Phase Referencing Using More Than One Calibrator Ed Fomalont NRAO

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Phase Referencing Using More Than One
CalibratorEd Fomalont (NRAO)
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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
  lt2 GHz
• .
• Using more than One Calibrator
• - Removes most of angular phase dependence.
• - Higher quality images and positions (8 GHz,
  0.8deg separation)
• Dynamic range 201 ? 601
• Position accuracy 30 ? lt10 microarcsec

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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.

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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)

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More Examples of Phase Wedge Behavior
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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

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IMAGE TESTS
Self-cal 0.8 d PR 3.2 d PR
PR-2
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
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
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Grav bending sensitivity Sep 8 AVG 2 /- 4
e/w --5 /- 9 n/s (Correlator model assumes
GR is correct)
unitsmJy
unitsmicroarcsec

• 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 lt5 microarcsec in
  R.A., 20 microarcsec in decl.

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Phase Referencing Properties at 8 GHz
Self 2 PR 1 PR 1 PR 1 PR
Cal 0.8,3.2d 0.8d 3.2d 4.1d
Coher. ( of Peak) Min Side-lobe Level Position
RMS Position offset (micro-arcset)
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Solving for the Phase Wedge
Two calibrators within 10d of linearity (calibra
tor position errors in a few slides)
General solution to Determine phase
wedge (algorithm on request)
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If Phase Error is Entirely Caused by Troposphere
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
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CALIBRATOR PROBLEMS

• 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).
• 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.

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SUMMARY

• If source is weak (lt201 dynamic range)
• Simple phase referening is okay. Image
• and position limited by SNR.
• 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.
• With care lt10 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!!