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Astron. Astrophys. 358, 169-176 (2000)

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3. Search sensitivity

To estimate the sensitivity of this survey, we make use of the following expression which is similar to that derived by Dewey et al. (1984) to find the minimum detectable flux density a pulsar has to have in order to be detectable:


Here the constant factor [FORMULA] takes into account losses in the hardware and the threshold signal-to-noise ratio above which a detection is considered significant ([FORMULA] in our case), [FORMULA] is the system temperature (see below), G is the gain of the telescope (1.5 K Jy-1 for Effelsberg operating at 21-cm), [FORMULA] is the observing bandwidth (16-MHz for this survey), the factor of [FORMULA] indicates that two polarisation channels were summed, [FORMULA] is the integration time per telescope pointing (35 min), P is the period of the pulsar and W is the observed width of the pulse.

The system temperature [FORMULA] is essentially the sum of the noise temperature of the receiver [FORMULA], the spillover noise into the beam side-lobes from the ground [FORMULA] and the excess background temperature [FORMULA] caused largely by synchrotron radiating electrons in the Galactic plane itself. From regular calibration measurements we found [FORMULA] to be 35 K. The spillover contribution [FORMULA] was estimated to be 5 K for typical telescope elevations during survey observations. We estimate [FORMULA] by scaling the 408-MHz all-sky survey of Haslam et al. (1982) to 1400 MHz assuming a spectral index of -2.7 (Lawson et al. 1987), finding a typical value in the direction [FORMULA] and [FORMULA] to be 15 K. With these values in Eq. (1), we find the minimum flux density for detecting a 0.5 s pulsar with a duty cycle of 4% to be about 0.3 mJy.

We caution that this sensitivity estimate should be viewed as a "best case scenario", valid for relatively long-period pulsars with low dispersion measures and narrow pulses observed at the beam centre. The effects of sampling and dispersion and pulse scattering significantly degrade the search sensitivity at short periods. Specifically, the observed pulse width W in Eq. (1) is often likely to be greater than the intrinsic width [FORMULA] emitted at the pulsar because of the scattering and dispersion of pulses by free electrons in the interstellar medium, and by the post-detection integration performed in the receiver. The sampled pulse profile is the convolution of the intrinsic pulse width and broadening functions due to dispersion, scattering and integration and is estimated from the following quadrature sum:


where [FORMULA] is the data sampling interval, [FORMULA] is the dispersion broadening across one filterbank channel and [FORMULA] is the interstellar scatter broadening.

To highlight the effects of pulse broadening on sensitivity, in Fig. 2 we present the effective sensitivity as a function of period for a hypothetical pulsar with an intrinsic duty cycle of 5% for assumed DMs of 0, 128 and 512 cm-3 pc. The scallops in the curves at short periods reflect the reduction in sensitivity due to the loss of higher-order harmonics in the Fourier spectrum (see e.g. Nice 1992). The severe degradation in sensitivity at short periods and high dispersion measures is clearly seen in this diagram. In particular, we note that due to the dispersion across individual filterbank channels, the present observing system is essentially insensitive to pulsars with periods less than 30 ms and DMs larger than 500 cm-3 pc.

[FIGURE] Fig. 2. The limiting sensitivity of the survey as a function of pulse period. The scattering times used in these calculations were estimated from the Taylor & Cordes (1993) electron density model for each DM for the Galactic coordinates ([FORMULA]). Solid points denote the three previously known pulsars. Stars show the four newly-discovered pulsars.

In the discussion hitherto we have implicitly assumed that the apparent pulse period remains constant during the observation. Given the necessarily long integration times employed to achieve good sensitivity, this assumption is only valid for solitary pulsars, or those in binary systems where the orbital periods are longer than about a day. For shorter-period binary systems, as noted by a number of authors (see e.g. Johnston & Kulkarni 1992), the Doppler shifting of the pulse period results in a spreading of the total signal power over a number of frequency bins in the Fourier domain. Thus, a narrow harmonic becomes smeared over several spectral bins.

As an example of this effect, as seen in the time domain, Fig. 3 shows a 35-min search mode observation of PSR B1744-24A; the 11.56 ms eclipsing binary pulsar in the globular cluster Terzan 5 (Lyne et al. 1990). Given the short orbital period of this system (1.8 hr), the observation covers about one third of the orbit! Although the search code nominally detects the pulsar with a signal-to-noise ratio of 9.5 for this observation, the Doppler shifting of the pulse period seen in the individual sub-integrations clearly results in a significant reduction in sensitivity.

[FIGURE] Fig. 3. A search-mode observation of the eclipsing binary pulsar B1744-24A in Terzan 5. Top panel: Data folded modulo the constant period reported by the search code (11.56 ms). The changing pulse period is clearly seen as a drift in phase from one sub-integration to the next. Lower panel: the integrated pulse profile whose signal-to-noise ratio is significantly degraded by the orbital motion during the integration.

The analysis reported in this paper makes no attempt to recover the loss in sensitivity due to this effect. To date, the only pulsar searches where this issue is tackled has been in searches for binary pulsars in globular clusters (e.g. Anderson et al. 1990; Camilo et al. 2000b). These searches applied a technique whereby the time series is compensated for first-order Doppler accelerations. Although these searches have been very successful they add significantly to the computational effort required to reduce the data, and have therefore only been applied to globular clusters where the DM is known a-priori from observations of solitary pulsars. For our data, where the DM is a-priori unknown, we are presently developing computationally-efficient algorithms which will permit us to greatly improve the sensitivity to binary pulsars by re-analysing these data in future. We note that the present analysis results in significantly reduced sensitivity to binary pulsars with orbital periods less than one day.

We conclude this discussion with some remarks on the search sensitivity to very long-period ([FORMULA] s) pulsars. The existence of radio pulsars with such periods are of great relevance to theories of pulsar emission, many of which predict that the emission ceases when the period crosses a critical value (see e.g. Chen & Ruderman 1993). Young et al. (1999) have recently demonstrated that the period of PSR J2144-3933, originally discovered in the Parkes Southern Sky Survey, is 8.5 s - three times that previously thought. This is presently the longest period for a radio pulsar. Young et al. make the valid point that such pulsars could be very numerous in the Galaxy since they have very narrow emission beams and therefore radiate to only a small fraction of the celestial sphere. An additional factor here is that the number of pulses emitted by e.g. a 10-s pulsar during typical pulsar survey integration times is [FORMULA]. If the pulsar undergoes significant periods in the null state, as might be expected (Ritchings 1976), it will be harder to detect in an FFT-based search (Nice 1999).

One way to tackle this problem is to employ longer integration times, such as we do here. The FFT-based periodicity search we use is, however, not an ideal means to find long period signals since the sensitivity is degraded by a strong "red noise" component in the amplitude spectrum. The noise itself is a result of DC-level fluctuations (e.g. in the receiver) during an observation. In the above analysis of the survey data, we minimised the effects of this red noise component by subtracting a baseline off the spectrum before normalising it. However, because of the rapid increase of the red noise below about 0.1-Hz, we chose to ignore all spectral signals with frequencies below this value. Whilst this is common practice in pulsar search codes, it obviously reduces our sensitivity to [FORMULA] s pulsars! In recognition of this selection effect, we are currently re-analysing our data using a so-called "fast folding" algorithm (e.g. Staelin 1969) to search for periodic signals in the period range 3-20 s. The results of this analysis, and a detailed discussion of the algorithm, will be presented elsewhere (Müller et al. in preparation).

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Online publication: June 26, 2000