High resolution/high frequency radio interferometry

Transcription

1 High resolution/high frequency radio interferometry Anita Richards UK ALMA Regional Centre Jodrell Bank Centre for Astrophysics University of Manchester thanks to fellow tutors, ALMA and JBCA colleagues and IYAS organisers

2 Outline Dish-based arrays sub-mm to m High-frequency considerations Earth Rotation Aperture Synthesis Field of view Brightness temperature - observability Correlation and spectral windows Atmosphere Calibration Instrumental measurements Astrophysical standards and phase referencing Self-calibration Mostly ALMA examples Principles same for NOEMA Differences in techniques summarised Data products

3 Dish-based arrays: (sub-)mm (a) (b) (a) Steerable dishes (e) (b) Subreflector (c) (Multiple) receivers cabin (d) Optical fibre links to correlator (e) Reconfigurable (d) to 0.8 mm Also SMA 0.45 mm; VLA 6 mm; ATCA 3mm; KVN 2.5mm (c) to 0.35 mm (e)

4 Atmospheric Transmission (0.5 mm PWV) (sub-)mm windows & bands ALMA NOEMA (mm)

5 cm-wave arrays: connected, ~open access 217 km (a) (a) e-merlin (UK); 217 km; cm - highest resolution (b) Westerbork (NL); 2.7 km; cm - largest field of view (c) Australia Telescope Compact Array; 6 km; cm - shortest wavelengths (d) VLA (USA); 36 km; cm; - most sensitive at short (e) Giant Metrewave Radio Telescope (India); 25 km; cm - most sensitive at long (+ dipole etc. arrays e.g. LOFAR, MWA) (b) & many more (c) (d) (e)

6 Very Long Baseline interferometry RadioAstron Satellite -arcsec resolution Often recorded pre-correlaton Link single dishes & arrays Coming: Meerkat SKA + AVN! cm-wave now xtending to mm And in space KVN, VERA, VLBA, new EVN... Global (sub-)mm VLBI with ALMA and NOEMA Event Horizon telescope

7 Point source overhead Signals in phase, interfere constructively Correlator Combined phase 0o, amp constant

8 Resolved source overhead Signals from overhead vector s0 Signals from lobe Angular offset vector s Path length s = s s 0 Combined depends on s Complex visibility amplitude is sinusoidal function of

9 Earth rotates Telescopes separated by baseline Bgeom Earth rotates Projected separation b = Bgeom cos 0 Samples different scales of source Additional geometric delay path Remove in correlator

10 Earth rotation aperture synthesis Combined depends on s(time) Complex visibility amplitude is sinusoidal function of

11 l Interferometry to images m Correlation makes complex visibilities V (u,v ) One V, Aei, per -chan per baseline per int per pol. Fourier transform gives sky brightness distribtion V (u,v ) e[2 i(u l + v m)] dudv = I (l,m) or V(u,v) I (l,m)* for short u b *I (l,m) can be written T(x,y) Sensitivity: Correlator σ rms v T sys N (N 1)/2 δ ν Δ t N pol Number antennas d freq. width per image, t total time on source

12 High-frequency considerations Same principles as any radio interferometry You are unlikely to be bothered by: Ionosphere ( delayionosphere 2) Confusion ( PrimaryBeam~ /B ~ 3mm, 12-m dish) Most bright extragal. sources have <0 where S You will suffer from: Small field of view ( PrimaryBeam 0.45 mm) Tropospheric refraction ( troposphere 1/ ) phase affected, amps if signal decorrelates Tropospheric absorption and emission amplitudes affected

13 ALMAconsiderations primary beam High-frequency 0.45mm ~9 ; 3mm ~55 beam VLA Same 18cm ~25' principles as any radio interferometry You are unlikely to be bothered by: Ionosphere ( delayionosphere 2) Confusion ( PrimaryBeam~ /B ~ 3mm, 12-m dish) Most bright extragal. sources have <0 where S 5 arcmin You will suffer from: Small field of view ( PrimaryBeam 0.45 mm) Tropospheric refraction ( troposphere 1/ ) phase affected, amps if signal decorrelates Tropospheric absorption and emission amplitudes affected

14 Estimate observability from low-res image Brightness temperature Tb = Ssource / 2kB emitting area (sr), (m), S (Jy) Resolved? Use S per measured Unresolved by low-resolution obs. e.g. single dish? Estimate actual source size for Use S per best estimate of to find Tb Predict ALMA flux density SALMA = Tb 2kB b2 / Substitute = b2 (ALMA synthesised beam) Use Sensitivity Calculator - need >5 rms on peak e.g. total source 1 Jy, =15, Tb~0.07 K at 1mm

15 Estimate observability from low-res image Brightness temperature Tb = Ssource / 2kB emitting area (sr), (m), S (Jy) Resolved? Use S per measured Unresolved by low-resolution obs. e.g. single dish? Estimate actual source size for Use S per best estimate of to find Tb Predict ALMA flux density SALMA = Tb 2kB b2 / Substitute = b2 (ALMA synthesised beam) Use Sensitivity Calculator - need >5 rms on peak e.g. total source 1 Jy, =15, Tb~0.07 K at 1mm b=0.15, flux density 1x(15/0.15)2 = Jy/beam

16 Correlator configurations Two sidebands, fixed spacing depending on band e.g. B7, B3 sideband centres separated by 12 GHz Max. continuous b/w <4 GHz (8 GHz Bands 9, 10) GHz Four basebands (BB), max. width 2 GHz 128 chans per BB (dual pol) TDM 4096 chans per BB (~0.5 km/s at 300 GHz) FDM Narrower spectral windows for higher resolution Useful max GHz (so 3840 channels usable) Factors of two down to 62.5 MHz (15.25 khz chans) Higher spectral resolution in single polarization See documentation and OT for full details

17 Correlator configurations Two sidebands, fixed spacing depending on band e.g. B7, B3 sideband centres separated by 12 GHz Max. continuous b/w <4 GHz (8 GHz Bands 9, 10) GHz GAP Four basebands (BB), max. width 2 GHz 128 chans per BB (dual pol) TDM 4096 chans per BB (~0.5 km/s at 300 GHz) FDM Narrower spectral windows for higher resolution Useful max GHz (so 3840 channels usable) Factors of two down to 62.5 MHz (15.25 khz chans) Higher spectral resolution in single polarization See documentation and OT for full details

18 Absorption and emission The atmosphere both absorbs the astrophysical signal, and adds noise T received =T source e τ atm /cos z +T atm (1 e τ atm /cos z ) where the source would provide temperature T if measured above the atmosphere and z is the zenith distance Same source, same baselines Raw amps lower at higher Preciptable Water Vapour PWV 0.25mm Short baseline Long baseline Amplitude PWV 0.6mm

19 Phase errors cause position errors Averaging over phase fluctuations causes decorrelation of amplitudes Visibility V = Voei iϕ (ϕ2rms )/ 2 V =V o e =V o e rms in radians Lose 9% amplitude for 5o rms Fluctuations on time-scales of few sec: raw data position jitter Water Vapour Radiometry Position per integration, raw IRAM PdBI data (Krips) Measure PWV, each antenna, every ~second Calculate phase delay Apply corrections to all observed data

20 RAW PHASE WVR before & after Phase Long baseline Short baseline WVR corrections Long Short WVR-Corrected PHASE WVR Corrections

21 Measure total noise Tsys Measure Tsys using hot & cold loads ALMA every few min, 128 channels per 2-GHz baseband NOEMA per baseband Tracks atmospheric & instrumental fluctuations Applied during data reduction

22 atmospheric line Visibility amplitude Raw data, coloured by baseline Tsys correction before & after Tsys corrections slight noise increase Tsys corrections applied Frequency

23 Phase referencing Observe phase-ref source close to target Point-like or with a good model Close enough to see same atmosphere Bright enough to get good SNR much quicker than atmospheric timescale ~2-15 degrees (isoplanatic patch) 10 min/30 s short/long B & low/high Nod on suitable timescale e.g. 5:0.5 min Derive time-dependent corrections to make phase-ref data match model Apply same corrections to target Correct amplitudes similarly Self-calibration works on similar principle

24 Astrophysical calibration sources Use flux standard (e.g. asteroid) to set scale in Jy Calibrate amplitude and phase as a function of : Pallas ~270 km Frequency (delay and BandPass calibration) Bandpass (mostly instrumental errors) stable for hours Time (all calibrators; phase referencing applied to target) Atmospheric fluctuation scale minutes (after WVR) Need signal/noise Scalsource/ ant > 15 if possible ~1/15 radians ~5o phase error, 10% amp decorrelation per calibration interval per antenna per polarization σ ant (δ t, δ ν) σ array N (N 1)/2 N 3 array is noise in all-baseline data per interval e.g. 30 antennas, ant ~ 4 x map noise per interval/pol.

25 Visibility amplitudes Visibility phase Phase-reference visibilities Time Time

26 Visibility phase Visibility amplitudes Corrections for point model Time Time Corrections Time Time

27 Raw phase (all baselines) Corrections (per antenna) Time Scatter reduced Phases aligned close to 0o -30o phase 30o -150o Visibility phase 150o Corrected phase-ref visibilities Corrected phase for point source

28 NOEMA calibration Bandpass and phase-ref sources Often too low S/N for self-cal phase amp phase Frequency Phase calibration Time Fit to series of phases RF (bandpass) cal Suitable for higher noise situations Controls for multiple calibrators, jumps... Phases 20th order Amps 12th order

29 Effects on imaging Phase-only self-cal: S/N 40 Residual, symmetric amplitude errors No astrophysical calibration: no source seen Bandpass, phase-ref etc. solutions applied: S/N 20 Anti-symmetric artefacts dominate - residual phase errors Amp & phase self-cal: S/N 50

30 Calibration: Measurement Equation basis for calibration in CASA Vij = MijBijGijDij EijPijTijFij S In (l,m)e-i2 (uijl+vijm)dldm +Aij Vectors V isibility = f(u,v) I mage to be calculated Additive baseline error Scalars S (mapping I to observer pol.) l,m image plane coords u,v Fourier plane coords i,j telescope pair Jones Matrices Multiplicative baseline error Bandpass response Generalised electronic gain Dterm (pol. leakage) E (antenna voltage pattern) Parallactic angle Tropospheric effects Faraday rotation etc.

31 Polarization Most (sub-)mm Rx use linear polarization X and Y combined in correlator ALMA Band 3 ( ~3mm) uses Ortho Mode Transducer Band 9 ( ~0.45mm) uses wire grid XX, YY for total intensity XX, YY, XY, YX used to provide Stokes IQUV Diagram thanks to Wikipaedia

32 ALMA polarization calibration Calibration source has unknown linear polarization Gain solutions decomposed into X and Y per antenna gx' = gx(1+q/i)0.5 gy' = gy(1 Q/I)0.5 Leakage between X and Y feeds ('D'-terms) Feeds rotate on sky as alt-az antenna tracks source Parallactic angle rotates Qobs time-dependent 3+ scans, >3hr HA coverage Known feed orientation Solve for leakage and source polarization Directly correct pol. angle VXX VYY Real VXY VYX For high pol. purity correct 2nd order terms Need source model (external or self-cal) Parallactic angle

33 ALMA data processing Each SB self-contained Pointing, flux scale, BP, (pol.) cal scans ~20-40 mins target(s)/phase ref Execute (EB) until sensitivity is reached Initial data processing (pipeline or staff script) same spectral & array configuration Convert ASDM to Measurement Set Calibrate Combine EBs for target imaging

34 What ALMA data do you get? Images/cubes for principal science target channels Science products & scripts might be all you need or you could use CASA scripts to regenerate edited, calibrated uv data Processing summary Data processing / pipeline scripts so you could tweak imaging/ self-cal using: ASDM (one per EB) Flag tables Calibration tables Self-calibrate if bright enough (S/N >~20 per scan) Re-image Weighting for higher spatial sensitivity/lower resolution or v.v. Change spectral resolution, make spectral index image etc. etc...

35 Observing support Observing Support Tool for quick simulations Splatalogue for line frequencies etc. Sensitivity Calculator Observing Tool for preparing proposals, observations Archive including public-domain data On-line Helpdesk ALMA Regional Centre Nodes face-to-face support Community days, schools RadioNet* MARCuS support to visit nodes for data redn IRAM Interferometry & single dish schools Biennial, alternate next mm-dedicated ERIS 2016 RadioNet* TNA support for observations * No RadioNet support in 2016

36 (sub-)mm Interferometry Summary Atmospheric refraction/absorption dominates quality Cold dry sites OK 370 GHz, exceptional sites 1 THz Troposphere affects phase & amp on 1s timescales Instrumental calibration (WVR, Tsys) etc. ALMA / NOEMA Jy sensitivity, 10 / 100 mas resolution Good sites, many or large antennas Sub-mJy sensitivity at sub-arcsec resolution Extended sources need multiple arrays/sd fill in Large fields need mosaicing Normally observe two separate sidebands May have 'mirror' or noise Plan night-time, dry season observing at sub-mm ALMA delivers calibrated data, sample images May want to self-calibrate, reimage changing resolution

37 ALMA Hands-on sessions Pre-main sequence TTauri star TW Hya ALMA ~345 GHz, here dust continuum & line NH2+ Visibility data have instrumental, bandpass and phasereference calibration applied already Use this as a model for self-calibration Make final 'best' continuum image Day One List what is in the visibility data set and plot Make a clean image of TW Hya continuum Split out calibrated visibility data for TW Hya Make clean line cube Image/spectral analysis Ready-made calibrated data/images available Don't worry if you don't quite finish Day One Day Two Identify line channels and subtract continuum