Introduction to Radio Telescopes Frank Ghigo, NRAO-Green Bank The Fourth NAIC-NRAO School on Single-Dish Radio Astronomy July 2007 Terms and Concepts Jansky Bandwidth Resolution Antenna power pattern Half-power beamwidth Side lobes Beam solid angle Main beam efficiency Effective aperture Parabolic reflector Blocked/unblocked Subreflector Frontend/backend Feed horn Local oscillator Mixer Noise Cal Flux density Aperture efficiency Antenna Temperature Aperture illumination function Spillover Gain System temperature Receiver temperature convolution

Pioneers of radio astronomy Grote Reber 1938 Karl Jansky 1932

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 Telescope 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 () A “Jansky” is a unit of flux density

Antenna Beam Pattern (power pattern) Beam solid angle (steradians) Main Beam Solid angle Note Pn is normalized to maximum = 1; Like optical PSF Pn = normalized power pattern Kraus, 1966. Fig.6-1, p. 153.

Some definitions and relations Main beam efficiency, M Antenna theorem Aperture efficiency, ap Effective aperture, Ae Geometric aperture, Ag

Power WA detected in a radio telescope Detected power (W, watts) from a resistor R at temperature T (kelvin) over bandwidth (Hz) Power WA detected in a radio telescope Due to a source of flux density S power as equivalent temperature. Antenna Temperature TA Effective Aperture Ae Factor of one-half because detector is only sensitive to one polarization.

another Basic Radio Telescope Kraus, 1966. Fig.1-6, p. 14.

Aperture Illumination Function  Beam Pattern A gaussian aperture illumination gives a gaussian beam: Trade off low side lobes (high main beam efficiency) for lower aperture efficiency. Kraus, 1966. Fig.6-9, p. 168.

Effect of surface efficiency Gain(K/Jy) for the GBT Including atmospheric absorption: Atmospheric absorption has been left out of this equation Effect of surface efficiency

System Temperature Thermal noise T = total noise power detected, a result of many contributions Thermal noise T = minimum detectable signal For GBT spectroscopy

Convolution relation for observed brightness distribution 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.

Physical temperature vs antenna temperature For an extended object with source solid angle s, And physical temperature Ts, then for for In general :

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