4 Marginally detected pulsars

The WENSS source finding routines have a flux density threshold at five times the local noise level ( $5S_{\rm noise}$). Since in this paper single trials are done to find a correlation at a very small number of positions, a $3S_{\rm noise}$ source can be marked as a marginal detection.

Figure 4: WENSS flux density as a function of the extrapolated pulsar flux density (PSR S325) for the 25 correlated objects (filled symbols) and for the marginal objects (clear symbols). PSR J0218+4232 is marked with a square. PSR B0329+54 and PSR B2021+51 show indications for a low frequency turnover and are marked with a triangle

However, source fitting is less acurate. Therefore, a 5 by 5 pixel box (1.75$^\prime$) centered around the pulsar position is searched for the pixel with the maximum flux density. This pixel was marked as a marginal detection, if its flux density was greater than $3S_{\rm noise}$. The positional uncertainty for these marginal sources is estimated using the same equation as for the fitted sources (Rengelink et al. 1997). The positional error for these marginal sources is approximately 42 $^{\prime \prime }$. Since a 1.75$^\prime$ box is searched, no marginal detection is missed.

The probability of finding a $3S_{\rm noise}$ (or higher) pixel in a map with Gaussian noise is 2.7 10^-3. About 5 WENSS FWHM beams fit into a 5 $\times$ 5 pixel box. Fifty-one boxes were searched. Effectively, 255 trials have been performed. The binomial probability that one $3S_{\rm noise}$ pixel is found is 0.35, the probability that two are found is 0.12 and that three are found is 0.03. Therefore, there is a 50 percent probability that (at least) one of our 14 marginal detection is just a noise fluctuation.

The maps of the marginal detections are shown in Fig. 6. The location of the pixel with maximum flux density is also indicated. The shapes of these sources is not as point-like as the strong detections with $S > 5 S_{\rm noise}$. The flux densities of the marginal detections are listed in Table 3, together with an estimate of the pulsar flux density based on a similar extrapolation of the pulsar spectrum as done in Sect. 3.2. The estimate for PSR J1518+4904 is based on its measured flux density at 370 MHz (Sayer et al. 1997), since its spectrum as plotted by Kramer et al. (1999) shows evidence for a low frequency turnover.

The ratios of the extrapolated pulsar flux density and the WENSS source flux density are displayed in Fig. 4. The spread is of the order of a factor 1.5, which is comparable with the spread for the detected sources that were discussed in the previous section. Five sources were detected, although their expected flux density was below three times the local noise level (see Table 3). The flux density at 325 MHz could not be estimated for three other pulsars, since no reliable flux density data at other frequencies were available.

The contours of four pulsars are confused by nearby radio sources. These sources are discussed in the following and are shown in Fig. 7.

PSR B0655+64: the WENSS source and the pulsar position are 4.3$\sigma$ apart. The estimated flux density of the pulsar at 325 MHz is $7\pm 2$ mJy, but the WENSS source is $23 \pm 5$ mJy. Also, the NVSS (see Sect. 7) shows a radio source at the WENSS position and clearly away from the pulsar position. Its flux density at 1400 MHz is about 5.6 mJy, while the pulsar flux density is expected to be $0.3\pm 0.1$ mJy. The pulsar has a proper motion, but it is small and directed towards negative declinations.

PSR B1112+50: The WENSS source is bright (135 mJy) and has an accurate position. The separation between the fitted WENSS position and the known pulsar position is $4.6\sigma$. Extrapolation of the pulsar spectrum results in an estimated flux density at 325 MHz of $16 \pm 3$ mJy, much less than that of the WENSS source. Kaplan et al. (1998) and Han & Tian (1999) searched the NVSS for pulsar counterparts and also noted that the pulsar is confused by a strong NVSS source 12 $^{\prime \prime }$ away.

PSR B1951+32: The coincident source in the WENSS catalog is marked as extended and the emission is dominated by the supernova remnant CTB80. The pulsar is associated with this remnant (Strom 1987; Kulkarni et al. 1988). The WENSS peak flux density is 983 mJy, which is about a factor 70 stronger than the expected pulsar flux density.

Figure 5: Maps of pulsars that are detected in the WENSS. The plots are centered around the pulsar position, marked with a cross. The grey oval in the lower left corner indicates the FWHM beam size. Contour levels are at 5, 10, 15, 20, 28, 40, 64, 128, 256, 512 and 1024 mJy (drawn lines) and at -5 and -10 mJy (dotted lines)

Figure 6: WENSS maps of the marginal detections which are correlated with a pulsar. The plots are centered around the pulsar position, marked with a cross. The dots indicate the maximum pixel in a 5 $\times$ 5 pixel box around the centrum. The grey oval in the lower left corner indicates the beam size. Contour levels at 5, 10, 15, 20, 28, 40, 64, 128, 256, 512 and 1024 mJy (drawn lines) and at -5 and -10 mJy (dotted lines)

  

Table 3: List of estimated pulsar flux densities (PSR S₃₂₅), WENSS maximum pixel flux densities (WENSS S₃₂₅), the local noise level in the WENSS map ( $S_{\rm noise}$) and the ratio R of the WENSS flux density and the noise level for the 14 marginal detections. PSR B0053+47 and PSR B0153+39 have only upper limits for their spectral index, so they have a lower limit for their 325 MHz flux density. The estimate for PSR J1518+4904 is based on its 370 MHz flux density (see text). "D'' in the last column indicates that a source near the pulsar position was detected, although its expected flux density was below three times the local noise level

$$\begin{tabular}{lr@{.}l@{ $\pm$ }r@{.}lr@{ $\pm$ }rrrl} \hlin... ...& 1&8 & 27 &12& 8.9 & 3.0 & D\\ \\ \hline\hline \end{tabular}$$

PSR B2306+55: It can be clearly seen in the map that this source has two components, of which the weaker one is probably the counterpart to the pulsar. This component is not listed in the WENSS source list. The estimated pulsar flux density is about $30 \pm 3$ mJy. The bright component of the WENSS source is $125 \pm 9$ mJy, separated $28\sigma$ from the pulsar position. The second component has a flux density of approximately 24 mJy.

Figure 7: WENSS maps of the pulsars, which are confused by other radio sources. The plots are centered around the pulsar position, marked with a cross. The grey oval in the lower left corner indicates the beam size. Contour levels at 5, 10, 15, 20, 28, 40, 64, 128, 256, 512 and 1024 mJy (drawn lines) and at -5 and -10 mJy (dotted lines)

In all these four cases I conclude that the source in the WENSS catalog and the pulsar are unrelated. Galama et al. (1997) reached the same conclusion for PSR B0655+64.