Radio flux density monitoring:a practical guide

Andy Biggs

(Joint Institute for VLBI in Europe)

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

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

B

= beam angular size = observing wavelengthB = baseline length

Resolution (diffraction limit)

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 (Bmax = 35 km)

– B configuration (Bmax = 10 km)

– C configuration (Bmax = 3.5 km)

– D configuration (Bmax = 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

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

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

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

Array pros and cons

• VLA– Practically perfect in every way– Excellent (u, v) coverage

– On-line Tsys 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 Tsys 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)

(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

VLA MERLIN WSRT

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, GA,

• A: amplitude, : phase

– Apply GA, to sources of unknown flux density

Before calibration After calibrationAmplitude corrections

Flux scale calibration assumptions

• Assume that1. 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

– GA, [t, ]

• Therefore, calibrator should lie as close to target as possible

Fast source switching

• Flux calibration source normally lies many degrees from target– Flux-stable, compact (bright) sources are rare

– Increases likelihood of GA, 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

High- observing (source variability)

• Flux density variability often increases with frequency

• Greater variability makes time delay determination easier!

Flu

x de

nsity

(J

y)

Time (days)

15 GHz

8.4 GHz

5 GHz

0218+357 VLA 15 GHz

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)

Gai

n co

rrec

tion

fact

or

90 elevation

VLA 15 GHzVLA 8.4 GHz

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

Flu

x de

nsity

(J

y)

Time (days)

After correction:

Before correction:

0218+357 VLA 15 GHz

High- observing (weather)

• Atmospheric opacity increases greatly for 15 GHz– Main absorbers are H2O and O2

– Biggest problem is H2O 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: H2ODashed: O2

Solid: Total

22 GHz

More weather

optical depth due to H2O

optical depth due to dry air

Goodweatherconditions

Badweatherconditions(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

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!

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)

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)

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 steps1. 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+357The cores are intrinsically ~10% polarised(Einstein ring is also polarised)

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

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 data Phase-calibrated data Amplitude-calibrated data

CSO flux stability (AR416)

Top plot: CSO flux density at each epoch divided byaverage of that CSO’s flux density over all epochs

Bottom plot: As top plot, but each epoch dividedby average of CSO flux densities at that epoch

Scatter in CSO flux densities < 0.5%

Large variation, but CSO flux densities track eachother very well variation due to phase calibrator!

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

22(%) UQP

Q

U1tan2

1

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 statisticallysignificant variability, but differentin each image (t = ~hours)

A

B

C

E

D

Determining the time delay

• Basic procedure1. 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!!!

B0218+357 (total intensity)

Time delay = 10.5 days (2 error = 0.4 days)Flux ratio (A/B) ~ 3.7

B0218+357 (polarisation position angle)

Position angles differ by ~15 due toFaraday rotation