5. Comparison of astrometry at all 4 epochs
In this section we make a comparison of the astrometric measurements from the series of 4 epochs of observations. Any increase of the temporal baseline in the program of monitoring the separation between A and B should result in a more precise identification of any systematic trends, with an improved elimination of random contributions. In Sect. 5.1 we justify comparing the astrometric values measured at the various epochs, even though non-identical observing, post-processing and analysis procedures were involved. In Sect. 5.2 we present the astrometric results from the 4 epochs. In Sects. 5.3, 5.4, 5.5 and 5.6 we present various analyses of these results, and attempt to quantify, or put upper-limits to, proper motions within and between the A and B quasars.
5.1. Comparison between the techniques used at different epochs
Before attempting a comparison of the astrometric results from the 4 observing epochs, we need to show that any bias in the astrometric estimates introduced by the use of different procedures is small compared with other errors in the measurements for the individual epochs. The consistency between the results from previous epochs of observations has been exhaustively tested (Marcaide et al. 1994; Rioja et al. 1997a). We outline here the largest changes involved in the fourth epoch, 1995.9, with respect to previous ones:
The magnitudes of all of the effects reported in this section are much smaller than our estimate in Sect. 4.3 of the uncertainity in reproducing the reference point in the source, from epoch to epoch, and we are thus justified in comparing the astrometric results from all 4 epochs.
5.2. Astrometric separations at the 4 epochs
The astrometric measurements of the separations between the reference points in A and B at 3.6 cm from 4 epochs are presented in Fig. 4. It includes our new 1995.9 measurement and those from three earlier epochs, in 1981.3, 1983.4 and 1990.5, reported in Marcaide & Shapiro (1984), Marcaide et al. (1994) and Rioja et al. (1997a), respectively. The origin of the plot represents the separation at epoch 1.
Changes with time in Fig. 4 represent the vector difference between any motions of the reference points in quasars A and B. The near-orthogonal nature of the source axes in 1038+52 A,B (along which one might expect any motion to occur) simplifies the interpretation of any trends seen. The new 1995.9 value follows the same steady trend towards the NW shown by the three previous epochs. Rioja et al. (1997a) interpreted this as an outward expansion of the reference component in quasar B at a rate of as yr-1, and quoted an upper bound on any proper motion of quasar A of as yr-1.
5.3. Vector decomposition
In this section we attempt to separate the individual contributions from the 2 quasars in the astrometric separation measurements presented in Fig. 4. We make no assumption about the stability of either component, but assume that any displacements of the A or B reference points from their positions at epoch 1 are along the corresponding source axis directions. This is a plausible assumption if the reference point coincides with a non-stationary component moving along a ballistic trajectory, or with the location of the peak of brightness within an active core or near the base of jet, where changes during episodes of activity are likely to occur along the jet direction. This approach is closely related to that used previously by Rioja et al. (1997a). For fixed assumed source axes for A and B, it results in a unique decomposition of the changes in the A-B separation into separate A and B displacements, from 1981 to 1995.
It is clear that the dominant contribution to the separation changes seen in Fig. 4 comes from quasar B, in which the source axis is well defined by the 127o PA of the separation between core and reference components. For quasar A the source axis bends, from the inner "core" region (PA = 15o) to the outer jet components, and it is not so clear which direction should be chosen.
In our analysis we tried a range of values for fixing the A source axis (0 to 45o in steps of 5o). For each, we calculated A and B reference-point displacements at epochs 2, 3 and 4 with respect to epoch 1. Then we performed a least-squares fit to the B displacements with time to estimate a linear expansion rate for the B reference feature along PA 127o. In Fig. 5 we plot the deconvolved B reference point displacements from the analysis with the A source axis fixed at PA 25o (the value adopted by Rioja et al. 1997a). The fitted expansion rate is as yr-1; the error and associated rms values take account of the small number of points and 2 degrees of freedom. This rate agrees well with the value of as yr-1 deduced by Rioja et al. (1997a). The rms residual from the fit (7 µas) is low, and vindicates our use of measurements derived from differing techniques for investigating the relative proper motion between A and B.
5.4. Structural evolution within 1038+528 B
Our deconvolution analysis of the changes in separation measured between all 4 epochs supports the finding, previously proposed, that the B reference component moves along the source axis, away from the B core. In this section we make an independent determination of the separation rate between the core and reference component in B from measurements within the maps at the 4 epochs.
Fig. 6 shows the separation between the core and reference component in B at the four epochs plotted against time. For epochs 1-3 we used the values given in Rioja et al. (1997a). For 1995.9 we used AIPS task UVFIT to estimate a separation from the B visibility data directly, in order to follow the methodology used for the other epochs as closely as possible; the value obtained was 1.895 mas. The slope from a least-squares fit corresponds to an expansion rate of as yr-1. In the standard picture of extragalactic radio sources, the "core" is stationary, so this corresponds to an outward expansion of the reference component along PA 127o.
The rms of the fit (8 µas) is again surprisingly low, implying typical errors in the separation measurements at each epoch (both within the B structure and between the reference points) of only about 10-12as along the direction of the B source axis. This is considerably less than the estimate of position separation errors given in Sect. 4.3.
5.5. Relative proper motion
The analysis presented in the previous sections demonstrate clearly that the chosen reference component within quasar B is unsuitable for use as a marker for tracing any relative proper motion between quasars A and B. The value of its expansion velocity derived in Sect. 5.4 appears to differ significantly from that deduced by vector-decomposition in Sect. 5.3. Although the difference between these estimates, if real, could be interpreted as motion of the core of B at a rate of as yr-1, this is not a conclusive result since differences of this order arise from choosing different values of PA for the motion in A in the vector decomposition method.
A more suitable tracer of relative proper motion between the quasars is the variation of the separation between the cores of A and B. We have used the separations between the core and reference component measured in the B map at each epoch, and the astrometric separations between A and B, to calculate the separations between the A and B cores at each epoch; these are plotted in Fig. 7. The area occupied by the points defines an upper limit of as yr-1 for any relative proper motion between the A and B cores, and hence between the quasars themselves, during the period of nearly 15 years for which the separation has been monitored with VLBI. The limit seems to be set by the relatively large deviation of the 1995.9 epoch point in the direction of the A source axis, presumably arising from the difficulty in defining the reference point at the A "core" from epoch to epoch.
5.6. Possible "core" motions?
Finally, we investigate any possible residual motions of the "cores" in A and B. The most likely causes of any such apparent motions are changes in the relative brightness or positions of features in the source structures at a resolution below that of the maps. One might expect that these, too, would produce effects predominantly along the source axis directions. We therefore used the vector deconvolution method on the plot of core-core separation with time to study displacements of the cores along their source axis directions. Fig. 8a and b show plots of the separated contributions from B and A, for an assumed A source axis PA 25o. The displacements for the B core seem to increase systematically. The fitted rate is as yr-1, indicating a possible slow outward motion. The displacements for the A core do not seem to vary systematically - the fitted slope is as yr-1. Here the scatter is considerably larger, reflecting both the difficulties of defining the reference point along the A core-jet axis, and also, perhaps, real "jitter" of the position of the peak due to variations in the "core" substructure. These plots indicate the level of stability of the individual core positions; the fits represent realistic upper limits to any possible systematic core motion in the A and B quasars along their source axis directions.
© European Southern Observatory (ESO) 2000
Online publication: March 9, 2000