Angular Resolution & u-v Coverage
Table 8.1 gives the maximum lengths (\(B^{\rm km}_{\rm max}\)) for each of the VLBA's 45 internal baselines as well as the baselines to HSA telescopes. A measure of the corresponding resolution (\(\theta_{\rm HPBW}\)) in milliarcseconds (mas) is
\[\theta_{\rm HPBW} \sim 2063 \times \frac{\lambda^{\rm cm}}{B^{\rm km}_{\rm max}} \; {\rm mas}\]
where \(\lambda^{\rm cm}\) is the receiver wavelength in cm (Wrobel 1995). A uniformly weighted image made from a long u-v plane track will have a synthesized beam with a slightly narrower minor axis.
SC | HN | NL | FD | LA | PT | KP | OV | BR | MK | EB | AR | GB | Y27 | |
SC | ... | 2853 | 3645 | 4143 | 4458 | 4579 | 4839 | 5460 | 5767 | 8611 | 6822 | 238 | 2708 | 4532 |
HN | 2853 | ... | 1611 | 3105 | 3006 | 3226 | 3623 | 3885 | 3657 | 7502 | 5602 | 2748 | 829 | 3198 |
NL | 3645 | 1611 | ... | 1654 | 1432 | 1663 | 2075 | 2328 | 2300 | 6156 | 6734 | 3461 | 1064 | 1640 |
FD | 4143 | 3105 | 1654 | ... | 608 | 564 | 744 | 1508 | 2345 | 5134 | 8084 | 3922 | 2354 | 515 |
LA | 4458 | 3006 | 1432 | 608 | ... | 236 | 652 | 1088 | 1757 | 4970 | 7831 | 4246 | 2344 | 226 |
PT | 4579 | 3226 | 1663 | 564 | 236 | ... | 417 | 973 | 1806 | 4795 | 8014 | 4365 | 2551 | 52 |
KP | 4839 | 3623 | 2075 | 744 | 652 | 417 | ... | 845 | 1913 | 4466 | 8321 | 4623 | 2939 | 441 |
OV | 5460 | 3885 | 2328 | 1508 | 1088 | 973 | 845 | ... | 1214 | 4015 | 8203 | 5255 | 3323 | 1025 |
BR | 5767 | 3657 | 2300 | 2345 | 1757 | 1806 | 1913 | 1214 | ... | 4398 | 7441 | 5585 | 3326 | 1849 |
MK | 8611 | 7502 | 6156 | 5134 | 4970 | 4795 | 4466 | 4015 | 4398 | ... | 10328 | 8434 | 7028 | 4835 |
EB | 6822 | 5602 | 6734 | 8084 | 7831 | 8014 | 8321 | 8203 | 7441 | 10328 | ... | 6911 | 6335 | 8008 |
AR | 238 | 2748 | 3461 | 3922 | 4246 | 4365 | 4623 | 5255 | 5585 | 8434 | 6911 | ... | 2545 | 4317 |
GB | 2708 | 829 | 1064 | 2354 | 2344 | 2551 | 2939 | 3323 | 3326 | 7028 | 6335 | 2545 | ... | 2516 |
Y27 | 4532 | 3198 | 1640 | 515 | 226 | 52 | 441 | 1025 | 1849 | 4835 | 8008 | 4317 | 2516 | ... |
Values of \(\theta_{\rm HPBW}\) for the longest VLBA baseline, at the center frequencies of the VLBA's observing bands (Table 5.1), are shown in Table 8.1. The longest VLBA baseline at 3 mm is currently that between MK and NL, which is about 30% shorter than the longest baseline at lower frequencies.
Observing band [cm]: | 90 | 50 | 21 | 18 | 13 | 6 | 4 | 2 | 1 | 0.7 | 0.3 |
\(\theta_{\rm HPBW}\) [mas]: | 22 | 12 | 5.0 | 4.3 | 3.2 | 1.4 | 0.85 | 0.47 | 0.32 | 0.17 | 0.12 |
Customized plots of the u-v plane coverage with the VLBA and/or other VLBI stations can be generated by VLBA program SCHED (Walker 2011).
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