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Pulse Studies

Pulsar pulse studies encompass a broad set of topics ranging from the study of the average properties of pulsar profiles to the study of microscopic pheonomena in individual pulses. Though individual pulses from a pulsar show tremendous variations in properties such as shape, width, amplitude and polarisation, it is found that when a few thousand pulses (typically) are accumulated synchronously with the pulsar period, the resulting average profile shows a steady and constant form which can be considered to be a signature of that pulsar. Such an average profile typically exhibits one or more well defined regions of emission within the profile window. These are usually referred to as emission components and they can be partially or completed separated in pulse longitude. Similarly, the average polarisation properties also show a well defined signature in terms of the variations (across the profile window) of the amplitudes of linear and circular polarisation, as well as the angle of the linear polarisation vector. The average profile however does change with observing frequency for a given pulsar, with the typical signature being that profiles become wider at lower frequencies. Average pulse profile studies are important for characterising the overall properties of a pulsar.

To obtain accurate average pulse profiles, one needs to observe the pulsar for a long enough stretch so that (i) the profile converges to a stable form and (ii) there is enough signal to noise. The time resolution should be enough to resolve the features of interest in the profile (typically $1\%$ to $0.1\%$ of the pulse period). Since the average profile is obtained by synchronous accumulation at the pulsar period (this is called `folding' in pulsar jargon), the period and the sampling interval need to be known with sufficient accuracy to avoid any distortions due to smearing effects. It is easy to show that the fractional error in the period and the resultant fractional error in phase are related by

\frac {\Delta P}{P} ~~=~~ \frac {1}{N_{p}}\,\frac {\Delta\phi}{\phi} ~~~,
\end{displaymath} (17.5.3)

where $N_{p}$ is the number of pulses used in the folding. As an example, if the distortions due to phase error are to be kept under one part in a thousand and $N_{p} \,=\,1000$, then the period needs to be known to better than 1 part in a million.

Let us know look at the signal to noise ratio (SNR) for an average profile observation. For a pulsar of period $P$ and pulse width $W$ having a time average flux $S_{av}$, observed with a telescope of effective aperture $A_{eff}$ and system noise temperature $T_{sys}$, using a bandwidth $B$ and time constant $\tau_{s}$, the signal to noise ratio at a point on a profile obtained from $N_{p}$ pulses is given by

SNR_{avg} ~~=~~ \frac { S_{av}\,A_{eff} } { k\,T_{sys} } \; \frac{P}{W} \;
\sqrt{B\tau_{s}} \; \sqrt{N_{p}} ~~~.
\end{displaymath} (17.5.4)

Here the $P/W$ term is to convert the time average flux to on-pulse flux and the $\sqrt{N_{p}}$ term accounts for the SNR improvement due to addition of $N_{p}$ pulses. The other terms are as for normal SNR calculations for continuum sources.

When single pulses from a pulsar are examined in detail, it is seen that the radiation in each pulse does not always occur all over the average profile profile window. Usually, the signal is found located sporadically at different longitudes in the profile window. These intensity variations are called sub-pulses and they have a typcial width that is less than the width of the average profile. For some pulsars, sub-pulses in successive pulses don't always occur randomly in the profile window; they are found to move systematically in longitude from one pulse to the next. These are called drifting sub-pulses and are thought be one of the intriguing features of the emission mechanism. For some pulsars, there are times when there is practically no radiation seen in the entire profile window for one or more successive pulses. This phenomenon is called nulling and is another of the unexplained mysteries of pulsar radiation. Polarisation properties of sub-pulses also show significant deviations from the overall polarisation properties of the average profile. Studies of sub-pulses require time resolutions that are $0.1\%$ of the pulse period, or better.

When single pulses are observed with still further time resolution, it is found that narrow bursts of emission are also seen with time scales much shorter than sub-pulse widths. This is called microstructure and the time scales go down to microseconds and less. Seeing pulsar microstructure almost always requires the use of coherent dedispersion techniques to achieve the desired time resolution. It is clear from the above that pulsar intensities show fluctuations at various time scales within a pulse period. A useful analysis technique that separates out the various time scales is the intensity correlation function.

It is worth pointing out that single pulse observations are the worst affected among all kinds of pulsar studies, from the point of view of signal to noise ratio. This is simply because the $\sqrt{N_{p}}$ advantage in equation (3) is not available. Also, as $\tau_s$ is reduced for higher time resolution studies, the SNR decreases further. Hence such studies need the largest collecting area telescopes and can often be done on only the strongest pulsars.

next up previous contents
Next: Interstellar Scintillation Studies Up: Pulsar Observations Previous: Dispersion and Techniques for   Contents