1. Arecibo Spectral line observing demo - basic concepts -- [Slides have been borrowed from talks by Frank Ghogo and Karen O’Neil of Green Bank, NRAO]

2. Intrinsic Power P (Watts) Distance R (meters) Aperture A (sq.m.)
Flux = Power/Area
Flux Density (S) = Power/Area/bandwidth
Bandwidth (β)
A “Jansky” is a unit of flux density

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

4. Antenna Beam Pattern (power pattern)
Gain(K/Jy)
Gain(305-m) ~10 K/Jy
Note Pn is normalized to maximum = 1;
Like optical PSF
Kraus, Fig.6-1, p. 153.

5. System Temperature Thermal noise ΔT
= total noise power detected, a result of many contributions
Thermal noise ΔT
= minimum detectable signal

6. Determining Tsource
Tmeas (α,δ,az,za) =
Tsrc(α,δ,az,za)

7. Determining Tsource Tmeas (α,δ,az,za) = Tsrc(α,δ,az,za)
+ TRX, other hardware
+ Tspillover (za,az)
+ Tcelestial(α,δ,t)
+ TCMB
+ Tatm(za)
Tmeas = Tsource Teverything else

8. Determining Tsource Tmeas (α,δ,az,za) = Tsrc(α,δ,az,za)
+ TRX, other hardware
+ Tspillover (za,az)
+ Tcelestial(α,δ,t)
+ TCMB
+ Tatm(za)
Tmeas = Tsource Teverything else

9. Off Source Observations
Position Switching
ON Source
OFF Source

10. Determining Tsource ON source OFF source
Tsource + Teverything else Teverything else
Arbitrary Units

11. (Tsource + Teverything else) - (Teverything else)
Determining Tsource
ON - OFF
(Tsource + Teverything else) - (Teverything else)
Arbitrary Counts

12. Determining Tsource (ON – OFF)/OFF
[(Tsource + Teverything else) - (Teverything else)]/ Teverything else
=(Source temperature)/(”System” temperature)
% Tsys

13. Determining Tsource (ON – OFF)/OFF
???
(ON – OFF)/OFF
[(Tsource + Teverything else) - (Teverything else)]/ Teverything else
=(Source temperature)/(”System” temperature)
% Tsys

14. Off Source Observations
Two basic concepts
Go off source in sky
Go off source in frequency/channels
Like most things in science:
Easy to state, complicated in practice

15. Determining Tsource Tsource Tsystem Result = (ON – OFF)/OFF
[(Tsource + Teverything else) - (Teverything else)]/ Teverything else
Tsource
Tsystem
Result =
Units are % System Temperature
Need to determine system temperature to
calibrate data

16. Determining Tsys
Noise Diodes

17. Determining Tsys Noise Diodes Tsrc/Tsys = (ON – OFF)/OFF
Tdiode/ Tsys = (ON – OFF)/OFF
Tsys = Tdiode * OFF/(ON – OFF)

18. OFF Determining Tsource Tsource = (ON – OFF) Tsystem
From diodes, Hot/Cold loads, etc.
Blank Sky or other
Telescope response has not been accounted for!

19. Telescope Response Ideal Telescope:
Accurate gain, telescope response can be modeled
Can be used to determine the flux density of ‘standard’ continuum sources
Not practical in cases where telescope is non-ideal
(blocked aperture, cabling/electronics losses, ground reflection, etc)

20. Telescope Response
Ideal Telescope:

21. Tsource = (ON – OFF) Tsystem 1 OFF GAIN
Determining Tsource
Tsource = (ON – OFF) Tsystem
OFF GAIN
Theoretical, or Observational
Blank Sky or other
From diodes, Hot/Cold loads, etc.