Angular Resolution & u-v Coverage

Table 5 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.

 

Table 5: Maximum VLBI Baseline Lengths in km (\(B^{\rm km}_{\rm max}\))
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 3), are shown in Table 6.  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.

 


Table 6:  \(\theta_{\rm HPBW}\) for VLBA Observing Bands for VLBA Observing Bands
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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