Fundamentals of radio astronomy

Transcription

1 Fundamentals of radio astronomy Sean Dougherty National Research Council Herzberg Institute for Astrophysics

2 Apologies up front! Broad topic - a lot of ground to cover (the first understatement of the day!) Touch on a lot of material Attempt to introduce concepts - derivations are largely missing - ideas addressed with figures & handwaving Borrowed a lot of material from other sources (via the web) - NRAO and ATNF summer schools Many excellent references: Kraus: Radio Astronomy Rohlfs & Wilson: Tools of Radio Astronomy Thompson, Moran & Swenson: Interferometry & Synthesis in Radio Astronomy Stanimirovic, Altschuler, Goldsmith & Salter: Single-dish radio astronomy: techniques & applications More apologies experts in the room those who attended the mm summer school, Victoria, 2006.

3 From the wonders of well sampled data. 27-image mosaic of the Cygnus region from DRAO: thermal (blue) non-thermal (red)

4 Some basic concepts (just a reminder)

5 Basic Concepts EM power in bandwidth δν from solid angle δω intercepted by surface δα is: Defines surface brightness I ν (W m -2 Hz -1 sr -1 ) ( aka intensity/specific intensity) Flux density S v (W m -2 Hz -1 ) integrate brightness over solid angle of source Convenient unit - the Jansky 1Jy = W m -2 Hz -1 = erg cm -2 s -1 Hz -1 Note:

6 Surface Brightness In general surface brightness is position dependent ie. I ν =I ν (θ,φ) i.e. surface brightness is described by a temperature distribution Back to flux: In general, a radio telescope maps the temperature distribution of the sky

7 Brightness Temperature Many astronomical sources DO NOT emit as blackbodies! However. Brightness temperature (T B ) of a source is defined as the temperature of a blackbody with the same surface brightness of a source at a given frequency. This implies that the flux density

8 What are we detecting and how?

9 Telescopes tools of the trade Nearly all we know of our universe is through observations of electromagnetic radiation. The purpose of an astronomical telescope is to determine the characteristics of this emission: Angular distribution Frequency distribution Polarization characteristics Temporal characteristics Telescopes imperfect devices their efficient use requires an understanding of their capabilities and limitations.

10 Radio telescopes Radio regime spans a vast range of wavelength Very different instruments to span this range λ > 1 m (=300 MHz) wire antennas

11 Radio instrumentation Radio regime spans a vast range of wavelength Very different instruments to span this range λ > 1 m (=300 MHz) wire antennas λ < 1 m -- reflector antennas λ ~ 1 m -- hybrid antennas (wire reflectors or feeds) Single telescopes Multi-elements arrays (interferometers)

12 Radio telescope systems Radio telescopes are devices for generating an electrical signal from incoming EM radiation Astrophysical radio signals are typically weak compared to background noise Telescope area 10,000 m 2 ; Bandwidth = 50 MHz; Flux = 1 mjy Total energy received in 1000 yrs = 1 erg = 10-7 Joules ~ few percent of energy of a falling snowflake! Radio telescopes have to be: highly directional (aka high gain), dependent on antenna beam/power pattern Extract energy from the incoming wavefront Antenna size Antenna Efficiency Receivers - convert EM signal to a voltage - amplify the noise Back end (correlator/power detector) - to detect the signal - signal that is buried in the noise

13 What does a radio telescope detect? Recall : Telescope of effective area A e receives power P rec per unit frequency from an unpolarized source (only sensitive to one mode of polarization) Telescope is sensitive to radiation from more than one direction with relative sensitivity given by the normalized antenna pattern P N (θ,ϕ)

14 Antenna temperature Nyquist theorem (1929): Power received by the antenna: Antenna temperature is what is observed by the radio telescope A convolution of sky brightness with the beam pattern It is an inversion problem to determine the source temperature.

15 Antenna temperature: some special cases For a point source ie Ω beam >> Ω source : P N (θ, ϕ)~1 => known point source flux density S ν, measure T A to get A e Gives a measure of reflector performance e.g. Arecibo 300m 0.07Jy/K JCMT 15m ~25 Jy/K

16 Antenna temperature: some special cases For an extended source ie Ω beam ~ Ω source. Assume T (θ, ϕ)=constant over the beam Antenna theorem : Beam filling factor For extended sources,must know the power pattern well

17 Noise in the machine! Unfortunately, the telescope system contributes noise to the source signal detected by the telescope i.e. P out = P A + P sys => T out = T A + T sys T sys represents the noise added by the system = T bg + T sky + T spill + T loss + T cal + T rx T bg = microwave and galactic background (3K, except below 1GHz) T sky = atmospheric emission (increases with frequency--dominant in mm) T spill = ground radiation (via sidelobes) and spillover (telescope design) T loss = losses in the feed and signal transmission system (design) T cal = injected calibrator signal (usually small) T rx = receiver system (often dominates at cm a design challenge) Note that T bg,t sky,t spill vary with position on the sky T sky also is time variable

18 System Noise cm regime T rx is the challenge! VLA =>T 1 needs to be small λcm T bg T sky T spill T loss T cal T rx T sys EVLA

19 Radio Frequency Interference (RFI) VLA GHz

20 RFI mitigation techniques 101 No digital switching devices in the telescope beam! No transmitters in the telescope beam!

21 Radiometry equation How to detect power from the source T A in the presence of T sys? The signal is correlated from one sample to the next - the noise is not. For a bandwidth Δν, samples taken less than Δt=1/Δν are not independent (another Nyquist theorem!) Time τ contains independent samples Gaussian noise : error for N samples is Radiometer equation

22 Flux sensitivity & antenna performance For a point source, flux density S ν recall Minimum detectable flux A e /T sys is the measure of the performance of a radio telescope

23 Flux sensitivity & antenna performance II cm Arecibo D (m) 300 T sys 31 A e (m 2 ) SEFD (Jy) 3.9 GBT Bonn VLBA PT Want A e big, T sys small Onsala

24 The essential qualities of a radio telescope Lots of effective area High antenna efficiency Good surface rms Low system temperature Low receiver temperature Low noise in the 1 st stage (LNA low noise amplifier) At mm, T sky is the challenge => low water content <1GHz, T bg is the challenge All this improves Receiver bandwidth drives down minimum detected flux Good pointing most especially at mm/sub-mm.

25 The quest for resolution

26 The quest for resolution 1 21cm requires D ~ 50 km! Single dishes: physical limit to antenna diameter is ~ 100m Need to synthesize larger aperture telescopes using combinations of smaller telescopes. Earth-rotation aperture synthesis technique developed in the 1950s in England and Australia Nobel Prize for Martin Ryle (Cambridge)

27 Output for a filled aperture Imagine the aperture to be subdivided into N smaller elementary areas; the voltage, V(t), at the output is the sum of the contributions V i (t) from the N individual aperture elements:

28 Aperture synthesis: basic concept Power measured by a receiver average of the square of the output voltage: Any measurement with the large filled-aperture telescope can be written as a sum, in which each term depends on contributions from only two of the N aperture elements Each term V i V k can be measured with two small antennas, if we place them at locations i and k and measure the average product of their output voltages with a correlation (multiplying) receiver Adding together all the N(N-1)/2 terms effectively synthesizes one measurement taken with a large filled-aperture telescope Can synthesize apertures much larger than can be constructed as a filled aperture higher resolution

29 The Monochromatic 2-element Interferometer Assume: a small (but finite) frequency width quasi-monochromatic. Assume: source is far-field ie. plane parallel waves at the interferometer Consider radiation from direction s. s s multiply average b X An antenna

30 The Cosine Correlator Response To determine the dependence of the response over an extended object, integrate over solid angle. Assume: no spatial coherence between emission from different directions: This expression links what we want the source brightness on the sky I ν (s) to something we can measure - R C, the interferometer response. Correlator output is sky brightness modulated by a fringe pattern with frequency ~ b/λ

31 Very briefly..odd and Even Functions R c, is insufficient only sensitive to the even part of the brightness, I E (s). Any real function, I(x,y), can be expressed as the sum of two real functions which have specific symmetries: I I E = + I O An even part: I E (x,y) = (I(x,y) + I(-x,-y))/2 = I E (-x,-y) An odd part: I O (x,y) = (I(x,y) I(-x,-y))/2 = -I O (-x,-y)

32 Recovering the Odd Part: The SIN Correlator The integration of the cosine response, R c, over the source brightness is sensitive to only the even part of the brightness: since the integral of an odd function (I O ) with an even function (cos x) is zero. To recover the odd part of the intensity, I O, we need an odd coherence pattern. Let us replace the cos with sin in the integral: since the integral of an even times an odd function is zero.

33 Define the Complex Visibility We now DEFINE the visibility, V, to be the complex sum of the two independent correlator outputs: where This gives a beautiful and useful Fourier relationship between the source brightness, and the response of an interferometer: This expression can be inverted to recover I(s) from V(b).

34 Comments on the Visibility Introducing a useful geometry: The visibility is a function of the source structure and the interferometer baseline The visibility is not a function of the absolute position of the telescopes (provided the emission is time-invariant, and is located in the far field) There is a unique relation between any source brightness distribution and the visibility function An observation of a source with a given baseline provides one measure of the visibility With many measurements of the visibility as a function of baseline, we can obtain an estimate of I(l,m)

35 Visibility and Sky Brightness

36 Visibility and Sky Brightness

37 Visibilities and the pictures we want! To recover I (l,m), just measure the visibilities V(u,v) for all possible baselines and then Fourier Transform Sounds easy --- but there are a few complications!

38 Arrays SAMPLE the Sky brightness Fourier Transform! An array of N antennas, contains N(N-1)/2 INTERFEROMETER pairs. Each pair has a different baseline length Different baselines sample simultaneously different spatial frequencies As the Earth rotates, the orientation of the baselines relative to the sky changes Earth rotation synthesis samples different spatial frequencies fills in the (u,v) plane The Fourier Transform of the sampled visibilities = DIRTY image BUT. An array does NOT sample every spatial frequency!!! More antennas + orientations => more (u,v) samples => better images! THE challenge for interferometer arrays

39 Impact of NOT sampling everywhere! Source(I) Ideal Visibilities(V) Model image(i ) FT FT -1 Sampled Visibilities Image

40 Formal Description of the DIRTY image Interferometer samples Fourier domain Obtain sampled visibility The DIRTY image is defined as Convolution theorem gives where Synthesized/ dirty beam (PSF) Fourier transform of sampled visibilities yields the true sky brightness convolved with the point spread function (the dirty image is the true image convolved with the dirty beam )

41 The DIRTY image Sampled Visibility Sampling function True visibility = x = * Dirty Image Beam True Image

42 An E-W array building an image Ideal visibilities (Fourier Plane) 7 antennas 21 interferometer pairs Dirty Image 1D array all baselines have same orientation Need to observe for at least 12 hours best to observe for 12x12 hrs Model Image

43 Building an image at DRAO 2 hrs

44 Building an image at DRAO 4 hrs

45 Building an image at DRAO 6 hrs

46 Building an image at DRAO 8 hrs

47 Building an image at DRAO 10 hrs

48 Building an image at DRAO 12 hrs

49 Building an image at DRAO After every 12 hrs synthesis move moveable antennas Build up all possible spacings between the shortest and the longest Why? To provide as much coverage of the Fourier plane as possible MAKES A BETTER BEAM hence BETTER DIRTY IMAGES

50 Building an image at DRAO 2 days

51 Building an image at DRAO 3 days

52 Building an image at DRAO 4 days

53 Building an image at DRAO 5 days

54 Building an image at DRAO 6 days

55 Building an image at DRAO 7 days

56 Building an image at DRAO 8 days

57 Building an image at DRAO 9 days

58 Building an image at DRAO 10 days

59 Building an image at DRAO 11 days

60 Building an image at DRAO 12 days

61 Comparison of Dirty images 12 hrs 12 days Better DIRTY images by better sampling of the Fourier Plane

62 The VLA building an image Dirty Image 27 antennas 351 interferometer pairs 2D array many baseline orientations Excellent instantaneous sampling of the Fourier plane Up to 36 km baselines samples higher spatial frequencies 12 hrs 4 hrs

63 From DIRTY to CLEAN images DIRTY image = Dirty BEAM * True image Need to deconvolve the beam from the DIRTY image This produces the CLEAN image - an attempt at deriving the true image Essentially attempting to fill-in the visibilities that were not sampled THIS IS WHY WE NEED TO OBSERVE AS MANY VISIBILITIES AS POSSIBLE IN THE FIRST PLACE! A number of techniques available in radio astronomy CLEAN ( in a range of brands ) is the most commonly used MAXIMUM ENTROPY SMERF developed by Rob Reid

64 CLEANing DRAO images DIRTY image Already very good because well sampled visibilities

65 CLEANing DRAO images CLEAN Remove effects of the beam

66 CLEANing DRAO images Final image (after calibration tweaks)

67 From the wonders of well sampled data. 27-image mosaic of the Cygnus region from DRAO Questions?

68 Deconvolution example DIRTY image CLEAN image Model image CLEAN image Model image SMERF image Simulated VLA observation

69 Beam Pattern - origin An antenna s response is a result of incoherent phase summation at the focus. First null occurs at the angle where the extra distance for a wave at center of antenna is in anti-phase with that from edge. D sin θ = λ/2 θ ~ λ/d On-axis incidence Off-axis incidence The larger D, the higher resolution D ~ 100 m e.g. 2 arcmins Larger D => interferometers

70 Antenna power pattern Defines telescope resolution Power pattern" P(θ,ϕ) of a telescope is the square of the complex far-field voltage pattern F(l,m) i.e. F(l,m) 2 = F(l,m)F * (l,m). (diffraction theory -- voltage pattern F(l,m) is the FT of the aperture distribution )

71 Beam sizes D θ GBT 100 m 2 cm 5GHz VLA dish VLA 25 m 36 km MERLIN 215 km 0.06 VLBA 8611 km D θ ( ) mm 345GHz AST/RO JCMT 1.7m 15m LMT 50m 4.5 SMA 508 m 0.35 ALMA 15 km Small beams need good and stable pointing mm λ

72 Surface Brightness of a Black body Surface brightness of a black body defined by the Planck Function Radiation emitted at ν depends only on ν and the blackbody temp T Special case Rayleigh-Jeans limit Note: Breaks down at low T and/or ν ~ 100 GHz ie. mm/submm range

73 Some 2D FT pairs Fourier Transform image (visibility) contains all information of original image Image Visibility amp

74 Some 2D FT pairs Image Visibility amp orientations are orthogonal in the (x,y) and (u,v) planes narrow features transform to wide features (and vice-versa) sharp edges result in many high spatial frequencies

75 2D Fourier Transform Pairs I(l,m) Amp{V(u,v)} structure on many scales I(l,m) is real, but V(u,v) is complex Real and Imaginary Amplitude and Phase Amplitude tells how much of a certain frequency component, Phase tells where V(-u,-v) = V*(u,v) where * is complex conjugation (Hermitian) V(u=0,v=0) = total flux

76 Schematic Illustration of Correlator response The correlator can be thought of casting a sinusoidal fringe pattern onto the sky. The correlator multiplies the source brightness by this wave pattern, and integrates (adds) the result over the sky. Orientation set by baseline geometry. Fringe separation set by baseline length and wavelength. λ/b rad. Source brightness Fringe Sign

77 Brightness Temperature Examples: Blank Sky 2.73 K Big Bang Orion 300 GHz K Warm molecular cloud Orion 1 GHz 10 4 K Thermal Quasar K Synchrotron Quiet 300 MHz 5x10 5 K Synchrotron 30 GHz 5800 K 30GHz T~5800K => Thermal 300MHz T~10 6 K => Non-thermal emission

78 Aperture Synthesis Telescopes ATCA (e)vla CARMA (=OVRO+BIMA) DRAO SMA