1. Phase Referencing Optimization Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA

2. Phase Referencing used for years Used for virtually all arrays VLA, ATCA, WSRT as well as VLBI Mainly for instrumental temporal errors Data flagging (scan beginning quack) Quality checking of antenna sensitivity, stability But for VLBI Above functions Most important to remove the effects of troposphere and ionosphere refraction above each VLBI antenna

3. How VLBI Attains 10  as Accuracy (1) Introductory Statements: Deal with troposphere delay errors only. Shami - At low frequency find an in-beam calibrator to deal with ionosphere! SKA below 22 GHz has so much sensitivity, there will always be in-beam calibrators. Imaging versus Astrometry. No difference in techniques. position accuracy 1% of resolution means 100:1 dynamic range images can be obtained. Example to be used: 5000 km at 23 GHz ( =1.3 cm): resolution:  f ~ /D ~ 400  as goal of 10  as relative position accuracy for one 8-hour experiment

4. How VLBI Attains 10  as Accuracy (2) Three astrometric limits: 1. Signal to noise: Target must have SNR >20 in image at 23 GHz position accuracy (  p) = 0.5  f / SNR ~ 10  as SNR limit is frequency dependent because of resolution. SNR > 60 needed for 8.4 GHz; SNR> 300 at 1.4 GHz 2. Semi-random small-scale delay errors:  r ~0.05 cm (~15 o  to  ~0.5 cm (~150 o  and is  weather related ‘pray for good weather’. Dynamic scheduling especially if one large telescope for sensitivity is needed (mega-masers) 3. Systematic large-scale (angle and time) delay error (  a ) Apriori  a >5cm. Must reduce to ~1 cm (GPS, special observations) Error still one wavelength which is why group delays are used for all-sky astrometry. Phases are ambiguous! 2. And 3. Accuracy is NOT frequency dependent

5. How VLBI Attains 10  as Accuracy (3) Solution: Phase reference target to calibrator d o away from target  p ~ (d/57)  a / D + decrease in  r (random) for d = 1 o,  a =1 cm, D=5000 km;  p ~ 15  as (residual 0.2 mm delay) per antenna --> 10  as averaging all antenna

6. How VLBI Attains 10  as Accuracy (3) Solution: Phase reference target to calibrator d o away from target  p ~ (d/57)  a / D + decrease in  r (random) for d = 1 o,  a =1 cm, D=5000 km;  p ~ 15  as (residual 0.2 mm delay) per antenna --> 10  as averaging all antenna CONGRATULATIONS: YOU HAVE DONE IT! BUT you were probably a little bit lucky

7. Typical VLBA Observing Sequence Use accurate correlator model Proper sampling, temporal, frequency sampling of visibility Apply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)

8. Typical VLBA Observing Sequence Atmospheric Cal Electronic Cal 40 min Source risingSource setting Time Phase Referencing Use accurate correlator model Proper sampling, temporal, frequency sampling of visibility Apply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys) 3 steps to processing (VLBA specific) Atmospheric + Electronic Cal + Phase referencing From Mark Reid

9. Electronic Frequency Calibration Phase versus Frequency Calibration Several short observations of a strong calibrator, not too far from the calibrator-target (20 o okay). Or use phase calibrator if strong enough. Although the phase is changing quickly with time, the phase versus frequency is stabile in most instruments For phase referencing on weak calibrators when all frequency channels must be coherently added for scan detection, this calibration is crucial. Also crucial for spectral line astrometry and spacecraft astrometry when sources are at different frequencies. Watch out for ionosphere calibration (GPS models) since this produces a phase/frequency slope versus position

10. Residual Troposphere Calibration Typical zenith path delay error  a >5 cm, after best apriori and GPS calibration. Error is somewhat stable over hours. This error produces a systematic delay difference,  c-t, between cal and target as a function of zenith angle z  c-t =  a sec(z) tan(z)  z c-t sec(z) tan(z) = 0.0 at z=0 o ; 3.5 at z=60 o ; 8.0 at z=70 o ] This is why low elevation observations should be avoided  c-t = for 1 o cal-sources separation at z=40 o for  a ~5 cm = 1 mm Need to reduce this error to 0.2 mm, otherwise >50  as accuracy Reid, Kogan, Mioduszewski (DELZN) Simplified astrometric observations to determine zenith-path delay (mentioned by Andreas yesterday)

11. Global Troposphere Residual Delay (DELZN) Observe ~15 ICRF sources over the sky for about 40 min. Spanned a bandwidth of about 500 MHz and measure group delays (phase slope with frequency) Each ‘blue’ box’ is the result of a 1-minute scan. Fit delay to  a using AIPS task DELZN. In this case  a = 7.0 cm, error of ~1 cm. Yellow crosses are the group delay after correcting for the tropospheric error. Typical total troposphere is 500 cm 100 psec=3 cm Strongly recommend observations every 4 hours

12. Typical VLBI Temporal Phase Behavior

13. =23 GHz 1  = 360 o = 1.3 cm 3C279 at z=40 o LA as reference Long-term variations: 3 over hours Medium term: 0.5 over 10 min Short term: 0.1 to 0.5 over 10 sec to 10 min sporadic Closer inspection at 19 h data 1800 km 3000 km 5. 5000 km 1100 km 4500 km

14. Phase Referencing Editing for Temporal Noise 23 GHz: 3C279 20-min of data Antenna-based phases LA as reference 40-sec cal, 40-sec target 3C279 strong so that 10-sec solution okay to see shorter fluctuations Question: Can you interpolate accurately between scans? ? = Ambiguous !! = No phase stability DELETE relevant target data Subjective BUT Images/positions are much better! ?? ? !! ? ? ?

15. Comparison with Target Phases (strong target) Target sources strong enough to be detected and checked. Position offsets removed All sources should define a continuous phase #

16. Time Coherence Editing Don’t be afraid to edit regions where phase coherence looks doubtful. Some automatic software available. Typical editing: 8 GHz 5% 23 GHz 20% 43 GHz 40% (usually SC) Images and astrometric precision are usually significantly better, even for weak targets. The main reason phase referencing pipelines are difficult to make For in-beam and VERA, can be more casual But, if phase is changing by 100 o in a minute, who knows what is happening only 2 o away?

17. The Angular Coherence Problem Cal & target Cal - target Cal - Target Nod

18. The Angular Coherence Problem Cal-target phase Cal-target phase Nodding observations Simultaneous 8 GHz simulations, 2.0 o separation,20-s nodding [Asaki et al] Cal & target Cal - target Cal - Target Nod Cal - Target Simultaneous (offset 30 o )

19. The Angular Coherence Effects Cal & target Cal - target Cal - Target Nod Cal - Target Simultaneous (offset 30 o ) Calibrator - Source separation is critical astrometric parameter coherence Astrometric precision Simultaneity versus nodding does not make a big difference Simultaneity increases SNR! Feed arrays in future simultaneous nodding

20. Cal & target Cal - target Cal - Target Nod Cal - Target Simultaneous (offset 30 o ) coherence The Bottom Line What we knew all along: The closer the calibrator is to the target, the higher the astrometric precision.

21. Cal & target Cal - target Cal - Target Nod Cal - Target Simultaneous (offset 30 o ) coherence The Bottom Line What we knew all along: The closer the calibrator is to the target, the higher the astrometric precision. Where we are now: ICRF forms basic quasi-inertial frame-work of calibrators now accurate position to <0.1 mas (ICRF2) VLBA Calibrator Survey (Petrov, Kovalev, Gordon, Fomalont) increased number to >2000 good quality calibrators > 80 mJy LBA Calibrator Survey + ICRF work in the South (Phillips + others) BUT----Average separation is 3 o in north. Need a increased factor of at least 5, especially near galactic plane. The best plan to find the calibrators?

22. Arrays have plenty of sensitivity Detection Level of Calibrator: Calibrator must also be detected in coherence time to be useful. Phase error ~ 50 o / antenna solution SNR SNR > 5.0 recommended (assumed all frequencies added) VLBA 23 GHz in 30 sec @ 256 Mb/s 6.0 mJy VLBA 8 GHz in 120 sec @ 256 Mb/s 2.0 mJy VLBA+GBT 23 GHz in 30 sec @ 256 Mb/s 2.6 mJy VLBA+GBT 8 GHz in 30 sec @ 256 Mb/s 1.0 mJy EVN 8 GHz in 120 sec @ 256 Mb/s 1.4 mJy Potentially many calibrators are available. You ‘just’ have to find them Until then, use more complicated schemes

23. Tricks: Multi-Source Calibration Cal & target Cal - target Cal - Target Nod Cal - Target (offset 30 o ) Observe several calibrators around target to remove angular phase dependence. J0839-top J0842-middle J0854-bottom LA-MK baseline 8 GHz Sep 8, 2002 P c 0842 = 0.75*P 0839 + 0.25*P 0854 - P 0842 In general, you need three calibrators. Hard to find, must be strong enough, fast cycling, position uncertainties Guirado’s talk on Polar cap surveys  =7mm

24. More Complicated Observing Scheme  A (t 1,     )  B (t 1,     ) Scan sequence: C-T-C-T-C-T-C-C 1 -C-T-C-T-C-T-C-C 1 -C-T-… C = Cal, T = target, C 1 = Secondary cal Switching time consistent with temporal coherence C is closest calibrator to target C 1 another calibrator within about 4 o (Check source) Analysis: Use C as main calibrator Image C 1 : It will probably be offset What are non-positional errors?

25. Example at 8 GHz  A (t 1,     )  B (t 1,     ) C 1 after phase referencing C 1 after position correction Image has offset -0.7, -0.3 mas Phase residual ~ delay errors Poor quality data indicated. Should remove this time perioid from target source as well since similar residuals occuring (but not seen).

26. Calibrator Source Structure 1.As the phase calibrator for a target: Okay as long as detectable at longest spacings Self-cal methods will provide image to compensate for non-closed phase problems in antenna solutions 2.Alignment for different frequencies important for spectral line comparisons, spectral index Definitely a problem since core shift with frequency is now well documented for most AGN calibrators Next page shows alignment of four sources they were phase-referenced together.

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28. Source Position vs Frequency How will the frequency dependence of source positions be found in general? Chris Jacobs talk about an ICRF at 23-43 GHz Compare with ICRF2 at 8 GHz Obtain requency offset for many strong calibrators A few sources having jets with very bright ejecta cannot be used.

29. 3. Source Position vs Time Most astrometric problems deals with changes with time. Calibrator changes add uncertainties to proper motion and parallax determinations. “Weak sources seems better behaved than strong sources.” Less structure and variability? Not sure this is true. Harder to determine if weak. Another reason to use more than one calibrator. If one goes ‘crazy’ you can recognize it. Dave Boboltz described pilot project to define methods for determining changes with time at several frequencies.

30. Calibrator Catalog Goal A catalog of thousands of calibrators Perhaps, many found specifically for certain targets Need Images/astrometric tie to ICRF that are made at several frequencies Catalog information: Position of ‘stationary’ location of each source core position at 43 or 86 GHz (~50  as) Position offset versus frequency Simple position motion down jet (~20  as) Anomalous sources noted

31. Summary We can reach 10  as now with good fortune Good apriori and supporting observations are important We need a much higher density of calibrators We are subject to the weather. Edit, dynamic schedule Frequency/time dependence of calibration positions needed