6 An example

As an example of these approaches, we present both interferometric and single-dish polarimetric observations of Vela-X, which is the plerionic component of the nearby Vela supernova remnant - see Bock et al. (1998) for a description. For the interferometric observations, we have used the Australia Telescope Compact Array (ATCA). We have imaged a region of approximately $2^\circ\times3^\circ$, using 35 pointings at a 20 cm wavelength. The pointings were on a hexagonal grid, with a distance between pointings of $11\hbox{$.\mkern-4mu^\prime$}4$ (the hexagonal grid Nyquist spacing is $19\hbox{$.\mkern-4mu^\prime$}6$ - the diameter of the ATCA antennas is 22 m). A fairly complete Fourier plane (u-v) coverage was observed from 30 m to 750 m spacings. The data were collected using the "pulsar bin mode'' of the ATCA's correlator, and images were made using de-dispersed data from the "off'' portion of the Vela pulsar's cycle. We excluded the pulsar emission as its extreme variability would have limited the dynamic range of our images. Normal polarimetric calibration (i.e. at the field centre) was done on the visibility data. The single-dish observations were made with the 64 m Parkes radio telescope as part of a larger survey. The region was covered twice, once scanning in Galactic longitude and once in Galactic latitude. Apart from the observing frequency, the observing mode was similar to that used by Duncan et al. (1995, 1997). In particular, the polarimetric calibration was done in a similar way. Given the single-dish observing technique and given Parkes observations of some bright, unpolarized sources, we estimate that the leakage of total intensity into the linear polarizations is less than 0.5%.

Note that interferometric and single-dish observations both had good sensitivity to the spacing between about 20 and 40 m. Using this overlap annulus in the Fourier plane, we verified that the flux calibrations of the interferometric and single-dish data were consistent.

We have tried a number of ways to deconvolve these data. First, we have separately deconvolved the interferometric Stokes images using a mosaiced Steer CLEAN algorithm (Steer et al. 1984; Sault et al. 1996). Second we have used a maximum entropy algorithm to deconvolve the Stokes images separately, using either the normal entropy measure for total intensity or the maximum emptiness measure for the polarized intensities. These maximum entropy deconvolutions were done both with and without a single-dish data $\chi^2$ constraint. Finally we have performed a joint deconvolution of the four Stokes images, both with and without a total-intensity single-dish $\chi^2$ constraint. We have not done a joint deconvolution with single-dish polarized-intensity data constraints. Flat default and scale images were used in the maximum entropy deconvolutions. All the images that we present are after the solution images have been convolved with a Gaussian beam and have had residuals folded back in.

In total intensity, the only significant differences between the various deconvolved images were in the structures larger than that well-sampled by the interferometric observations. The Steer deconvolution grossly underestimated the large-scale structure, whereas the maximum entropy deconvolution without single-dish constraint overestimated it (this overestimate, however, is as much to do with the default image as the maximum entropy algorithm itself). Of course, the deconvolution with single-dish constraint, by its very nature, will produce the correct large-scale structure. Apart from the large-scale structure, the images were very similar, except that the Steer CLEAN image showed faint features that were obviously artifacts. There was no significant difference between the corresponding joint and separate deconvolutions of total intensity. Figure 1 gives the total intensity image resulting from the joint deconvolution including the single-dish data.

 

Figure: 1 Total intensity image of a portion of the Vela-X region, resulting from the joint deconvolution with single-dish constraint

In the linearly polarized images, we find the differences between the various deconvolutions to be comparatively minor. In terms of features that were plainly artifacts, the Steer CLEAN images showed the most, whereas the separate approach showed the least. Including the total intensity single-dish constraint in the joint deconvolution had negligible effect on the polarized intensity images. Similarly, including the single-dish polarized-intensity data had little effect on the result. This indicates that there is little structure larger than that which we sample with the interferometry. Figure 2 show the joint and separate deconvolutions of Q and U images, at a greyscale saturation of twice that in Fig. 1. The maximum fractional linear polarization in some regions is about 60%. Such a large fractional polarization is not inconsistent with previous Vela observations.

In the processing we have assumed that the ATCA has no off-axis polarimetric impurity, and that the primary beam response was circularly symmetric (note that the ATCA feed design at 20 cm means that the off-axis polarimetric response is substantially better than the 13 cm response investigated by Sault & Ehle 1996b). To justify these assumptions, we have measured the ATCA response of an unpolarized point source at many points in the primary beam. These measurements showed a small level of leakage of total intensity into linear polarization, but were unable to detect leakage into circular polarization. Using the approach of Sault & Ehle, we made a model of the off-axis response and then used this model to simulate our Vela observations. The simulations show that in the central region of the mosaiced image the expected leakage of total intensity into linear polarization is $\approx 0.05$%, with this degrading to a maximum of $\approx 0.5$% near the edges of the image. This degradation near the edges is caused by there being less averaging from different pointings. This analysis also shows that the expected error in total intensity, caused by the deviation of the primary beam from circular symmetry, was 0.03% in the centre of the image, degrading to 0.3% towards the edges.

Some degree of confirmation that the off-axis polarimetric impurity is insignificant is that the Stokes-V image reached thermal noise (integrating the Stokes-V image over large regions did reveal some structure above the noise, but this was consistent with the errors in our polarimetric calibration). We also note that all the point sources in the field appear unpolarized and that there are no apparent artifacts at the locations of these point sources in the polarized images. It is difficult to imagine such a result if there was significant polarimetric impurity. Our interpretation of this is that the polarimetric impurity is negligible and that the point sources are background ones which are being Faraday depolarized by Vela and the Galaxy.

 

Figure 2: Deconvolved Q and U images of a portion of the Vela-X region: a) Q using separate deconvolution (maximum emptiness criterion); b) Q using joint deconvolution; c) U using separate deconvolution (maximum emptiness criterion); d) U using joint deconvolution