A short description of pulsar observing techniques is in
order. As pulsars have quite steep radio spectra (see,
e.g., [93]), 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., [92
]), 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., [92
]). 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.
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., [92]) 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 [57] 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., [10,
66,
123]). Some of the highest-precision experiments described below
have used this approach to collect their data. Figure
3
illustrates the advantages of this technique.
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Testing General Relativity with Pulsar Timing
Ingrid H. Stairs http://www.livingreviews.org/lrr-2003-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |