Nature of the Signal

The signal is essentially a narrow broadband noise pulse (usually about 5% duty-cycle) repeated at pulse periods from 11.8 seconds (0.085 Hz) down to 1.4 ms (716 Hz). As the flux density figure is averaged over the pulse period, those pulsars with smaller duty cycles (smaller W50 w.r.t. to P0, i.e., a narrower pulse w.r.t. to P0) will generally be easier to detect as their peak signals will poke their noses above the noise higher. Broadband signal energy from pulsars can extend from 10s of MHz up to microwave frequencies. But because the radio waves are generated by the synchrotron mechanism, the signal is stronger at lower frequencies.

Note that the signal strength is quoted in Janskys, where 1 Jy = 10⁻²⁶ watts per square metre per hertz. To collect more energy from the pulsar we can receive energy over more square metres (bigger antenna) or more hertz (wider bandwidth). Unfortunately, there is a limit to the bandwidth unless complicated processing is done. This is due to dispersion, where the effects of the traversal of space cause lower frequencies of a pulse to arrive later than higher frequencies. Inconveniently the degree of delay over a given bandwidth increases rapidly the lower the observation receiving frequency - where the signal is much stronger. If the bandwidth chosen is too wide for the observation receiving frequency such that the effects of dispersion cause too much delay, the pulse is 'smeared' and is harder to detect. You can imagine if the delay over the chosen bandwidth is equal to the period of the pulse then the pulse completely disappears.

Without a doubt the most useful parameter for pulsar detection is aperture - the collecting area of your antenna. The bigger the antenna the easier it will be to detect a pulsar - an obvious statement for sure, but what is not so obvious is how quickly it becomes increasingly difficult as the size of the antenna is reduced. Reducing the diameter of a dish antenna by a factor of 2 (say, 6 metres to 3 metres) would need an increase in observation time by a factor of 16 to maintain sensitivity, or a factor of 16 increase in bandwidth. Fortunately these compensations can be combined as a product, e.g., 4 times the bandwidth combined with 4 times the observation time provides the factor of 16 required.

Each pulsar has its own period, pulse width, flux density and dispersion measure. Evaluating the ease, or otherwise, of detection of a particular pulsar requires taking all those into account.