High-precision measurements of radio source absolute positions which are required for alignment of VLBI images at different frequencies are not readily available in most cases. Extensive absolute astrometry (see Fomalont 1995) observations are necessary, in order to establish a reliable link between VLBI data at different frequencies. In quasi-simultaneous multifrequency observations, the phase-referencing technique (Beasley & Conway 1995) can be sufficient for the purpose of image alignment. If neither of the abovementioned techniques is available, the frequency dependent shift of the core position can be deduced from comparison of observations made at close epochs, assuming that the moving features observed in parsec-scale jets are optically thin and therefore should have their positions unchanged. In this case, the offsets between the component locations measured at different frequencies will reflect the frequency dependent shift of the position of the source core.
An extensive long-term VLBI monitoring database is available for 3C 345 (Zensus et al. 1995, 1997; Lobanov 1996). In the data for 3C 345, there are three close pairs of VLBI observations: (1989.24 at 22.2 GHz)-(1989.26 at 10.6 GHz), (1992.44 at 22.2 GHz)-(1992.45 at 5 GHz), (1993.69 at 5 GHz)-(1993.72 at 22.2 GHz). In these pairs, the separations between the observations in these pairs do not exceed 10 days. We also use two other close pairs with separations of 51 days: (1992.71 at 8.4 GHz)-(1992.86 at 22.2 GHz), and 70 days: (1993.69 at 5 GHz)-(1993.88 at 8.4 GHz). We measure the offsets in the closest and brightest components which have most reliably measured positions. For the pairs with 51 and 70 days separation, the positions of jet components have been corrected for the proper motions measured from the polynomial fits to the components trajectories (Lobanov 1996).
The average angular offsets are compared in Table 2 with the restoring beam sizes of spectral index maps made from the corresponding frequency pairs. The direction of the core shift () is similar to the position angle of the innermost part of the jet observed at 43 GHz (Krichbaum & Witzel 1992). Between 5 and 8.4 GHz, the position shift cannot be measured reliably because of the insufficient resolution and errors due to the proper motion corrections. The measured shift constitutes only about 5% of the restoring beam. With increasing frequency separation, the position shift becomes a prominent fraction of beamsize (up to 27% for spectral index maps between 5 and 22.2 GHz). Fig. 3 shows the measured offsets with respect to the reference frequency (22.2 GHz). The 5-8.4 GHz measurements are not included. The dashed line in Fig. 3 represents the best fit: .
Whenever an offset constitutes a significant fraction of restoring beam, it can influence substantially the derived spectral properties. An example of this effect is shown in Fig. 4. The 5-22 GHz spectral index profiles shown in Fig. 4 are measured along the jet ridge line in the nuclear region of 3C 345. The core extends from to mas. The profile obtained by aligning the images on their respective core positions shows a strong gradient, with optically thin spectral index across a significant fraction of the core. Applying the measured core position offset between 5 and 22.2 GHz levels the spectral index across the entire core, with . Similar corrections applied to several other spectral index maps of 3C 345 have resulted in decreased peak values, and smoother spectral index distributions across the nuclear region.
© European Southern Observatory (ESO) 1998
Online publication: January 8, 1998