3. Search sensitivity
The sensitivity of the survey can be expressed in terms of the minimum detectable flux density which is a function of a number of parameters. Following Dewey et al. (1984), we write:
In this expression is the threshold signal-to-noise ratio above which a detection is considered significant (7 in our case), is a constant which reflects losses to hardware limitations, G is the gain of the telescope (1.0 K Jy-1 for the Lovell telescope operating at 606 MHz), n is the number of polarisations used, is the observing bandwidth, is the system temperature, is the integration time, P is the period of the pulsar and W is the observed width of the pulse. With the parameters for this survey, the above expression simplifies to
The system temperature is the sum of separate components: the set noise of the receiver ; the sky background noise and the contribution from continuum flux of the supernova remnant. Regular calibration measurements made during the survey indicated to be typically 50 K. The contribution to from the Galactic background and the supernova remnant covers a large range. This is shown in Table 1 where we list the estimated sky background temperatures from a machine-readable version of the Haslam et al. (1982) all-sky survey, scaled to 606 MHz assuming a spectral index of -2.7 (Lawson et al. 1987) together with the expected contribution from each supernova remnant. To calculate the latter values, we estimated the flux density of the remnant at 606 MHz from spectral information in Green's (1996) catalogue and multiplied this by the beam filling factor, defined as the lesser of unity and , where is the angular diameter of the supernova remnant. Using these values in Eq. 2, we have estimated the minimum flux density required to detect a 0.1 s pulsar with a duty cycle of 4% in each remnant. These limiting flux densities are listed in Table 1 for reference. With typical values of 1 mJy at 606 MHz, they demonstrate the excellent sensitivity of the survey. We note from Table 1 that is a significant factor for only 3 of the 33 SNRs searched.
The observed pulse width W in Eqs. 1and 2is likely to be greater than the intrinsic width 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 observed sampled pulse profile will therefore be the convolution of the intrinsic pulse width and broadening functions due to dispersion, scattering and integration and can be estimated approximately from the following quadrature sum:
where is the data sampling interval, is the dispersion broadening across one filterbank channel and is the interstellar scatter broadening. Pulse scattering becomes particularly important when observing distant pulsars towards the inner Galaxy at frequencies 1 GHz. Many of the supernova remnants in our sample are relatively nearby 5 kpc so that we do not expect a significant effect on our sensitivity due to scattering.
The effects of sampling and dispersion do, however, significantly affect the search sensitivity at short pulse periods. This is shown in Fig. 1, where is plotted against P for a pulsar with a dispersion measure of 150 cm-3 pc, a typical value for a pulsar at the distance of one of the remnants in our sample (see Sect. 5.2). We have also calculated the reduction in sensitivity at short periods due to the loss of higher order harmonics in the power spectrum - shown by the abrupt jumps in the sensitivity curve shown in Fig. 1.
It is worth noting that our search had only limited sensitivity to any high-velocity pulsars that may have moved outside the projected boundaries of their parent supernova remnants. The dotted curve in Fig. 1 gives the approximate sensitivity to a pulsar lying 0.25 degrees outside the remnant boundary and indicates a limiting 600 MHz flux density 20 mJy. Such bright pulsars should have been found in previous large scale surveys of the northern sky. Future surveys targeted specifically outside the periphery of the remnants will substantially improve the sensitivity to fainter pulsars.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998