Method of Detection

As mentioned previously, the signal from a pulsar appears in the receiver as short pulse of broadband noise. The pulsar signal is extracted by measuring the broadband noise power from the receiver.  This can be done by a number of ways, e.g., a simple analogue circuit RMS power detector (which responds fast enough to catch the narrow pulsar pulse signal), or capturing RF data and performing power detection in software (e.g., RTLSDR IQ data converted to power: P=I2+Q2).

Although the signals from pulsars are weak, the time between the pulses is stable to an extraordinary degree.  Some pulsars have pulse period stabilities better than the accuracy of the best terrestrial clocks. For radio astronomers who have antennas large enough to detect single pulses, it is possible, after receiving a pulse, to predict the arrival time of subsequent pulses many hours - or even days - later.

For those observers whose antennas are of a more modest size - say a dish less than 20 metre in diameter - it is not generally possible to receive single pulses of sufficient S/N to be useful.  For those scenarios use can be made of the extreme regularity of the pulses to dig them out of the noise.  This introduces a critical requirement for receiving pulsars - data must be acquired with high temporal accuracy.  Many amateurs use atomic clock standard disciplined data acquisition.

The usual method for amateurs of detecting known pulsars is by synchronous averaging ("Handbook of Pulsar Astronomy" - Lorimer & Kramer - page 165) of many pulses to reduce noise.  This method goes by a few names such as "folding" or "coherent integration". Note: it is the author's opinion that the term 'coherent' should not be used in this context because 1. it is not used in prominent references by those who would know and 2. it will confuse the distinction in descriptions of processes where it is a correct usage of the term (see "Handbook of Pulsar Astronomy" - Lorimer & Kramer - Section 5.2 'Incoherent De-dispersion'; Section 5.3 'Coherent De-dispersion').

Any process of detecting pulsars is governed by the general radiometer equation ("Radio Astronomy" - Kraus)...

where

ΔSmin = minimum detectable flux density (watts per square metre per hertz)

k = Boltzmann's constant (1.38064852 × 10-23 Joules • K-1)

Ks = factor for a particular observatory system, hopefully near to 1

Tsys = System noise temperature (Ko)

Ae = Effective aperture of the antenna (m2)

Δf = pre-detection bandwidth (Hz)

t = post-detection integration time (seconds)

n = number of records averaged

The above equation is a general relationship for continuum measurements and so is modified for the pulse-like signal from a pulsar (Eqns. A1-14 & A1-21 - "Handbook of Pulsar Astronomy" by D. Lorimer & M. Kramer)

where

ΔSmin = minimum detectable flux density (watts per square metre per hertz - averaged over the period of the pulse)

β = factor for imperfections in the observatory system, usually near to 1 (values >1 makes the system less sensitive)

kb = Boltzmann's constant (1.38064852 × 10-23 Joules • K-1)

S/Nmin = required minimum linear S/N for validation of result (professional require at least 6, amateurs ≥ 4)

Tsys = System noise temperature (Ko)

Ae= antenna aperture (m2)

np = number of polarisations (usually 1 for amateurs, generally a maximum of 2)

tint = integration time (observation time in seconds)

Δf = pre-detection bandwidth (Hz)

W = width of pulse (seconds)

P = period of pulse (seconds)