Phase Referencing Optimization

Ed FomalontNational Radio Astronomy Observatory Charlottesville, VA USA

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

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

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 (~15oto~0.5 cm (~150oand isweather 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

How VLBI Attains 10 as Accuracy (3)

Solution:

Phase reference target to calibrator do away from target

p ~ (d/57) a / D + decrease in r (random)

for d = 1o, a=1 cm, D=5000 km; p ~ 15 as (residual 0.2 mm delay) per antenna --> 10 as averaging all antenna

How VLBI Attains 10 as Accuracy (3)

Solution:

Phase reference target to calibrator do away from target

p ~ (d/57) a / D + decrease in r (random)

for d = 1o, 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

Typical VLBA Observing Sequence

Use accurate correlator modelProper sampling, temporal, frequency sampling of visibilityApply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)

Typical VLBA Observing Sequence

Atm

ospheric Cal

Electronic C

al

40 min

Source rising Source setting

Time

Phase Referencing Phase Referencing

Use accurate correlator modelProper sampling, temporal, frequency sampling of visibilityApply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)

3 steps to processing (VLBA specific) Atmospheric + Electronic Cal + Phase referencing

From Mark Reid

Electronic Frequency Calibration

Phase versus Frequency Calibration

Several short observations of a strong calibrator, not too far from the calibrator-target (20o 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

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) zc-t

sec(z) tan(z) = 0.0 at z=0o; 3.5 at z=60o; 8.0 at z=70o]

This is why low elevation observations should be avoided

c-t = for 1o cal-sources separation at z=40o 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)

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

<- 40 min ->

Strongly recommend observations every 4 hours

Typical VLBI Temporal Phase Behavior

Typical VLBI Temporal Phase Behavior

=23 GHz1= 360o = 1.3 cm3C279 at z=40o

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

Phase Referencing Editing for Temporal Noise

23 GHz: 3C27920-min of dataAntenna-based phases LA as reference40-sec cal, 40-sec target3C279 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 dataSubjectiveBUT Images/positions are much better!

? ? ?

!! ?

!!?

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Comparison with Target Phases (strong target)

Target sources strong enough to be detected and checked. Position offsets removedAll sources should definea continuous phase

#

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 100o in a minute, who knows what is happening only 2o away?

The Angular Coherence Problem

Cal &target

Cal -target

Cal -TargetNod

The Angular Coherence Problem

Cal-target phase Cal-target phase Nodding observations Simultaneous

8 GHz simulations, 2.0o separation,20-s nodding [Asaki et al]

Cal &target

Cal -target

Cal -TargetNod

Cal -TargetSimultaneous(offset 30o)

The Angular Coherence Effects

Cal &target

Cal -target

Cal -TargetNod

Cal -TargetSimultaneous(offset 30o)

Calibrator - Source separation is critical astrometric parameter

coherence

Astrometric precision

Simultaneity versus nodding does not make a big differenceSimultaneity increases SNR! Feed arrays in future

simultaneous

nodding

Cal &target

Cal -target

Cal -TargetNod

Cal -TargetSimultaneous(offset 30o)

coherence

The Bottom Line

What we knew all along: The closer the calibrator is to the target, the higher the astrometric precision.

Cal &target

Cal -target

Cal -TargetNod

Cal -TargetSimultaneous(offset 30o)

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 3o in north. Need a increased factor of at least 5, especially near galactic plane.

The best plan to find the calibrators?

Arrays have plenty of sensitivity

Detection Level of Calibrator: Calibrator must also be detected in coherence time to be useful. Phase error ~ 50o / 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

Tricks: Multi-Source Calibration

Cal &target

Cal -target

Cal -TargetNod

Cal -Target(offset 30o)

Observe several calibrators around target to remove angular phase dependence.

J0839-topJ0842-middleJ0854-bottom

LA-MK baseline 8 GHzSep 8, 2002

Pc0842 = 0.75*P0839 + 0.25*P0854 - P0842

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

More Complicated Observing Scheme

A(t1, ) B(t1, )

Scan sequence:

C-T-C-T-C-T-C-C1-C-T-C-T-C-T-C-C1-C-T-… C = Cal, T = target, C1 = Secondary cal

Switching time consistent with temporal coherenceC is closest calibrator to targetC1 another calibrator within about 4o (Check source)

Analysis: Use C as main calibrator Image C1: It will probably be offset What are non-positional errors?

Example at 8 GHz

A(t1, ) B(t1, )

C1 after phase referencing C1 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).

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.

s

Source Position vs Frequency

How will the frequency dependence of sourcepositions be found in general?

Chris Jacobs talk about an ICRF at 23-43 GHzCompare with ICRF2 at 8 GHzObtain requency offset for many strong calibrators

A few sources having jets with very bright ejecta cannot be used.

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.

Calibrator Catalog Goal A catalog of thousands of calibratorsPerhaps, 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

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