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

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3. Data reduction

We used the NRAO AIPS package for the data reduction. We applied standard fringe-fitting, amplitude and phase (self-) calibration techniques and produced hybrid maps of each quasar. The astrometric analysis was done using two different mapping methods: a "standard" phase-referencing approach, transferring phase solutions from one quasar to the other (see e.g. Alef 1988; Beasley & Conway 1995) and a novel mapping method for astrometry of close pairs of sources, hybrid double mapping (HDM) (Porcas & Rioja 1996). Both routes preserve the signature of the relative separation of the source pair present in the calibrated phases. These analysis paths are described in Sects. 3.1 to 3.3 below.

3.1. Hybrid mapping in AIPS

We applied standard VLBI hybrid mapping techniques in AIPS for the analysis of the observations of both quasars A and B. We used the information on system temperature, gain curves and telescope gains measured at the individual array elements, to calibrate the raw correlation coefficients. We used the AIPS task FRING to estimate residual antenna-based phases and phase derivatives (delay and rate) at intervals of a few minutes. It is important to realise that FRING is a global self-calibration algorithm, and performs an initial phase self-calibration also. We ran FRING on the A quasar data set, with a point-source input model.

Anticipating our phase-referencing scheme (Sect. 3.2) we applied the antenna phase, delay and rate solutions from A to both the A and B data sets, and averaged them in time to 60 s, and over the total observed bandwidth of 32 MHz. After suitable editing of the data, we made hybrid maps of both quasars, using a number of iterations of a cycle including the mapping task MX and further phase self-calibration with CALIB.

Fig. 1a and b show the hybrid maps for both sources at 3.6 cm in 1995.9. The maps are made using uniform weighting of the visibilities, a map cell size of 0.15 mas and a circular CLEAN restoring beam of 0.5 mas (these same mapping parameters are used throughout this work). The "dirty" beam has a central peak of 0.57 x 0.47 mas in PA -29o (PA = position angle, defined starting at North, increasing through East). The root-mean-square (rms) levels in the A and B maps, in regions away from the source structures (estimated using AIPS task IMSTAT) are 1.0 and 0.12 mJy/beam respectively, an indication that dynamic range considerations dominate over thermal noise in determining the map noise levels.

[FIGURE] Fig. 1a and b. VLBI hybrid maps of 1038+528 at 3.6 cm. Uniform weighting, CLEAN beam 0.5 x 0.5 mas, pixel size 0.15 mas, tick interval 1 mas. a Quasar A. Contours at 3,6,12,24... mJy/beam. b Quasar B. Contours at 1.5,3,6,12... mJy/beam.

3.2. Phase referencing in AIPS

In order to make an astrometric estimate of the separation between quasars A and B at this 4th epoch, we first used a "conventional" phase-reference technique to make maps of the quasars which preserve the relative phase information. In practice this consists of using the antenna-based residual terms derived from the analysis of the data of one "reference" source (A), to calibrate the data from simultaneous observations of the other "target" source (B). The reference quasar source structure must first be estimated from a hybrid map, and then fed back into the phase self-calibration process to produce estimates of the antenna-based residuals, free from contamination by source structure.

Phase referencing techniques work under the assumption that the angular separation between the reference and target sources is smaller than the isoplanatic patch size (i.e. the effects of unmodelled perturbations, introduced by the propagation medium, on the observed phases of both sources are not very different) and that any instrumental terms are common. Geometric errors in the correlator model must also be negligible.

Assuming that the antenna residuals have been "cleanly" estimated using the reference source data, the calibrated phases of the target source should be free from the errors mentioned above, but still retain the desired signature of the source structure and relative position contributions. The Fourier Transformation of the calibrated visibility function of the target source produces a "phase referenced" map. The offset of the brightness distribution from the centre of this map reflects any error in the assumed relative separation in the correlator model. If the reference source has a true "point" structure and is at the centre of its hybrid map, this offset will be equal to the error; more generally, one should also measure the offset of a reference point in the reference source map, and estimate the error in the source separation used in the correlator model from the difference between the target and reference source offsets.

In general, the success of the phase-referencing technique is critically dependent on the angular separation of the target and reference sources. Simultaneous observation of the sources, as was possible here, significantly simplifies the procedure, eliminates the need for temporal interpolation, and reduces the propagation of errors introduced in the analysis. While random errors increase the noise level in the phase referenced map, systematic errors may bias the estimated angular separation.

For our implementation of phase-referencing using AIPS, we chose to re-FRING the (calibrated) A data set, using our hybrid map of quasar A as an input model, and applied the adjustments to the antenna phase, delay and rate solutions to both the A and B data sets before re-averaging. We then made maps of both A and B using MX, performing no further phase self-calibration. These are our "phase-reference astrometry" (PRA) maps (shown in Fig. 2a and b) on which we performed astrometric measurements (see Sect. 4.2). Although the rms noise levels in the PRA maps are slightly higher than in the corresponding hybrid maps (2.0 mJy beam-1 for A and 0.24 mJy beam-1 for B), our procedure ensures that the A and B visibility functions from which they are derived have been calibrated identically.

[FIGURE] Fig. 2a and b. VLBI phase-reference astrometry maps. Map parameters as in Fig. 1. Astrometry reference points are indicated with a cross. a Quasar A. Contours at 3.5,7,14,28... mJy beam-1. b Quasar B. Contours at 1.5,3,6,12... mJy beam-1.

3.3. New mapping method for astrometry of close source pairs

While the conventional phase-referencing approach worked well for our November 1995 observations of 1038+52A and B, the method relies on making a good estimate of the antenna residuals from just one of the sources - the reference. We have devised an alternative method which extends the standard VLBI self-calibration procedure to work on both sources together, for cases where they have been observed simultaneously, and when either could be used as the reference (see Appendix A).

The basis of the new method is to recognise that, since the visibility functions for both sources are corrupted by the same (antenna-based) phase and phase derivative errors, the sum of the two visibilities also suffers the same errors. We form the point-by-point sum of the two data sets, creating a new one which represents the visibility function of a "compound source" consisting of a superposition of the two structures, corrupted by the common antenna phase errors. If the source separation is close enough, the (summed) data as a function of the (averaged) uv-coordinates can be Fourier Transformed to form a map of the compound source structure, and (iterative) self-calibration in FRING or CALIB yields the antenna-based residuals. The advantage of this approach is that the antenna-based residuals are determined using both source structures simultaneously, and may thus reduce the chance that reference source structural phase terms contaminate the residuals. We term this process "Hybrid Double Mapping" (HDM); a detailed description is given in Porcas & Rioja (1996).

It is convenient to shift the source position in one of the data sets (by introducing artificial phase corrections) prior to the combination into a compound-source data set, to avoid superposition of the images in the map. The phase self-calibration steps which are then applied to the combined data set are identical to the case of a single source. In HDM the information on the angular separation between the sources is preserved in the process of self-calibration of the combined visibilities, and can be measured directly from the compound-image map; the relative positions between the individual source images in the compound map, taken together with any artificial position shift introduced, give the error in the assumed angular separation in the correlator model. In this approach one must be careful to use the same number of visibility measurements in each time interval from the two data sets, in order to avoid the predominance of data from a particular source.

Fig. 3 shows the HDM map of quasars A and B in 1995.9 at [FORMULA] 3.6 cm; the B source is artificially offset by -4 mas in declination. The rms noise in the map is 0.82 mJy beam-1 - higher than that in the hybrid map of B but lower than in that of A.

[FIGURE] Fig. 3. HDM map of 1038+52 (A+B). Map parameters as in Fig. 1. Quasar B has been offset by -4.0 mas in declination. Contours at 3,6,12,24... mJy beam-1.

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Online publication: March 9, 2000