Introduction to Radio Telescopes

Frank Ghigo, NRAO-Green Bank The Fourth NAIC-NRAO School on Single-Dish Radio Astronomy July 2007 Parabolic reflector Blocked/unblocked Subreflector Frontend/backend Feed horn Local oscillator Mixer Noise Cal Flux density

Terms and Concepts

Jansky Bandwidth Resolution Antenna power pattern Half-power beamwidth Side lobes Beam solid angle Main beam efficiency Effective aperture Aperture efficiency Antenna Temperature Aperture illumination function Spillover Gain System temperature Receiver temperature convolution

Pioneers of radio astronomy Karl Jansky 1932 Grote Reber 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 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 10  26

Watts

/

m

2 /

Hz P

 10  26 4 

R

2

S



Antenna Beam Pattern (power pattern) Kraus, 1966. Fig.6-1, p. 153.

 

HPBW

 

D

Beam solid angle (steradians) 

A

  4 

P n

(  ,  )

d

 Main Beam Solid angle 

M

 

main P n lobe

(  ,  )

d

 P n = normalized power pattern

Some definitions and relations Main beam efficiency,  M 

M

  

M A

Antenna theorem 

A

  2

A e

Aperture efficiency,  ap Effective aperture, A e Geometric aperture, A g 

ap



A e A g



ap

 

pat



surf



block



ohmic



A g

(

GBT

)   1 2 ( 100

m

) 2  7854

m

2

Detected power (W, watts) from a resistor R at temperature T (kelvin) over bandwidth  (Hz)

W



kT

 Power W A detected in a radio telescope Due to a source of flux density S power as equivalent temperature.

Antenna Temperature T A Effective Aperture A e

W A

 1 2

S

 2

kT A A e AS



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

Aperture Illumination Function  Beam Pattern A gaussian aperture illumination gives a gaussian beam: 

pat

 0 .

7 Kraus, 1966. Fig.6-9, p. 168.

S

 2

kT A A e

Gain(K/Jy) for the GBT

G



T A S

 

ap A g

2

k G

(

K

/

Jy

)  2 .

84  

ap

 Including atmospheric absorption:

S

 2

kT A e



a A e

Effect of surface efficiency 

ap

 

pat



surf

 

System Temperature = total noise power detected, a result of many contributions

T sys



T ant



T rcvr



T atm

( 1 

e

 

a

) 

T spill



T CMB

   Thermal noise  T = minimum detectable signal 

T



k

1

T sys

  

t

int For GBT spectroscopy

Convolution relation for observed brightness distribution

S

(  )  

source A

(  '   )

I

(  ' )

d

 ' 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 T s , then for 

s

 

A T A

 

s



A T s

for 

s

 

A T A



T s

In general :

T A

 1 

A



source P n

(  ,  )

T s

(  ,  )

d



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

G



C cal



on T cal



C cal



off T sys



G



C sys

 1 2

G

 (

C offsource

,

calon



C offsource

,

caloff

)  1 2

T cal T ant



G



C source