1. Radio flux density monitoring: a practical guide Andy Biggs (Joint Institute for VLBI in Europe)

2. Outline Which telescope? Flux-scale calibration –With special attention to high-frequency observations –Calibration sources Polarisation calibration Measuring image flux densities Determining the time delay

3. Available instruments Several arrays have been used for gravitational lens monitoring –VLA –MERLIN –ATCA –WSRT Factors to consider –Baseline lengths –Available frequencies (and agility) –Sensitivity –Gain stability –Aperture (u, v) coverage –Location (northern/southern hemisphere) –Weather conditions/time of year  = beam angular size = observing wavelength B = baseline length Resolution (diffraction limit)

4. Very Large Array (VLA) Located in New Mexico, USA –Latitude = 34  27 telescopes (‘Y’ configuration) –25-m diameter Maximum baseline = 35 km –~70 km with VLBA Pie Town antenna Array changes size every ~3 months –A configuration (B max = 35 km) –B configuration (B max = 10 km) –C configuration (B max = 3.5 km) –D configuration (B max = 1 km) Frequency coverage –400, 90, 20, 6, 3.6, 2, 1.3, 0.7 cm Resolution = 0.2  at 8.4 GHz (A) Current developments –Broad-banding –Possible addition of longer baselines C configuration D configuration

5. MERLIN* Located in United Kingdom –Latitude = 53  6 telescopes –~25-m diameter –76-m Lovell telescope at  5 GHz Maximum baseline = 217 km Frequency coverage –200, 73, 20, 6, 1.3 cm –Limited agility Resolution = 50 mas at 5 GHz Current developments –Broad-banding –Increased frequency coverage –Upgrade of Lovell telescope *Multi Element Radio-Lined Interferometer Network

6. Australia Telescope Compact Array (ATCA) Located in Australia (Duh!) –Latitude =  30  6 telescopes –East-west array –22-m diameter Maximum baseline = 6 km Frequency coverage –20, 13, 6, 3 cm Resolution = 1  at 9 GHz Current developments –mm receivers –Broad-banding

7. WSRT* Located in the Netherlands –Latitude = 53  14 telescopes –East-west array –25-m diameter Maximum baseline = 3 km Frequency coverage –  8.4 GHz Resolution = ~2  at 8.4 GHz Current developments –Low frequency receivers (~100 MHz) –Integration with LOFAR *Westerbork Synthesis Radio Telescope

8. Array pros and cons VLA –Practically perfect in every way –Excellent (u, v) coverage –On-line T sys correction –Resolution is only real problem Most lens monitoring only possible in A configuration Possible systematic errors in fluxes measured in different configurations MERLIN –High and consistent resolution –Poor “snapshot” (u, v) coverage –No T sys measurement ATCA and WSRT –Low resolution –Very elongated beam for short observations –ATCA recently monitored PMN J1838-3427 (no time delay measured) –Only B2108+213 monitorable from CLASS (  ~4.5  )

9. (u, v) coverage Consequences of incomplete (u, v) coverage include –Difficulties in making maps of sources –Systematic offsets in flux densities measured from maps Telescopes have very different (u, v) coverage –The VLA is an excellent snapshot instrument –MERLIN usually observes for many hours or uses multiple snapshots –WSRT only samples a single position angle at a time VLAMERLINWSRT

10. Flux scale calibration Flux scale is initially not calibrated –Data often delivered as correlation coefficients Set flux scale using a calibrator source –Flux density should be known (at least approximately) –Determine antenna gain corrections, G A,  A: amplitude,  : phase –Apply G A,  to sources of unknown flux density Before calibrationAfter calibrationAmplitude corrections

11. Flux scale calibration assumptions Assume that 1.the same corrections apply at the time when the lens is observed 2.the same corrections apply at the position of lens on the sky Unfortunately, the above assumptions are, in general, not valid –Atmosphere changes with time and position on sky –Antenna gain changes with elevation –Antenna electronics are also time variable –G A,  [t,  ] Therefore, calibrator should lie as close to target as possible

12. Fast source switching Flux calibration source normally lies many degrees from target –Flux-stable, compact (bright) sources are rare –Increases likelihood of G A,  being different for lens and calibrator Problem is resolution –Straightforward to find steep-spectrum sources close to target (NVSS) –Usually resolved by MERLIN or VLA –But not to WSRT! Lens-calibrator distance small (~ 0.5  ) –Target and calibrator seen through same atmosphere Slew times very short (~10 s) –Atmospheric changes apply to target and calibrator

13. High- observing (source variability) Flux density variability often increases with frequency Greater variability makes time delay determination easier! Flux density (Jy) Time (days) 15 GHz 8.4 GHz 5 GHz 0218+357 VLA 15 GHz

14. High- observing (gain-elevation correction) Antenna efficiency varies with elevation (surface deformation) Much more pronounced at high frequencies Can be corrected in AIPS (perhaps necessary  15 GHz) Gain correction factor 90   elevation VLA 15 GHz VLA 8.4 GHz

15. Effect of gain-elevation correction Reduced scatter in VLA 15-GHz data (JVAS B0218+357) Flux calibrator (3C84) lay ~13  away Previously unseen features were revealed Flux density (Jy) Time (days) After correction: Before correction: 0218+357 VLA 15 GHz

16. High- observing (weather) Atmospheric opacity increases greatly for  15 GHz –Main absorbers are H 2 O and O 2 –Biggest problem is H 2 O as this is highly variable (clouds, rain, snow) –22 GHz is particularly badly affected –Opacity fairly constant at 5 and 8.4 GHz Optical depth for VLA site Dotted: H 2 O Dashed: O 2 Solid: Total 22 GHz

17. More weather optical depth due to H 2 O optical depth due to dry air Good weather conditions Bad weather conditions (snow) 0218+357 VLA 15 GHz Can correct VLA data with seasonal model and surface weather data ‘Tipping’ scans can measure opacity –BUT take up valuable time Figures below show effect of snow on VLA 15-GHz data

18. High- observing (antenna pointing) Pointing more important at  15 GHz due to smaller telescope beam –VLA pointing errors ~10-20  –Telescope beam = 2.8 (15 GHz), 1.8 (22 GHz), 1.0 (43 GHz) VLA pointing can be improved using ‘referenced pointing’ –Error reduced to ~2-5  –Special (~1 min) scans required –Usually performed at 8.4 GHz Referenced pointing used with VLA 0218+357 monitoring at 15 GHz –Effectiveness unknown!

19. Possible flux scale calibrator sources “Phase” calibrators –Typical flux densities ~0.5 Jy –Point sources –Many of them (can be easily found within 5  of lens) –BUT variable flux densities!!! Flux density standards (3C48, 3C286, etc) –Many Jy –Non-variable –BUT complex structures –AND usually located far from lens Useful (compact and non-variable) calibrators include –Compact Symmetric Objects (CSOs) –Gigahertz Peaked Spectrum sources (GPS) –Compact Steep Spectrum sources (CSS)

20. Compact Symmetric Objects (CSOs) Core plus two lobes Linear size < 1 kpc (~50 mas) Flux density variability is very low –Lie in plane of sky (core emission not beamed) –Lobe emission (often) dominates Rare (~2% of sources)

21. Polarisation calibration Polarisation measured by correlating orthogonal components of radiation –Usually detect circular polarisation of incident radiation (R and L) –An un-polarised source will have no correlation between R and L Polarisation calibration involves two steps 1.Calculating the leakage between R and L (magnitude) 2.Calculating the phase difference between R and L (position angle) Leakage (D-terms) –Observe an un-polarised source Position angle –Observe a source of known position angle –OR constant position angle Right: VLA 15-GHz map of B0218+357 The cores are intrinsically ~10% polarised (Einstein ring is also polarised)

22. Observational strategy Phase calibrator –Not essential for bright sources (can self-calibrate) –Often used to set initial flux scale Amplitude calibrators –Preferably  1 CSO-type source –Multiple calibrators will reveal if one of them varies Polarisation calibrators if necessary Observe as efficiently as possible –Short projects more likely to be approved by TAC –MERLIN will require multiple Hour Angles to improve (u, v) coverage Usually require  1 hour for a single epoch

23. Amplitude calibration in practice (AR416) VLA 8.4-GHz monitoring of two lens systems –CLASS B2045+265 –CLASS B2319+051 Project code: AR416 (PI = Dave Rusin) 8 epochs (only checking for variability) Flux scale set with 2045 phase calibrator 4 CSO sources also observed Raw dataPhase-calibrated dataAmplitude-calibrated data

24. CSO flux stability (AR416) Top plot: CSO flux density at each epoch divided by average of that CSO’s flux density over all epochs Bottom plot: As top plot, but each epoch divided by average of CSO flux densities at that epoch Scatter in CSO flux densities < 0.5% Large variation, but CSO flux densities track each other very well  variation due to phase calibrator!

25. Measuring image flux densities Various methods available –Model-fit in image plane Can correct for incomplete (u, v) coverage using simulated data (Cohen et al. 2000) –Model-fit in (u, v) plane Incomplete (u, v) coverage is less of a problem Can ignore short-baseline data corresponding to complex, extended emission Difmap –Doesn’t calculate parameter errors (but Difwrap script available…) –Some doubt over polarisation capability AIPS OMFIT –AIPS Difmap-esque model-fitting program –Not finished or maintained –Nightmare to run! –BUT reports error bars Must fit to Stokes Q and U parameters to measure polarisation

26. Results of model-fitting (AR416) Model-fitting of 5 delta components in Difmap Positions allowed to vary Self-calibration employed Brightest three (cusp) images shown here Data appear to show statistically significant variability, but different in each image (  t = ~hours) A B C E D

27. Determining the time delay Basic procedure 1.Shift one “light curve” by a trial time delay 2.Y-offset also (flux density ratio) 3.Calculate a goodness-of-fit parameter –Cross Correlation Function,  2 –Uneven sampling will require interpolation 4.Repeat Complications –Don’t want to interpolate? Discrete correlation function (Edelson & Krolik 1988) Dispersion method (Pelt et al. 1994) –Microlensing Fit a time variable flux density ratio Many other methods (often very complicated) have been tried!!!

28. B0218+357 (total intensity) Time delay = 10.5 days (2  error = 0.4 days) Flux ratio (A/B) ~ 3.7

29. B0218+357 (polarisation position angle) Position angles differ by ~15  due to Faraday rotation