1Out of the opticalTransmission of the atmosphereRayleigh scattering water vapor IR bandsPlasma frequency of ionosphere 10-15 Mhz, \ atmosphereopaque at lower frequenciesRadio band (1cm - 100m) was the first non-optical band explored2History of Radio AstronomyKarl Jansky (Bell labs) detectedinterence at 21 MHz from MilkyWay (NY Times May 5, 1933)Extraterrestrial emission (the Sun)commonly detected during WWII (Hey)WWII radar devlopment stimulated thefieldJansky 1933 First dish, Reber 1937 Sky map at 12° resolution3Radio astronomy potted historyCyg A: Hey et al. (1946)Sydney 1948: first interferometer(8 arcmin using sea reflection)Cass A: Ryle & Smith (1948)HI emission: Ewen & Purcell (1951)M32: Brown & Hazard (1951)3C 273: Ryle/Hazard/Schmidt 19633K CMB: Penzias & Wilson (1964)Pulsars: Bell & Hewitt (1968)4Simple radio recieverSuperheterodyne detectiontiwtwwitiwtiwtiwbeebaaebeae221121))(1()(+-+=+-aba+bRadio signal from aerial mixed with carrier frequency,signal at beat frequencey (Intermediate Frequency) and isfiltered and amplified. Tuning = changing the carrierfrequency.5Detection of wavesConsider a random phasesuperposition of N waves at thesame frequency4222*xxxfNENEEeEkik>=D<fi=><fi=ÂEnergy density in the fieldAverage fluction thereof(e.g. M. Longair, Theoretical Concepts of Physics, p242-258)The fluctuations in the field are of the same magnitude asthe energy density of the radiation itselfe.g. electric field of EM waveNumber of modes in a box:uupVdcdN238=KT permodekTcu238)(upu=classicalBB formula1-kThehuuper mode18)(33-=kThehcuuupuQuantumBB formula6Johnson NoisePower delivered:(Noise signal measured by a receiver in thermalequilibrium)In 1D transmission line at temperature T):)(1kThkTehWkTh<<Æ-=uuuWatts/HzKnowing <DE 2> = <E 2> in each mode:The noise power measured by a receiver integratingfor a time t with a bandwidth Du :( )2/1tWWuD=DNumber ofindependentsamplesSo for a radio receiver (hu << kT):( )2/1tkTWsysuD=DThermal equilibrium+ number wave modesRadio receiver sensitivity usually characterized by Tsys=W/k7So what happened to photons?Full quantum treatment (Einstein1909). Outline:kSeW/=Boltzmamn relation probability (W)/entropyEnergy fluctuations Dei in cells has normaldistribution:eesseddSTSkWi=∂∂=˙˙˚˘ÍÍÎÈDµÂ1/where)(21exp22222these combine to derive:˜˜¯ˆÁÁËÊ+=˜˜¯ˆÁÁËÊ+=modesphotons2322118NNVdchupueuesuueduV )(where =optical regime (Wien) radio regime (Rayleigh-Jeans)8Waves vs photons – Example1mJy radio source, u = Du =1GhzTelescope = 10m2, Receivertemperature = 1K, integration time= 104 secnegligible04.0 Æ=kThuSource: 10-28 W/HzNoise power = = 3¥10-30 W/HzS/N = 32(c.f. photons : 1/Np = 10-9)( )2/1tkTWuD=D9Photon/wave crossoverhu=kTT=100Ku = 2000 Ghz l=144 mmT=10Ku = 200 Ghz l=1.4 mmT=1Ku = 20 Ghz l=1.4 cm10A radio telescope ‘antenna’Diffraction limit:305m dish at21cmfi 2.4 arcminParabolicreflectorreceiver feedhornDescribed by antennapatterns.Jargon: ‘main beam’ &side lobes (oftensuppressed by feedhorn)Arecibo observatory11BrightnessBrightness B(q,f ) is energy received from a source perm2 of collecting area and per steradian on the sky atposition q,fFor a BLACKBODY:regime Jeans-Rayleighin 212232luukTehcBkTh=-=i.e. pure f(T,l). Hence we can relate all surfaces brightnessmeasurements to the temperature of an equivalent blackbody.Power/unit bandwidth (at frequency u) received by a flat collecting plate of area A: Watts/Hz:s Unitcos),(ÚÚWW= dBAWqfq12Antennae DefinitionsNormalized antennapattern Pn(q,f )(max = 1) † Received power W =12AeB(q,f)Pn(q,f) dWWÚÚ Extended source : Size >> beam of brightness temperature TBW ª12B AeWA=kTBl2AeWAAntenna theorem : AeWA=l2 \W = kTB Turn this round and define antenna temp. TA= W /kCompact source : write SA= B(q,f)Pn(q,f) dWWÚÚ=2kTBl2WSW = kTA=12AeSA=kTBl2AeWS_ frompolarisationEXACT result. Can see thisis roughly the same as q =l/D (diffraction limit)Definitionof TB & WSeAAAkTS2=source) (extendedsource)(compact BAASBATTTT=WW=fiAntenna Temperature,brightness temperateand measured powerRadio astronomerslike to relateeverything totemperature!13Characterising radio telescopesWrite:Johnson noise:( )minsysTktkTW D=D=D2/1ueminminATkSD=D2Let’s us define a sensitivity: kASTeminmin2=DDe.g. the Arecibo 1.28-1.50 Ghz receiverhas a ‘sensitivity of 12 K/Jy’.\ Ae=33120 m2 (≡ 205m dish)The ‘system temperature is 30 K’, so ina 100s over the full 0.22 Ghz band wecan detect 3DTmin = 0.2 mK, or 3DSmin = 0.02 mJy14Recall: the Fourier TransformSpectrographDifference in distance x, phase difference f =2p x/lIntensityIs Fourier Transform of Spectrum f(n)\ Can be be inverted to give the spectrum (at each pointon the focal plane!)Ú+=nnpndcxfxI )]/2cos(1)[(2)(15Phase difference between twotelescopesqI(f)( )[ ]( )[ ]Ú+=+=+=qqupqqqupqfdcxBxI:extent) angular (source over integrate time ThiscxBbIsin)/2(cos1)(2)(sin)/2(cos1)(2)cos1(22fibebIntensity vs separation is FT of the source brightness distribution (all at same fixed observed frequency)FT pair variables are sinq, x (c.f. u, x in FTS)16Some Fourier theoremsÚÚ•+•-+••--==dkekHxhdxexhkHikxikxpp22)()()()(Basictransforms-a/2 +a/2h(x)= top hat H(k) = x -1/a +1/akÚ+--fi2/2/2aaikxdxepÚÚÚÚ-=¢¢-¢=¢¢-¢¤*dxexhxgkdkkHkGdkekHkGxd)xh(x)xg(eikHkGhg:theorem nConvolutioikxikxpp22)()()()(&)()(..)()(ÚÚ== dkkHdxxh PowerTotal:Theorem sParseval'22)()(( )kkappsin17Diffraction limitxkikxikxiexIgives kk( sourcepointdxexIBkwheredkeBxIoffset zero ignore & small):simplicityWrite for 02022)())()()()((sinpppdqlqqqqq=-====ÚÚ--D/2 D/2( ))()(sin)(: baseline finiteby truncatedIf002/2/)(20kkkkDdxekBDDDxkkiobs--==Ú+---pppB(k)obs is a sinc function with first zero at k=1/D, i.e.Dq =l /D fi Rayleigh criteria for diffraction limit (in1D)scan -1/D +1/Dkk0fringesxNOTE: k ≠ wavenumber of light!! (c.f. FTS k=1/l)18General arrayA(x):( )( )˙˚˘ÍÎÈ*=*==Ú-dkNdkB theorem nconvolutioby FT(A(x)))xIFT(dxexAxIB:array Generaltruexkiobsppqqpsinsin)()()()()(2N antennae, spacing dNd = DÂ=-=NmmdxxA1)()(dk=q/lDq = l / ddq = l / DAngular Resolution is set by the maximum baseline.Aliasing limits the image size, Number of resolution elements = D/d = NN=10d Effective aperture: Ae(total) = N Ae (tel)19Aperture synthesis for realHow do we fill the 2D plane? (called u,v plane infourier space)Imagine VLA is at North Pole,