1. Phase Referencing Using More Than One Calibrator Ed Fomalont (NRAO)

2. Summary Nodding between Calibrator and Target - Lessens short-term temporal phase fluctuations VERA two simultaneous beams Imaging of weak sources possible Position of target wrt calibrator obtained - Persistent systematic phase differences between source and target produce position shifts and large side-lobes. - The smaller the Calibrator-Target separation the better. In-beam calibrator(s) best, but only <2 GHz. Using more than One Calibrator - Removes most of angular phase dependence. - Higher quality images and positions (8 GHz, 0.8deg separation) Dynamic range 20:1  60:1 Position accuracy 30  <10 microarcsec

3. PR Experiment Used for Jupiter Bending - Cycle among three sources for 10 hours on five days - 4.5-min cycling time - Measure change of position of J0842 on Sept 8, 2002 - Parameters: J0842 - J0839 Sep = 48’ J0842 - J0854 Sep =193’ J0842 = 0.3 Jy (peak) J0854 = 1.5 Jy (OJ287) J0839 = 0.08 Jy - Good test of PR with one or two sources.

4. Angular Phase Dependence of VLBI Observations Phase for each source using calib with self-cal image Angular dependence of phase separation: Ph(J0842) – Ph(J0854) = 4xPh(J0842) – Ph(J0839) (low elevation problems) Consistent with phase wedge in sky Main contribution is ionosphere/troposphere plus geometric residuals (calibrator position errors later) PR of J0842 using Ph(J0839) is not a good as using 0.8xPh(J0839) + 0.2xPh(J0854)

5. More Examples of Phase Wedge Behavior

6. Phase Referencing Schemes Self-calibration Images J0842 image, position using PR J0839 (0.8 d) J0842 image, position using PR J0854 (3.2 d) J0842 image, position using PR (0.8 x J0839 + 0.2 x J0854) Compare results among five days to determine image quality and position stability

7. IMAGE TESTS Self-cal 0.8 d PR 3.2 d PR PR-2 Sep 4 Sep 8 Lowest contour level 3 mJy 6 12 3 Peak in image 333 mJy 290 200 325 Most negative SL -2 mJy -14 -26 -6 VLBA + Effelsberg 8.4 GHz, 64 MHz BW 10-hour integrations Data editing during times of poor stability 20 x 12 mas field of view

8. COMPARISON OF 1-PR to 2-PR RESULTS: --Significantly higher coherence with 2-PR. 97% versus 86% --Negative side-lobes lower with 2-PR: 1.5% versus 5% --RMS scatter of positions: 9 microasec for 2-PR versus 35 microarcsec for 1-PR --Systematic position change: <5 microarcsec in R.A., 20 microarcsec in decl. Grav bending sensitivity Sep 8 – AVG +2 +/- 4 e/w --5 +/- 9 n/s (Correlator model assumes GR is correct) units=mJy units=microarcsec

10. Phase Referencing Properties at 8 GHz 100% 97% 86% 59% 47% <1% 2% 5% 18% 23% <1 9 35 48 71 ----- <5~20 ~70 ---- Coher. (% of Peak) Min Side-lobe Level Position RMS Position offset (micro-arcset) Self 2 PR 1 PR 1 PR 1 PR Cal 0.8,3.2d 0.8d 3.2d 4.1d

11. Two calibrators within ~10d of linearity (calibrator position errors in a few slides) General solution to Determine phase wedge (algorithm on request) Solving for the Phase Wedge

12. Source structure and position must be accurately known Phase difference between calibrators gives tropospheric zenith path length correction, L Use C2 for frequent calibration Use C1 less occasionally to determine angular phase offset If Phase Error is Entirely Caused by Troposphere

13. CALIBRATOR PROBLEMS 1.Position Offsets: Introduces position offset to target = to linear sum used for combining calibrator phases. BUT harmful if assuming atmosphere is main cause of phase error (includes large astrometric errors also). 2.Non-stationarity of Calibrators BIG problem for long-term, high frequency obs. Will introduce errors in long-term position stability. Using more than one calibrator can help sort out more unstable calibrators.

14. SUMMARY 1.If source is weak (<20:1 dynamic range) Simple phase referening is okay. Image and position limited by SNR. 2.Two or three calibrators within about four deg will increase image fidelity and positional accuracy even though less time is spent on target and cycling time is a bit longer. 3.With care <10 microarcsec relative position accuracy is obtainable with the VLBA. 4. If the calibrators are well-chosen, more simpler calibration schemes can take out troposphere if this is dominant error. 5. Over long-term projects, position errors are affected by calibrator changes. Try to register calibrator(s) as well as possible!!