2 Spectral imaging using VLBA data  

Many of the usual technical problems in making spectral index maps from VLBI data can be avoided by using the VLBA (see Zensus et al. 1995). With the VLBA, it is possible to achieve array homogeneity, have an improved flux calibration, and make the time separation between observations at different frequencies negligible. The major remaining problems are image alignment and uneven spatial samplings of VLBI data taken at different frequencies. At an observing frequency $\nu_{\rm obs}$, the spatial sampling of a baseline $B = \sqrt{B_{X}^2 + B_{Y}^2 + B_{Z}^2}$formed by two antennas whose positions differ by B_X, B_Y, B_Z is characterised by the spatial frequency (e.g. Thompson et al. 1986)  

$$\zeta = (\nu_{\rm obs} B /c)\sin\theta_{\rm 0} \,,$$ (1)

where $\theta_{\rm 0}$ is the angle between the baseline vector and the direction to the observed object. The quantity $\zeta$ is often represented by its coordinate components u and v measured in the spatial frequency plane (uv-plane). The spatial sampling of a VLB array is described by the distribution of spatial frequencies accumulated during the observation at all available baselines ( uv-coverage). In VLBI data at different frequencies, these distributions can differ significantly.

To overcome, or at least reduce, the negative effect of uneven uv-coverages, the following scheme of observation and data reduction can be used:

1) Quasi-simultaneous multi-frequency observations. The reliability of interleaved frequency observations can be demonstrated by Fig. 1 which compares a VLBI image of 3C 345 obtained from a full-track observation and an image made from simulated data that were sampled so that they represent the uv-coverage achieved in a 5/15 duty cycle observation (corresponding to an observation at three frequencies, with 5 minutes-long scans at each frequency). Despite some loss of dynamic range and sensitivity, the extended structure is still well detected in the simulated image. The jet appearance in the simulated image is consistent with the jet structures seen in the actual map.

 

Figure 1: Maps of 3C345 at 5GHz (Zensus et al., in preparation) obtained from a real full-track global VLBI observation (top) and from a simulated interleaved-frequency VLBA+VLA observation (bottom). The contour levels are the same in both images: $(-1,1,2,4,8,16,32,64,128,256,512)\times 3.2$mJy

2) Careful choice of wavelengths. The choice of wavelengths must be a compromise between the possibility of detecting the source structure and the VLBA sensitivity. Typically, at frequencies higher than 22GHz, the requirements on brightness temperature limit the sensitivity. Also, there is a stronger dependence of the high frequency data on atmospheric instabilities. At frequencies lower than 2.3GHz, many sources will become too complicated to warrant a successful structure detection without a full-track observation (see Table 1).

3) Applying the phase-cal information for aligning the relative phases in separate frequency bands (Cotton 1995).

4) Improved amplitude calibration, due to frequent system temperature measurements and a relatively weak elevation dependence of the power gains of the VLBA antennas (Moran & Dhawan 1995).

 

Table 1: Maximum sampling intervals [min] and maximum detectable structure sizes [mas] for a 8600km-long baseline  

5) Applying appropriate uv-tapering, in order to provide matching uv-ranges for data taken at different frequencies.

6) Convolving data at different frequencies with the same, artificially circular beam.

7) Using SNR and flux threshold cutoffs, in order to leave out the remaining sidelobe-induced artifacts.

8) If strong sidelobe effects remain present, matching the uv-coverages within certain uv-ranges or over the whole uv-plane.