VLBI techniques and LOFAR

Transcription

1 GLOW interferometry school VLBI techniques and LOFAR Olaf Wucknitz Hamburg, 2 September 2010

2 VLBI techniques Need for long baselines What defines VLBI? Techniques VLBI science Practical issues VLBI arrays, how to observe calibration New developments space VLBI e-vlbi titlepage introduction contents back forward previous next fullscreen 1

3 VLBI techniques and LOFAR Fringe-fitting Clock offsets Faraday rotation Imaging issues titlepage introduction contents back forward previous next fullscreen 2

4 Need for long baselines baseline D wavelength λ resolution θ λ/d [ rad ] D = 100 m 1 km 10 km 100 km 1000 km km λ = 10 m mas 4 m mas 80 mas 2 m mas 40 mas 1 m mas 20 mas 20 cm mas 40 mas 4 mas 6 cm mas 12 mas 1 mas 2 cm mas 40 mas 4 mas 400 µas 7 mm mas 15 mas 1.5 mas 150 µas 3 mm mas 50 mas 5 mas 500 µas 50 µas titlepage introduction contents back forward previous next fullscreen 3

5 Early developments (50s/60s) Australia: radio-linked interferometers up to D = 10 km at λ = 3 m θ = 1 Cambridge One-Mile and 5-km telescopes Jodrell Bank: portable antennas radio-linked with 250-ft up to D = 130 km at λ = 2 m down to 6 cm θ < 1 later MTRLI (Multi-Telescope-Radio-Linked- Interferometer), later renamed to MERLIN (Multi- Element-Radio-Linked-Interferometer-Network) (1980) direct connections or radio-link difficult for longer baselines titlepage introduction contents back forward previous next fullscreen 4

6 The need for longer baselines some sources still unresolved at these scales (< 50mas) interplanetary scintillation: few mas synchrotron self-absorption: 1 mas flat-spectrum sources: flux variations on time-scales of months or less: mas resolving these source not possible with connected (or radio-linked interferometers) Very Long Baseline Interferometry titlepage introduction contents back forward previous next fullscreen 5

7 Very Long Baseline Interferometry very long baselines no direct connection between stations record signals on tapes, disks, etc. play back simultaneously and correlate later synchronisation: also record time-stamps observe at exactly the same frequency titlepage introduction contents back forward previous next fullscreen 6

8 Connected interferometer VLBI [ Thompson (1999) ] titlepage introduction contents back forward previous next fullscreen 7

9 Connected VLBI : more details connected interferometer mix down to IF amplify and transmit at IF mix down to baseband correlate VLBI mix down to IF amplify at IF mix down to baseband record, fly, play back correlate need accurate LOs / clocks! [ Napier (1999) ] LOFAR: no mixing titlepage introduction contents back forward previous next fullscreen 8

10 The role of the local clock keep the time need to play back signals synchronised required accuracy: coherence time coherence time 1/ bandwidth keep synchronisation over observation define the observing frequency observing frequency ν shifted to baseband (mixing with LO) recorded frequency ν : ν = ν ν 0 error in ν 0 translates to error in ν,ν [ Thompson (1999) ] titlepage introduction contents back forward previous next fullscreen 9

11 The correlation direct correlation of signals V 1 and V 2 signals V 1 (t) = A 1 e 2πiνt V 2 (t) = A 2 e 2πiνt correlation:c 12 := V 1 (t)v2 (t) = A 1 A 2 e 2πi(ν ν)t = A 1 A 2 correlation of down-mixed signals V 1 and V 2 frequencies of local oscillators: ν 1 and ν 2 signals V 1 (t) = A 1 e 2πi(ν ν 1)t V 2 (t) = A 2 e 2πi(ν ν 2)t correlation: C 12 := V 1(t)V 2 (t) = A 1 A 2 e 2πi(ν 1 ν 2 )t titlepage introduction contents back forward previous next fullscreen 10

12 VLBA station system titlepage introduction contents back forward previous next fullscreen 11

13 Sampling and digitisation mix down to baseband (for several bands) frequency range 0 bandwidth Nyquist sampling 2 bandwidth typical sampling width 1 or 2 bits recording bandwidth limited optimal 1 2 bit typical 2 bit bits per sampling relative bandwidth total sample sensitivity bandwidth sensitivity sensitivity /2 1/ /4 1/ titlepage introduction contents back forward previous next fullscreen 12

14 Recording systems Canadian analog system studio TV recorders, 4 MHz, 3 h MkI digital 7-track computer tape, 330 khz, 1-bit, 150 sec MkII video recorders (later VCR), 1-bit, 2 MHz MkIII 28-track tape recorders, 1-bit, 4 MHz per track Canadian S2 VCR (8 in parallel), 128 Mb/s Japanese K-2, K-3, K-4 VLBA 1 or 2-bit, 8 bands, 32-track tape, 256 Mb/s per recorder MkIV similar to VLBA but up to 512 Mb/s Mark 5 Mark 5C disk recording, 1024 Mb/s ( 4096) PC-EVN, Japanese K5,... [ Alef (2004) ] titlepage introduction contents back forward previous next fullscreen 13

15 Stability of local oscillators atomic clocks (rubidium or hydrogen masers) long-term synchronisation with GPS receiver titlepage introduction contents back forward previous next fullscreen 14

16 Geometric delays τ 10000km km/s 30ms 1 ν 1ns τ ν titlepage introduction contents back forward previous next fullscreen 15

17 Delays, phases, rates effect of a delay τ telescope signal V j (t) = A j e 2πiν(t τ j) correlation V 1 V2 = A 1A 2 e2πiν(τ 2 τ 1 ) phase φ = 2πν(τ 2 τ 1 ) frequency dependence φ ν = 2πτ delay is frequency-derivative of phase phase rate and delay rate φ t = 2πν τ t equiv. Doppler effect, frequency error titlepage introduction contents back forward previous next fullscreen 16

18 Delays: connected vs. VLBI titlepage introduction contents back forward previous next fullscreen 17

19 Delay model predictable delays are corrected by the correlator geometric delay earth rotation aberration dry atmosphere unpredictable delays have to be calibrated later [ Walker (1999) ] wet atmosphere ionosphere station clocks titlepage introduction contents back forward previous next fullscreen 18

20 Calibration of VLBI data very similar to connected interferometers additional steps due to long baselines high resolution need accurate source positions no amplitude calibrators available use T sys to calibrate limited field long baselines unstable phases need bright fringe-finder source phase-referencing stop phase-winding: fringe-fitting other issues sparse uv coverage titlepage introduction contents back forward previous next fullscreen 19

21 Amplitude calibration correlation coefficient C jk = B V jk Nj N k B: digitisation etc., V : visibility amplitude [Jy] N: Source Equivalent Flux Density (SEFD) [Jy] N = T sys G G: antenna gain [K/Jy] elevation dependent increase in system temperature for a 1 Jy source T sys : system temperature [K] highly variable T sys measured (with additional noise source) VLBA: continuously EVN: during recording gaps titlepage introduction contents back forward previous next fullscreen 20

22 Practical amplitude calibration in AIPS T sys and G already in data (EVN, VLBA) FITLD the data with TY and GC table otherwise load ASCII tables with ANTAB use APCAL to produce SN table CLCAL to apply SN and produce CL table titlepage introduction contents back forward previous next fullscreen 21

23 Phase-cal (a.k.a. pulse calibration) calibrate instrumental delays for each observing band phase-cal tones (e.g. VLBA) injection of pulses every 1µs near feed regular coherent spikes every 1 MHz intrumental phases and delays from them PCLOD to load ASCII table PC table PCCOR to produce SN table, CLCAL CL table manual phase-cal (e.g. EVN) use strong calibrator source fringe-fit (see later) for delay and phase apply solutions to all data titlepage introduction contents back forward previous next fullscreen 22

24 The need for fringe-fitting large time-varying delays phases change rapidly phase changes frequency-dependent standard calibration techniques determine phases regularly constant between the measurements had to do this every few seconds! fit delays and rates instead of phases allows for rapid changes rate of changes and delays vary more slowly titlepage introduction contents back forward previous next fullscreen 23

25 Linear approach for residual phases φ(t,ν) = φ 0 + φ φ ν + ν t t have to determine [+dispersive delay] phase φ 0 delay φ ν rate φ t delays and rates are stable over a longer time and wider band than φ(t,ν) the process to find phase, delay, rate is called fringe-fitting titlepage introduction contents back forward previous next fullscreen 24

26 Practical fringe-fitting with AIPS tasks FRING or KRING more sophisticated version of CALIB (but no amplitudes) first step: coarse grid-based search for baselines (maybe with stacking) FFT from frequency-time to delay-rate domain find peak delay and rate second step: refine on station-basis least-squares solution SN table can use multi-band or dispersive delay transfer solutions from calibrators to target sources CLCAL to apply SN table and produce CL table titlepage introduction contents back forward previous next fullscreen 25

27 high resolution Other issues use small pixels for maps (CELLSIZE in IMAGR) field very small maybe clean several sub-fields simultaneously uv coverage mapping and self-calibration not very stable hopefully simple source structure field-size limitations primary beams (same as connected interferometers) maximal field width: (array size) / (telescope size) ( ) 2 pixels bandwidth smearing, time-averaging smearing wide-field VLBI is a challenge! titlepage introduction contents back forward previous next fullscreen 26

28 VLBI science: objects sensitivity (µjy/beam) not less than other arrays but: beam is much, much smaller surface-brightness sensitivity is poor need bright but small sources high brightness temperature Planck-law: I ν = 2hν3 c 2 1 e hν/(kt ) 1 Rayleigh-Jeans approximation: I ν 2kT ν2 c 2 titlepage introduction contents back forward previous next fullscreen 27

29 Planck and Rayleigh-Jeans titlepage introduction contents back forward previous next fullscreen 28

30 Flux density and brightness temperature Rayleigh-Jeans approximation: I ν 2kT ν2 c 2 flux density S ν per beam: multiply with beam area ( ) 2 λ beam area = c2 L ν 2 L 2 baseline length L S ν 2kT L 2 independent of ν! e.g. L = km, S ν = 1mJy T = K VLBI sensitive mostly to non-thermal processes titlepage introduction contents back forward previous next fullscreen 29

31 VLBI science jets from AGN, microquasars superluminal motion gravitational lenses extragalactic supernovae masers circumstellar megamasers in AGN astrometry geodesy titlepage introduction contents back forward previous next fullscreen 30

32 Some pictures... titlepage introduction contents back forward previous next fullscreen 31

33 Wide-field VLBI at 90 cm [ Lenc et al. (2008) ] titlepage introduction contents back forward previous next fullscreen 32

34 Geodesy titlepage introduction contents back forward previous next fullscreen 33

35 VLBI arrays Very Long Baseline Array (VLBA) 10 identical telescopes of 25 m (USA) full-time VLBI array European VLBI Network (EVN) 20 telescopes (Europe, Asia, South Africa, Arecibo) 3 sessions each year (+ e-vlbi) VLBI Exploration of Radio Astrometry (VERA) 4 stations (Japan) High Sensitivity Array (HSA) VLBA + VLA + Arecibo + Green Bank + Effelsberg Long Baseline Array (LBA) 8 telescopes in Australia global VLBI VLBA + EVN + anything titlepage introduction contents back forward previous next fullscreen 34

36 VLBA titlepage introduction contents back forward previous next fullscreen 35

37 EVN titlepage introduction contents back forward previous next fullscreen 36

38 EVN now (courtesy Richard Porcas) titlepage introduction contents back forward previous next fullscreen 37

39 EVN correlator at JIVE titlepage introduction contents back forward previous next fullscreen 38

40 VERA titlepage introduction contents back forward previous next fullscreen 39

41 LBA titlepage introduction contents back forward previous next fullscreen 40

42 Special developments: Space VLBI VLBI Space Observatory Programme (VSOP) satellite HALCA (Highly Advanced Laboratory for Communications and Astronomy) launched 1997 last contact m antenna 1.6 GHz and 5 GHz VSOP2 is planned titlepage introduction contents back forward previous next fullscreen 41

43 uv coverage with HALCA [ Ulvestad (1999) ] titlepage introduction contents back forward previous next fullscreen 42

44 e-vlbi classical VLBI record on tape/disk ship tapes/disks to correlator correlate later e-vlbi send data directly to correlator high-bandwidth data links ( internet ) advantages of e-vlbi immediate feedback quick turnaround disadvantages of e-vlbi cannot repeat correlation no multiple passes titlepage introduction contents back forward previous next fullscreen 43

45 How to observe choose array, frequency, correlator mode, etc. write proposal deadlines for VLBA, EVN, global: 1 Feb, 1 Jun, 1 Oct special sessions for e-vlbi wait... write the schedule with SCHED wait for the correlated data (less if e-vlbi) calibrate, analyse,... general recommendation: ask the experts! titlepage introduction contents back forward previous next fullscreen 44

46 Long-baseline LOFAR: no standard procedures yet titlepage introduction contents back forward previous next fullscreen 45

47 VLBI aspects of LOFAR sources resolved weak signal less calibrators have to average coherently in time and frequency have to correct for delays ( φ/ ν) have to correct for rates ( φ/ t) need fringe fitting dispersive: ionosphere (τ ν 2 ) non-dispersive: clocks, positions (τ =const) larger ionospheric delays (and rates) larger clock offsets differential Faraday rotation poorer uv coverage titlepage introduction contents back forward previous next fullscreen 46

48 Fringe-fitting for LOFAR either for single subbands ( τ 5µsec) or coherent multi-band ( τ 0.02µsec) beware of multiple peaks in delay/rate produce 2-d delay/rate spectra simultaneously fit for four parameters dispersive/nondispersive delays/rates own simple flagger (based on Gaussian noise statistics) titlepage introduction contents back forward previous next fullscreen 47

49 Single-band, Ef-NL, 3C196, 20 August 2009 first long-baseline-fringes! titlepage introduction contents back forward previous next fullscreen 48

50 Delays and phases 5 subbands continuous mod phase [full turns] freq [MHz] titlepage introduction contents back forward previous next fullscreen 49

51 do not fit phases directly Delay fitting only know phase modulo 2π data are noisy equivalent (but better!): maximise the corrected signal measured and original visibility V (ν) = e 2πiντ(ν) V 0 (ν) hope that V 0 (ν) = const and correct for delay find maximum of dν e 2πiντ(ν) V (ν) 2 this is Fourier transform if τ = const titlepage introduction contents back forward previous next fullscreen 50

52 Multi-band delay fitting delay almost constant within subbands apply FFT for all subbands combine the results incoherently combine the results coherently f i (τ i ) = F [τ] = i i dν e 2πi(ν ν i)τ i V (ν) e 2πiν iτ(ν i ) f i ( τ(νi ) ) with coarse FFT on fine grid, interpolation τ(ν) arbitrary function of frequency (non-/dispersive) titlepage introduction contents back forward previous next fullscreen 51

53 Include fringe rates have to integrate in time to increase S/N take into account rates (time-derivatives) do not use phase rates but delay rates r = τ t f i (τ i,r i ) = dispersive/non-dispersive F [τ,r] = i i dν e 2πi(ν ν i)τ i e 2πiν iτ(ν i ) f i ( τ(νi ),r(ν i ) ) dt e 2πi(t t 0)r i V (ν,t) all phase rates are frequency-dependent titlepage introduction contents back forward previous next fullscreen 52

54 Interfering sources (observations of 3C48) titlepage introduction contents back forward previous next fullscreen 53

55 First Tautenburg fringes: delay and phase rates titlepage introduction contents back forward previous next fullscreen 54

56 Clock offsets / delays station clocks (Rubidium standard + GPS) should be accurate to 20 ns some Dutch stations have offsets 90 ns Effelsberg typically 1 µs Tautenburg once had 18µs makes fringe-fitting harder reason unclear clock offsets or differential delays? are the offsets constant? titlepage introduction contents back forward previous next fullscreen 55

57 Faraday rotation (and swapped polarisations) titlepage introduction contents back forward previous next fullscreen 56

58 Converting XX/XY/YX/YY to RR/RL/LR/LL titlepage introduction contents back forward previous next fullscreen 57

59 Long-baseline LOFAR imaging fundamental problem sparse uv coverage practical problems (not implemented in pipeline) fringe-fitting correct clock-offsets Faraday rotation (and swapped polarisations) current solution : own ad hoc software do all this + flag + calculate weights convert to uvfits this is no user software! then continue with AIPS, difmap, CASA,... titlepage introduction contents back forward previous next fullscreen 58

60 First LBA long-baseline map: some details 3C196, LBA, 31 / 160 subbands, / MHz (ripple!) bandwidth 6 MHz / 48 MHz D h on 12/13 Feb NL + 3 DE stations (Effelsberg, Unterweilenbach, Tautenburg) corrected for 1 µsec and 17 µsec constant delays RR and LL from XX/XY/YX/YY using geometric model (self-)calibrated and imaged LL/RR in difmap MFS with/without spectral index correction titlepage introduction contents back forward previous next fullscreen 59

61 UV coverage with long and short baselines titlepage introduction contents back forward previous next fullscreen 60

62 MTRLI (MERLIN) observations of 3C196 at 408 MHz [ Lonsdale & Morison (1980) ] titlepage introduction contents back forward previous next fullscreen 61

63 LOFAR maps: short and long baselines NL only, beam NL+DE, beam titlepage introduction contents back forward previous next fullscreen 62

64 LOFAR LBA vs. MERLIN 408 MHz [ Wucknitz + Lonsdale & Morison (1980) ] titlepage introduction contents back forward previous next fullscreen 63

65 News & Views, Nature Physics, July 2010 titlepage introduction contents back forward previous next fullscreen 64

66 HBA observations of 3C196: some details 3C196, HBA, 120 / 244 subbands, MHz bandwidth 24 MHz L h, 22nd May NL + 2 DE stations (Effelsberg, Tautenburg) corrected for 8 µsec in superterp,... (self-)calibrated and imaged YY in difmap phase jumps, rates, inconsistent delays (in freq) low S/N in German stations most of the time imaging very tough, details not reliable yet titlepage introduction contents back forward previous next fullscreen 65

67 HBA observations: uv coverage, dirty beam beam size titlepage introduction contents back forward previous next fullscreen 66

68 LBA + HBA images of 3C196 titlepage introduction contents back forward previous next fullscreen 67

69 Your task for tutorial / exercises not: run my software on original data but: use uvfits output flagged converted to circular polarisations delay-corrected averaged organised into IFs with several channels limited fringe-fitting in AIPS imaging/self-calibration attempts with difmap titlepage introduction contents back forward previous next fullscreen 68

70 Contents 1 VLBI techniques 2 VLBI techniques and LOFAR 3 Need for long baselines 4 Early developments (50s/60s) 5 The need for longer baselines 6 Very Long Baseline Interferometry 7 Connected interferometer VLBI 8 Connected VLBI : more details 9 The role of the local clock 10 The correlation 11 VLBA station system 12 Sampling and digitisation 13 Recording systems 14 Stability of local oscillators 15 Geometric delays 16 Delays, phases, rates 17 Delays: connected vs. VLBI titlepage introduction contents back forward previous next fullscreen 69

71 18 Delay model 19 Calibration of VLBI data 20 Amplitude calibration 21 Practical amplitude calibration in AIPS 22 Phase-cal (a.k.a. pulse calibration) 23 The need for fringe-fitting 24 Linear approach for residual phases 25 Practical fringe-fitting with AIPS 26 Other issues 27 VLBI science: objects 28 Planck and Rayleigh-Jeans 29 Flux density and brightness temperature 30 VLBI science 31 Some pictures Wide-field VLBI at 90 cm 33 Geodesy 34 VLBI arrays 35 VLBA 36 EVN 37 EVN now (courtesy Richard Porcas) 38 EVN correlator at JIVE titlepage introduction contents back forward previous next fullscreen 70

72 39 VERA 40 LBA 41 Special developments: Space VLBI 42 uv coverage with HALCA 43 e-vlbi 44 How to observe 45 Long-baseline LOFAR: no standard procedures yet 46 VLBI aspects of LOFAR 47 Fringe-fitting for LOFAR 48 Single-band, Ef-NL, 3C196, 20 August 2009, first long-baseline-fringes! 49 Delays and phases 50 Delay fitting 51 Multi-band delay fitting 52 Include fringe rates 53 Interfering sources (observations of 3C48) 54 First Tautenburg fringes: delay and phase rates 55 Clock offsets / delays 56 Faraday rotation (and swapped polarisations) 57 Converting XX/XY/YX/YY to RR/RL/LR/LL 58 Long-baseline LOFAR imaging 59 First LBA long-baseline map: some details titlepage introduction contents back forward previous next fullscreen 71

73 60 UV coverage with long and short baselines 61 MTRLI (MERLIN) observations of 3C196 at 408 MHz 62 LOFAR maps: short and long baselines 63 LOFAR LBA vs. MERLIN 408 MHz 64 News & Views, Nature Physics, July HBA observations of 3C196: some details 66 HBA observations: uv coverage, dirty beam 67 LBA + HBA images of 3C Your task for tutorial / exercises 69 Contents titlepage introduction contents back forward previous next fullscreen 72