Brief Introduction to

Frank Ghigo, NRAO-Green Bank

October 2016

Terms and Concepts

Parabolic reflector Aperture efficiency Blocked/unblocked Bandwidth 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 () convolution density Main beam efficiency Effective aperture Pioneers of radio

Karl Jansky 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 Subreflector and receiver room On the receiver turret Basic Radio

Verschuur, 1985. Slide set produced by the Astronomical Society of the Pacific, slide #1. Signal paths Intrinsic Power P () 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

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 = Ω A = M A Ω A e 1 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

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. 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 () 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 Gain(K/Jy) for the GBT

2kT Including atmospheric absorption: 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 W s, 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

T = K ⋅ C € sys sys 1 1 = K ⋅ (C + C ) − T 2 offsource,calon offsource,caloff 2 cal

€ Tant = K ⋅ Csource

€ Position switching