Effects of Dispersion

On its way from the pulsar to receivers on Earth, the pulsar signal passes through the Inter Stellar Medium (ISM).  One of the effects (in addition to scintillation effects) is dispersion.  Essentially this effect causes signals at lower frequencies to arrive later in time w.r.t. to higher frequencies.  For continuum signals this effect is hidden because there is no temporal information markers to detect the delay.  In contrast, pulsar radio band signals start their journey aligned in time (those moments in time when the radiation beam is pointing in our direction) independent of frequency.  By the time the signals reach our receivers the passage through the ISM has introduced a significant delay between lower and higher frequencies.  The journey of the pulsar signal involves different paths and path lengths for each pulsar - imparting varying degrees of dispersion on different pulsars.  This unique pulsar signal characteristic is given as the 'dispersion measure' or DM.

A general equation which gives the relative delay between two frequencies (assuming the difference between the frequencies is small compared to the absolute frequencies) is as follows...

...where the delay is in milliseconds and frequencies are in MHz.

The effect of this delay is to smear the pulse shape when received over a wide bandwidth.  This means that the pulse signals over the bandwidth don't line up in time and so do not add together to improve the S/N in the folded profile.

For the same DM value, observation frequency and bandwidth, a pulsar with a narrow pulse width (PW50) is going to be affected more compared to one with a wider pulse.

To counteract the effects of dispersion a process of de-dispersion can be applied to the data.  Coherent de-dispersion applies a filter whose response is the inverse of the ISM before detection; incoherent de-dispersed applies a time correction across data split into separate frequency channels (to line up the pulses in each channel in time) after detection.   Incoherent de-dispersion is the simpler of the two techniques to both understand and implement.  However, is not as accurate as the coherent technique (which implements continuous 'perfect' de-dispersion) because the time delay corrections for incoherent de-dispersion are implemented on individual channels in a step-wise fashion and there can still be some residual dispersion across the channel bandwidths.

Comparing two of the strongest pulsars: Vela (PW50=2.1 ms; DM=68) and B0329+54 (PW50=6.6 ms; DM=27) at 400 MHz, the bandwidth at which the delay is equal to PW50 (at which point smearing starts to cause loss in sensitivity) is 240 kHz for Vela and 1900 kHz for B0329+54.  Using bandwidths above those respective values will require de-dispersion of the data.

NOTE: dispersion results in a delay differential between signal frequencies - it does not affect the period (as can be seen in the graphic above).