Astron. Astrophys. 344, 61-67 (1999)

3. Model fitting: a precessing inner jet

In order to apply the model we shall assume that the inner jet of 3C 273 precesses with constant angular velocity , defining a cone of opening angle . Its instantaneous axis is characterized by the viewing angle and the position angle in the plane of the sky . Shocks are formed near the origin of the jet and will move outwards in ballistic trajectories with constant superluminal velocities. The viewing and position angles of these features will represent the corresponding angles of the jet at the epoch at which the shocks were formed. Denoting by and the corresponding angles of the axis of the precessing cone, we obtain that the jet movement is described by (Abraham & Carrara 1998):

with

where the time is measured in the frame fixed at the central source. The viewing angle is not directly observable but it is related to the superluminal velocity of the components at the ejection time by:

where . The Doppler factor will be also a function of time due to the jet movement.

In order to obtain the parameters , , and of the model, we first fit the data in the , )-space. The best fitting, independent of the value of the Hubble constant, is seen in Fig. 1. The set of parameters that fits the data, for several values of the Hubble constant km s^-1 Mpc^-1, are presented in Table 2.

Fig. 1. Apparent velocities of the superluminal features in the jet of 3C 273 (points), scaled by the constant , as a function of their position angles in the plane of the sky. The solid line represents the model fitting of a precessing jet, with the parameters presented in Table 2 for three values of h.

Table 2. Parameters of the precessing model

The values of and were used to adjust the period in the observer's frame (Fig. 2). The results clearly indicate a period yr. The jet has completed one and a half cycles during the time for which there are reliable VLBI data. The viewing angle is currently increasing and will reach a new minimum towards the year 2011. The previous minimum was in 1995, so if some new superluminal components were ejected close to this epoch, its apparent velocity should be similar to that of C5 (i.e. ). Instead, the velocities of components ejected around 2002 should be .

Fig. 2a and b. Apparent superluminal velocities, scaled by the value of , and position angle in the plane of the sky of the superluminal features in the jet of 3C 273 as a function of the epoch at which they were formed. The continuous line represents the result of the models with the precession parameters given in Table 2.

© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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