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Basics of mm interferometry Turku Summer School – June 2009 Sébastien Muller Nordic ARC Onsala Space Observatory, Sweden.

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Presentation on theme: "Basics of mm interferometry Turku Summer School – June 2009 Sébastien Muller Nordic ARC Onsala Space Observatory, Sweden."— Presentation transcript:

1 Basics of mm interferometry Turku Summer School – June 2009 Sébastien Muller Nordic ARC Onsala Space Observatory, Sweden

2 Interests of mm radioastronomy -> Cold Universe Giant Molecular Clouds -> COLD and DENSE phase Site of the STAR FORMATION -> Continuum emission of cold dust -> Molecular transitions - Diagnostics of the gas properties (temperature, density) - Kinematics (outflows, rotation)

3 Interests of CO Molecular gas  H 2 But H 2 symmetric -> electric dipolar momentum is 0 Most abundant molecule after H 2 is CO [CO/H 2 ] ~ First rotational transitions of CO in the mm GHz GHz GHz E J=1,2,3 = 6, 17, 33 K Easily excited CO is difficult to destroy high ionization potential (14eV) and dissociation energy (11 eV) Where the atmosphere is relatively transparent

4 Handy formulae - HI line emission: N(HI) (cm -2 ) =  T B dv (K km/s) - Molecular line emission: N(H 2 ) (cm -2 ) = X  T CO dv (K km/s) X = Or use optically thin lines ( 13 CO, C 18 O) - Visual extinction: N(HI)+2N (H 2 ) (cm -2 ) = A V (mag)

5 Needs of angular resolution 10m65’’32’’22’’ 30m22’’11’’7’’ 100m7’’3’’2’’ 1000m0.6’’0.3’’0.2’’ Resolution  /D (theory of diffraction)

6 Would need very large single-dish antennas BUT - Surface accuracy (few 10s of microns !) -> technically difficult and expensive ! - Small field of view (1 pixel) - Pointing accuracy (fraction of the beam) Let’s fill in a large collecting area with small antennas And combine the signal they receive -> Interferometry (Aperture synthesis)

7 Mm antennas need Good surface accuracy D APEX 12m<20 microns IRAM-30m30m55 microns (GBT 100m300 microns) PdBI 15m<50 microns SMA 6m<20 microns ALMA 12m <25 microns

8 Holography measurement

9 - uv positions are the projection of the baseline vectors B ij as seen from the source. -The distances  (u 2 + v 2 ) are refered to as spatial frequencies - Interferometers can access the spatial frequencies ONLY between B min and B max, the shortest and longest projected baselines respectively. geometrical time delay source baseline antenna uv plane Baseline, uv plane and spatial frequency

10 V(u,v) =  P(x,y) I(x,y) exp –i2  (ux+vy) dxdy = FT { P I } Interferometers measure VISIBILITIES V But astronomers want the SKY BRIGHTNESS DISTRIBUTION of the source : I(x,y) P(x,y) is the PRIMARY BEAM of the antennas - P has a finite support, so the field of view is limited - distorded source informations - P is in principle known ie. antenna characteristic

11 I(x,y) P(x,y) =  V(u,v) exp i2  (ux+vy) dudv Well, looks easy … BUT ! Interferometers have an irregular and limited uv sampling : - high spatial frequency (limit the resolution) - low spatial frequency (problem with wide field imaging) Incomplete sampling, non respect of the Nyquist’s criterion = LOSS of informations ! The direct deconvolution is not possible Need to use some smart algorithms (e.g. CLEAN)

12 Let’s take an easy example: 1D P = 1 I(x) = Dirac function: S  (x-x 0 ) S = constant V(u) = FT(I) = Sexp(-i2  ux 0 )-> this is a complex value x0x0 x I u S Amplitude u Phase Slope = -2  x 0

13 Illustration : dirty beam, dirty image and deconvolved (clean) image resulting in some interferometric observations of a source model

14 Atmosphere « The atmosphere is the worst part of an astronomical instrument » - emits thermally, thus add noise - absorbs incoming radiation - is turbulent ! (seeing) Changes in refractive index introduce phase delay Phase noise -> DECORRELATION (more on long baselines) exp(-   2 /2) - Main enemy is water vapor ( Scale height ~2 km)

15 O2O2 H2OH2O

16 Calibration V obs = G V true + N V obs = observed visibilities V true = true visibilies = FT(sky) G = (complex) gains usually can be decomposed into antenna-based terms: G = G ij = G i x G j * N = noise After calibration: V corr = G’ –1 V obs

17 Calibration - Frequency-dependent response of the system Bandpass calibration -> Bright continuum source - Time-dependent response of the system Gain (phase and amplitude) -> Nearby quasars - Absolute flux scale calibration -> Flux calibrator

18 Bandpass calibration

19 Phase calibration

20 Amplitude calibration

21 From SMA Observer Center Tools

22 From SMA Observer Center Tools

23 From SMA Observer Center Tools

24 Quasars usually variable ! -> need reliable flux calibrator From SMA Observer Center Tools

25 Preparing a proposal 0) Search in Archives SMA: PdBI: ALMA … 1) Science justifications -> Model(s) to interpret the data 2) Technical feasibility: - Array configuration(s) (angular resolution, goals) - Sensitivity use Time Estimator ! Point source sensitivity Brightness sensitivity (extended sources)

26 Array configuration CompactDetection Mapping of extended regions IntermediateMapping ExtendedHigh angular resolution mapping Astrometry Very-extendedSize measurements Astrometry

27 PdBI 1 Jy = W m -2 Hz -1

28 For extended source: Take into account the synthesized beam -> brightness sensitivity T (K) = 2ln2c 2 /  k 2 x Flux density/  maj  min Use Time Estimator !

29 Short spacings V(u,v) =  P(x,y) I(x,y) exp –i2  (ux+vy) dxdy V(0,0) =  P(x,y) I(x,y) dxdy (Forget P), this is the total flux of the source And it is NOT measured by an interferometer ! -> Problem for extended sources !!! -> Try to fill in the short spacings

30 Courtesy J. Pety

31

32 Advantages of interferometers - High angular resolution - Large collecting area - Flatter baselines - Astrometry - Can filter out extended emission - Large field of view with independent pixels - Flexible angular resolution (different configuration)

33 Disadvantages of interferometers - Require stable atmosphere - High altitude and ~flat site (usually difficult to access) - Lots of receivers to do - Complex correlator - Can filter out extended emission - Need time and different configuration to fill in the uv-plane

34 Mm interferometry: summary - Essential to study the Cold Universe (SF) - Astrophysics: temperature, density, kinematics … - Robust technique High angular resolution High spectral/velocity resolution

35

36 Let’s define - Sampling function S(u,v) = 1 at (u,v) points where visibilities are measured = 0 elsewhere - Weighting function W(u,v) = weights of the visibilities (arbitrary) We get : I obs (x,y) =  V(u,v) S(u,v) W(u,v) exp i2  (ux+vy) dudv

37 Due to the Fourier Transform properties : FT { A B } = FT { A } ** FT { B } Can be rewritten as : where I obs (x,y) =  V(u,v) S(u,v) W(u,v) exp i2  (ux+vy) dudv I obs (x,y) = P(x,y) I(x,y) ** D(x,y) D(x,y) =  S(u,v) W(u,v) exp i2  (ux+vy) dudv = FT { S W }

38 If I sou =  (x,y) = Point source then I obs (x,y) = D(x,y) That is : D is the image of a point source as seen by the interferometer. ~ Point Spread Function I obs (x,y) = P(x,y) I(x,y) ** D(x,y)

39 D(x,y) = FT { S W } D(x,y) is called DIRTY BEAM This dirty beam depends on : - the uv sampling (uv coverage) S - the weighting function W Note that :  D(x,y) dxdy = 0because S(0,0) = 0 And that : D(0,0) > 0because SW > 0 The dirty beam presents a positive peak at the center, surrounded by a complex pattern of positive and negative sidelobes, which depends on the uv coverage and the weighting function.

40 I obs (x,y) is called DIRTY IMAGE We want I obs (x,y) I(x,y) This includes the two key issues for imaging : - Fourier Transform (to obtain I obs from V and S) - Deconvolution (to obtain I from I obs ) I obs (x,y) = P(x,y) I(x,y) ** D(x,y)


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