The main goal of our program has been to monitor the time dependence of the location of the centre of mass of quasar A relative to an external reference. There is no guarantee that the fiducial points selected for the data analysis either coincide with, or are at fixed positions relative to, the centre of mass. Hence, the detection of a significant change in the position of these points does not necessarily imply motion of the centre of mass. We would expect any transverse motion of the centre of mass to be constant, while any "erratic" component could reasonably be interpreted as the relative proper motion of the reference points with respect to the centre of mass.
Here we interpret the changes in the separation observed at 3.6 cm (Fig. 3) as due to relative changes in reference-point locations in the two sources. A possible interpretation of the nature of these changes in each quasar is described below.
We outline below some of the results from our independent imaging and astrometric analyses:
1. The vector which describes the angular separation between 1038+528 A and B in 1990.5 relative to their separation in 1981.2, as shown in Fig. 3, has modulus as (P.A. ) and is closely aligned with the direction of the jet in the 3.6 cm map of quasar 1038+528 B (Fig. 1 and Table 1).
2. The difference between the separation of the components in the model for 1038+528 B for 1990.5 and that for 1981.2, as shown in Table 1, is as ; the relative orientation of the components is the same for both epochs, to within the estimated standard errors (P.A. ). These estimates measure the evolution of the relative separation between the two components in 1038+528 B, regardless whether the core component remains stationary or not.
3. The 3.6 cm maps of quasar A at epochs 1981.2 and 1990.5 do not show any significant differences from each other.
We conclude that the main contribution to the as difference in the estimated angular separation between 1038+528 A and B in 1990.5 from that in 1981.2, is the displacement of the reference point in the quasar B. This displacement corresponds to an average near-luminal rate of change of the position of the peak of brightness of quasar B of as yr-1 [v= c] between 1981.2 and 1990.5; in this model, the eastmost (steep spectrum) component in the 3.6 cm maps moves along the "jet" direction (i.e., towards the southeast, P.A. ) away from the northmost (inverted spectrum; ) component. The reference point used in the astrometric analysis, as noted above, is defined by the centre of the eastmost (steep-spectrum) component. The change in the position of this reference point measured by astrometry is thus quite compatible with the changes measured in the maps of 1038+528 B.
The combination of the structural information in the maps (Fig. 1) with the astrometric results shown in Fig. 3 leads in a natural way to this interpretation for the change in the angular separation between 1981.2 and 1990.5.
The changes in position of the chosen reference point in 1038+528 A can be deduced from the global astrometric results shown in Fig. 3 and the postulated evolution of the reference point in quasar B. The expansion of quasar B at a rate of as yr-1 at P.A. translates into a change of ca. as in the angular separation between quasars A and B over the period from 1981.2 to 1983.4. On the other hand, between these epochs, Fig. 3 shows a measured change of the angular separation of as towards the North (P.A. ). According to our scenario, the difference between these changes must represent a change of the reference point location in quasar A from 1981.2 to 1983.4 of as in P.A. . Such a change is less than a tenth of a beamwidth at 3.6 cm and is in the direction of the jet in the maps of quasar A at 3.6 cm, as shown in Fig. 1. The uniform motion attributed to the reference point in quasar B also accounts for the angular separation between the two quasars measured in 1990.5 relative to that in 1981.2 (Fig. 3). Thus, the position of the reference point in quasar A in 1990.5 is the same, or nearly the same, as in 1981.2.
Fig. 4 shows the estimated angular separations of quasars A and B in 1990.5 and 1983.4 relative to that in 1981.2, first as observed and then after including the contribution attributed to the postulated motion of the reference point in B. The resulting random appearance of the motion of the reference point in A suggests that it is some kind of "jitter" of the observed core. It does not necessarily imply a physical displacement of a feature in the source; it might result from activity in the core region, and the early stage of ejecting new components as yet unresolved in the maps, or from changes in the physical conditions in the medium, or it might represent no motion at all, given that its magnitude is only of the order of its estimated standard error.
The results found at 13 cm in 1990.5, being essentially the same as those found earlier, support the explanation proposed by Marcaide and Shapiro (1983), namely that opacity effects in the core region of the quasar A are responsible for the wavelength-dependence of its observed position. The monitoring over a decade provides a firmer measure of the characteristic length for this kind of effect of the order of pc ( as). The changes in angular separation inferred from the 3.6 cm data would not be detectable reliably at 13 cm because of the almost fourfold poorer resolution at 13 cm.
© European Southern Observatory (ESO) 1997
Online publication: May 5, 1998