2.2 Pulsar observations

Figure 2: Pulse profile shapes for PSR J1740–3052 at multiple frequencies, aligned by pulse timing. The full pulse period is displayed at each frequency. The growth of an exponential scattering tail at low frequencies is evident. All observations taken with the Green Bank Telescope [58] (Stairs, unpublished), except for the 660-MHz profile which was acquired at the Parkes telescope [107, 121].

A short description of pulsar observing techniques is in order. As pulsars have quite steep radio spectra (see, e.g., [94]), they are strongest at frequencies of a few hundred MHz. At these frequencies, the propagation of the radio wave through the ionized interstellar medium (ISM) can have quite serious effects on the observed pulse. Multipath scattering will cause the profile to be convolved with an exponential tail, blurring the sharp profile edges needed for the best timing. Figure 2 shows an example of scattering; the effect decreases with sky frequency as roughly (see, e.g., [93]), and thus affects timing precision less at higher observing frequencies. A related effect is scintillation: Interference between the rays traveling along the different paths causes time- and frequency-dependent peaks and valleys in the pulsar’s signal strength. The decorrelation bandwidth, across which the signal is observed to have roughly equal strength, is related to the scattering time and scales as (see, e.g., [93]). There is little any instrument can do to compensate for these effects; wide observing bandwidths at relatively high frequencies and generous observing time allocations are the only ways to combat these problems.

Figure 3: Pulse profile of the fastest rotating pulsar, PSR B1937+21, observed with the 76-m Lovell telescope at Jodrell Bank Observatory [69]. The top panel shows the total-intensity profile derived from a filterbank observation (see text); the true profile shape is convolved with the response of the channel filters. The lower panel shows the full-Stokes observation with a coherent dedispersion instrument [123, 122]. Total intensity is indicated by black lines, and linear and circular power by red and blue lines, respectively. The position angle of the linear polarization is plotted twice. The coherent dedispersion observation results in a much sharper and more detailed pulse profile, less contaminated by instrumental effects and more closely resembling the pulse emitted by the rotating neutron star. Much better timing precision can be obtained with these sharper pulses.

Another important effect induced by the ISM is the dispersion of the traveling pulses. Acting as a tenuous electron plasma, the ISM causes the wavenumber of a propagating wave to become frequency-dependent. By calculating the group velocity of each frequency component, it is easy to show (see, e.g., [93]) that lower frequencies will arrive at the telescope later in time than the higher-frequency components, following a law. The magnitude of the delay is completely characterized by the dispersion measure (DM), the integrated electron content along the line of sight between the pulsar and the Earth. All low-frequency pulsar observing instrumentation is required to address this dispersion problem if the goal is to obtain profiles suitable for timing. One standard approach is to split the observing bandpass into a multichannel “filterbank,” to detect the signal in each channel, and then to realign the channels following the law when integrating the pulse. This method is certainly adequate for slow pulsars and often for nearby millisecond pulsars. However, when the ratio of the pulse period to its DM becomes small, much sharper profiles can be obtained by sampling the voltage signals from the telescope prior to detection, then convolving the resulting time series with the inverse of the easily calculated frequency-dependent filter imposed by the ISM. As a result, the pulse profile is perfectly aligned in frequency, without any residual dispersive smearing caused by finite channel bandwidths. In addition, full-Stokes information can be obtained without significant increase in analysis time, allowing accurate polarization plots to be easily derived. This “coherent dedispersion” technique [60] is now in widespread use across normal observing bandwidths of several tens of MHz, thanks to the availability of inexpensive fast computing power (see, e.g., [11, 68, 122]). Some of the highest-precision experiments described below have used this approach to collect their data. Figure 3 illustrates the advantages of this technique.