Brief Introduction to Radio Telescopes Frank Ghigo NRAO/GBO Summer Student Workshop May 26, 2020 Terms and Concepts Parabolic reflector Jansky Aperture efficiency Blocked/unblocked Bandwidth Antenna Temperature Subreflector Resolution Aperture illumination function Frontend/backend Antenna power pattern Spillover Feed horn Half-power beamwidth Gain Local oscillator Side lobes System temperature Mixer Beam solid angle Receiver temperature Noise Cal dB (deciBels) convolution Flux density Main beam efficiency Effective aperture Text books on Radio Astronomy • Essential Radio Astronomy • https://science.nrao.edu/opportunities/courses/era Pioneers of Radio Astronomy Karl Jansky Grote Reber 1932 1938 Unblocked Aperture • 100 x 110 m section of a parent parabola 208 m in diameter • Cantilevered feed arm is at focus of the parent parabola Spherical reflector : Arecibo telescope Subreflector and receiver room On the receiver turret Basic Radio Telescopes Verschuur, 1985. Slide set produced by the Astronomical Society of the Pacific, slide #1. Signal paths Intrinsic Power P (Watts) Distance R (meters) Aperture A (sq.m.) Flux = Power/Area Flux Density (S) = Power/Area/bandwidth Bandwidth (b) A “Jansky” is a unit of flux density 10−26Watts / m2 / Hz P =10−264πR2Sβ Antenna Beam Pattern (power pattern) Beam Solid Angle Ω = P (θ ,φ)dΩ (steradians) A ∫∫ n 4π Main Beam Ω = P (θ ,φ)dΩ Solid Angle M ∫∫ n main λ lobe θ = HPBW D Pn = normalized power pattern Kraus, 1966. Fig.6-1, p. 153. € dB ?? P1 Δp(dB) =10log10 ( ) P2 P1/P2 Δp(dB) € 1 0 2 3 10 10 € 100 20 1000 30 Convolution relation for observed brightness distribution S(θ ) ∝ ∫ A(θ '−θ )I(θ ')dθ ' source (Note: A is antenna pattern, Means the same as P in Previous slides.) Thompson, Moran, Swenson, 2001. Fig 2.5, p. 58. Smoothing by the beam Kraus, 1966. Fig. 3-6. p. 70; Fig. 3-5, p. 69. Some definitions and relations Antenna theorem Main beam efficiency, eM 2 ΩM λ ε M = Ω A = Ω A Ae Aperture efficiency, eap Effective aperture, Ae Geometric aperture, Ag Ae 2 &1 # 2 ε ap = Ag (GBT) = π % (100m)" = 7854m 2 Ag $ ! ε ap = ε patε surf εblockεohmic ! another Basic Radio Telescope Kraus, 1966. Fig.1-6, p. 14. Aperture Illumination Function ßà Beam Pattern A gaussian aperture illumination gives a gaussian beam: ε pat ≈ 0.7 Kraus, 1966. Fig.6-9, p. 168. Not-quite-perfect parabola s = rms surface error Surface efficiency -- Ruze formula −(4 πσ / λ)2 εsurf = e s = rms surface error Effect of surface efficiency € ε ap = ε patε surf ⋅⋅⋅ John Ruze of MIT -- Proc. IEEE vol 54, no. 4, p.633, April 1966. Detected power (P, watts) from a resistor R at temperature T (kelvin) over bandwidth b(Hz) P = kTβ Power PA detected in a radio telescope 1 Due to a source of flux density S PA = 2 ASβ power as equivalent temperature. 2kT Antenna Temperature T S = A A A Effective Aperture Ae e System Temperature = total noise power detected, a result of many contributions −τa Tsys = Tant +Trcvr +Tatm (1− e ) +Tspill +TCMB + ⋅⋅⋅⋅ Tsys Thermal noise DT ΔT = k1 = minimum detectable signal Δν ⋅tint The Radiometer Equation Gain(K/Jy) for the GBT Including atmospheric absorption: 2kT S = A 2kTA τa Ae S = e Ae TA εap Ag G = = G(K / Jy) = 2.84⋅ε ap S 2k € Physical temperature vs antenna temperature For an extended object with source solid angle Ws, And physical temperature Ts, then Ω T s T for Ωs < Ω A A = s Ω A for Ωs > Ω A TA = Ts 1 T P ( , )T ( , )d In general : A = ∫∫ n θ φ s θ φ Ω Ω A source Calibration: Scan of Cass A with the 40-Foot peak baseline Tant = Tcal * (peak-baseline)/(cal – baseline) (Tcal is known) More Calibration : GBT Convert counts to T T K = cal Ccal−on − Ccal−off € Tsys = K ⋅ Csys 1 1 = K ⋅ (C + C ) − T 2 offsource,calon offsource,caloff 2 cal € Tant = K ⋅ Csource € Position switching greenbankobservatory.org The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc..