Radio Telescope Sensitivity

What is modelled

A radio telescope receives a source that is far weaker than the receiver noise. Averaging helps: for noise-like signals the scatter of the average falls as one over the square root of the product of bandwidth and integration time. The source is detected when its antenna temperature, the temperature of a resistor that would give the same power, is several times that scatter. Slow drift of the receiver gain adds a floor that no amount of averaging can remove, which is why receivers are Dicke-switched.

Equations

• Antenna temperature TA = S Aeff / 2k with Aeff = η π D² / 4 (one polarisation).
• Radiometer equation ΔT = Tsys / √(Δν τ); with gain drift ΔT = Tsys √(1/(Δντ) + (ΔG/G)²).
• Dicke switching ΔT = 2 Tsys / √(Δντ).
• Faintest 5-sigma flux Smin = 10 k ΔT / Aeff; gain-limit time τ* = 1 / (Δν (ΔG/G)²).

Checks run in the page

• A Monte Carlo of the scatter of an average of squared Gaussian noise.
• The antenna temperature of 1 Jy on a 100 m dish.
• The integration time that gives a signal to noise of five, put back into the formula.
• The equal point of the white and drift terms, and the Dicke break-even time.

Honest simplifications

The noise is treated as white and Gaussian, the drift is a single number, the source is unresolved and unpolarised, atmospheric and ground-pickup variations are inside the system temperature, and the trace shown is a schematic drift scan with a fresh random noise draw every few seconds.

• Press Bright source, 1 s and then Faint source, 1 minute to see how long integration pulls a weak source out.
• Press Gain-limited, long run and watch the noise stop falling in the first graph.
• Press Small dish and Cooled receiver and compare the faintest flux each can reach.