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Astron. Astrophys. 355, 552-563 (2000)

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6. Conclusions

The series of astrometric VLBI measurements of the separation between the quasar pair 1038+528 A and B, spanning nearly 15 years, provides excellent material for investigating the relative proper motion of two extragalactic radio sources and the positional stability of their cores. The changes measured in the separations between quasars A and B at 3.6 cm are dominated by the motion of the reference feature in quasar B. These astrometric results, and measurements in the hybrid maps of B are compatible with an expansion rate for the B reference component of 13-17[FORMULA]as yr-1. At a redshift of 2.296 this translates to an apparent transverse velocity of 0.55-0.70 c h-1. We note that this is an order of magnitude smaller than the more typical superluminal velocities seen in many quasars; it is a rare example of a subluminal velocity measured for a knot in a quasar jet.

After correcting for the motion of the reference component in B, we can put a conservative upper bound to any relative proper motion between the quasars of [FORMULA]as yr-1. Despite the increase in temporal baseline, this upper bound is no better than that given by Rioja et al. (1997a). Its value is related to the difficulty in reproducing a stable reference position along the A source axis near its "core".

Theories in which the redshifts of quasars do not indicate cosmological distances, and in which quasars are "local" and have high Doppler redshifts (e.g. Narlikar & Subramanian 1983) are incompatible with our measured upper-limit to relative proper motion. Quasars at 100 Mpc distance moving at relativistic speeds would have proper motions of the order of [FORMULA]as yr-1, nearly 2 orders of magnitude greater than our limit. Assuming cosmological distances, our limit corresponds to apparent transverse velocities of 0.43 c h-1 and 0.22 c h-1 at the redshifts of the B and A quasars, respectively.

We have investigated the way in which the definition of reference points in a map may be only loosely "fixed" to the radio source structure, especially when the latter is strongly asymmetric. We have also developed an alternative analysis route - Hybrid Double Mapping - for imaging both sources of a close pair simultaneously, and at the same time preserving their relative astrometric information in a single map.

The surprisingly low rms from the fits of linear expansion in quasar B, and the discrepancy between the two estimates ([FORMULA]as yr-1 from the astrometric measurements and [FORMULA]as yr-1 from the hybrid maps) are suggestive of (but do not prove) a residual motion of the core in quasar B; our decomposition along the source axis direction gives a fit of [FORMULA]as yr-1, corresponding to an apparent transverse velocity of 0.17 c h-1. If real, this might indicate a steady change in physical conditions at the base of the jet, or perhaps the emergence of a new knot component moving outwards with a velocity similar to the reference component, but as yet unresolved by our 0.5 mas beam. In this regard, it is interesting to note the slight extension of the core of quasar B in PA 132o given by the Gaussian model fit.

The low rms derived from fits to the expansion of the B reference component indicate that we have been overly conservative in our estimate of [FORMULA]as for the error in reference point positions. Errors at least 2 times smaller are implied, corresponding to a sixtieth of the beamwidth. It is interesting to note that such small errors are also implied in the work of Owsianik & Conway (1998), where the low scatter in the plot of expansion of the CSO source 0710+439 allows an expansion rate of [FORMULA]as yr-1 to be determined.

There are no obvious systematic motions within quasar A, but the "noise" in the estimates of position along its axis are much larger. This noise, along with any associated underlying changes in source substructure, provides a fundamental limit to estimates of any systematic core motion in A. Improvements on the estimates of (or upper bounds to) the relative motion between the quasars, or of the individual motion of the A core, will require a considerable increase in the temporal baseline of VLBI monitoring.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000