During the observation, the data regularly receive a time stamp, usually based on a caesium time standard or hydrogen maser at the observatory plus a signal from the GPS (Global Positioning System of satellites) time system . The TOA of this mean pulse is then defined as the arrival time of some fiducial point on the profile. Since the mean profile has a stable form at any given observing frequency (§ 2.2) the TOA can be accurately determined by a simple cross-correlation of the observed profile with a high signal-to-noise ``template'' profile -- obtained from the addition of many observations of the pulse profile at the particular observing frequency.
Success in pulsar timing hinges on how precisely this fiducial point can be determined. This is largely dependent on the signal-to-noise ratio (SNR) of the mean pulse profile. The uncertainty in a TOA measurement is given roughly by the pulse width divided by the SNR. Based on equation 3, we can express this as follows
where W is the equivalent width of a top hat function having the same mean flux density as the observed pulse with a period P . The observing system is parameterised by the available bandwidth , the integration time , and the system equivalent flux density . Optimum results are thus obtained for observations of short period pulsars with large flux densities and narrow duty cycles (W / P) using large telescopes with low-noise receiver systems (both effects reduce ) and large observing bandwidths.
One of the main problems of employing large bandwidths is pulse dispersion. As discussed in § 2.3, the velocity of the pulsed radiation through the ionised interstellar medium is frequency-dependent: Pulses emitted at higher radio frequencies travel faster and arrive earlier than those emitted at lower frequencies. This process has the effect of ``stretching'' the pulse across a finite receiver bandwidth, reducing the apparent signal-to-noise ratio and therefore increasing . For most normal pulsars, this process can largely be compensated for by the incoherent de-dispersion process outlined in § 3.1 .
To exploit the precision offered by millisecond pulsars, a more precise method of dispersion removal is required. Technical difficulties in building devices with very narrow channel bandwidths require another dispersion removal technique. In the process of coherent de-dispersion  the incoming signals are de-dispersed over the whole bandwidth using a filter which has the inverse transfer function to that of the interstellar medium. The maximum resolution obtainable is then the inverse of the receiver bandwidth. For typical bandwidths of 10 MHz, this technique makes it possible to resolve features on time-scales as short as 100 ns. This corresponds to regions in the neutron star magnetosphere as small as 30 m!
|Binary and Millisecond Pulsars
D. R. Lorimer (firstname.lastname@example.org)
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