where SNR is the threshold signal-to-noise ratio, and are the receiver and sky noise temperatures, G is the gain of the antenna, is the observing bandwidth, is the integration time, W is the detected pulse width and P is the pulse period.
The smearing across the individual frequency channels, however, still remains and becomes significant at high dispersions when searching for short-period pulsars. Multi-path scattering results in a one-sided broadening due to the delay in arrival times which scales roughly as , which can not be removed by instrumental means. A simple scattering model is shown in Fig. 13 in which the scattering electrons are assumed to lie in a thin screen between the pulsar and the observer .
Dispersion and scattering are most severe for distant pulsars in the inner Galaxy where the number of free electrons along the line of sight becomes large. The strong frequency dependence of both effects means that they are considerably less of a problem for surveys at observing frequencies [56, 109] compared to the usual 400 MHz search frequency. An added bonus for such observations is the reduction in , since the spectral index of the non-thermal Galactic emission is about -2.8 . Pulsars themselves have steep radio spectra. Typical spectral indices are -1.6 , so that flux densities are roughly an order of magnitude lower at 1400 MHz compared to 400 MHz. Fortunately, this can usually be compensated for by the use of larger receiver bandwidths at higher radio frequencies. For example, the 1370-MHz system at Parkes has a bandwidth of 288 MHz  compared to the 430-MHz system, where 32 MHz is available .
As an example of this effect, as seen in the time domain, Fig. 14 shows a 22.5-min search mode observation of Hulse & Taylor's famous binary pulsar B1913+16 [102, 239, 240]. Although this observation covers only about 5% of the orbit (7.75 hr), the effects of the Doppler smearing on the pulse signal are very apparent. While the standard search code (seeking constant periodicity) nominally detects the pulsar with a signal-to-noise ratio of 9.5 for this observation, it is clear that the Doppler shifting of the pulse period seen in the individual sub-integrations results in a significant reduction in signal-to-noise.
It is clearly desirable to employ a technique to recover the loss in sensitivity due to Doppler smearing. One such technique, the so-called ``acceleration search'' , assumes the pulsar has a constant acceleration during the integration. Each time series can then be re-sampled to refer it to the frame of an inertial observer using the Doppler formula to relate a time interval in the pulsar frame to that in the observed frame at time t, as . Searching over a range of accelerations is desirable to find the time series for which the trial acceleration most closely matches the true value. In the ideal case, a time series is produced with a signal of constant period for which full sensitivity is recovered (see right panel of Fig. 14). Anderson et al.  used this technique to find PSR B2127+11C, a double neutron star binary in M15 which has parameters similar to B1913+16. Camilo et al.  have recently applied the same technique to 47 Tucanae to discover 9 binary pulsars, including one in a 96-min orbit around a low-mass () companion. This is currently the shortest binary period for any known radio pulsar.
For the shortest orbital periods, the assumption of a constant acceleration during the observation clearly breaks down. Ransom et al.  have developed a particularly efficient algorithm for finding binaries whose orbits are so short that many orbits can take place during an integration. This phase modulation technique exploits the fact that the pulses are modulated by the orbit to create a family of periodic sidebands around the nominal spin period of the pulsar. This technique has already been used to discover a 1.7-hr binary pulsar in NGC 6544 . The existence of these short-period radio pulsar binaries, as well as the 11-min X-ray binary X1820-303 in NGC 6624 , implies that there must be many more short-period binaries containing radio or X-ray pulsars in globular clusters that are waiting to be discovered by more sensitive searches.
|Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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