4.2 The Timing Model4 Pulsar Timing4 Pulsar Timing

4.1 Observing basics 

As each new pulsar is discovered, the standard practice is to add it to a list of pulsars which are regularly observed at least once or twice per month by large radio telescopes throughout the world. The schematic diagram shown in Fig.  11 summarises the essential steps involved in such a ``time-of-arrival'' (TOA) measurement. Incoming pulses emitted by the rotating neutron star traverse the interstellar medium before being received by the radio telescope. After amplification by high sensitivity receivers, the pulses are de-dispersed (see below) and added to form a mean pulse profile.


Click on thumbnail to view image

Figure 11: Schematic showing the main stages involved in pulsar timing observations.

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 [10]. 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 tex2html_wrap_inline2153 is given roughly by the pulse width divided by the SNR. Based on equation 3Popup Equation, we can express this as follows


where W is the equivalent width of a top hat function having the same mean flux density tex2html_wrap_inline2157 as the observed pulse with a period P . The observing system is parameterised by the available bandwidth tex2html_wrap_inline1955, the integration time tex2html_wrap_inline1957, and the system equivalent flux density tex2html_wrap_inline2165 . 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 tex2html_wrap_inline2165) 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 tex2html_wrap_inline2153 . 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 [68] 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!

4.2 The Timing Model4 Pulsar Timing4 Pulsar Timing

image Binary and Millisecond Pulsars
D. R. Lorimer (dunc@mpifr-bonn.mpg.de)
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de