 3C 275.1 (Fig. C2). There are not significant features at distances above 40 mas from the core (the centre of the map). Probably, the information about it was lost by reason of a very poor u-v coverage of the data. The frequency 1.6 GHz was too low and the baselines too short to resolve the core of the quasar. Fig. C2 shows an elongation of the radio structure at a distance [FORMULA] 30-40 mas from the core with position angle about [FORMULA]. It may be the result of interaction between out-flowing plasma of the QSO and the nonuniform ionized gas strongly emitting in forbidden [OII] and [OIII] lines. The contour levels of the elongation are only about 0.5-1% of the peak. We suggest, that further studies of the milliarcsecond structure of 3C 275.1 leading to resolving the core of the quasar and to confirming the elongation of its radio structure are needed.

[FIGURE] Fig. C1. The phase vs. time for the u-v data used to obtain the "clean" map in Fig. C2. The solid line indicates the model visibilities from the phase-reference map (Fig. C2).

[FIGURE] Fig. C2. The "clean" EVN map of 3C 275.1 at frequency 1.6 GHz. The peak of the map is 212.9 mJy/beam. The beam is: [FORMULA]   mas, P.A. [FORMULA].49 . The contour levels are: dashed: -1.5, -0.5; solid: 0.5, 1, 2, 5, 15, 25, 50, 75 % of the peak.

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Online publication: May 15, 1998