Intrinsic Power P (Watts) Distance R (meters) Aperture A (sq.m.)

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. 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 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 Kraus, 1966. Fig.6-1, p. 153.

5. System Temperature = 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. 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 Determining Tsource

8. 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 Determining Tsource

9. Off Source Observations Position Switching ON Source OFF Source

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

11. 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 [(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. Tsource Tsystem Result = Determining Tsource (ON–OFF)/OFF [(Tsource + Teverything else)- (Teverything else)]/ Teverything else 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. From diodes, Hot/Cold loads, etc. Determining Tsource Tsource = (ON–OFF)Tsystem OFF 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 Theoretical, or Observational Blank Sky or other From diodes, Hot/Cold loads, etc.