6. Pulsar-Supernova remnant pair statistics
In this section, we address the question: How many pulsar-supernova remnant pairs (which we shall hereafter refer to simply as pairs) are likely to occur by chance in the present sample? As mentioned previously, this question has been tackled in some detail by Gaensler & Johnston (1995a&b) who concluded that the majority of claimed associations are likely to be chance alignments. The main motivation for the present analysis is partly to approach the question from a different direction than the modelling of Gaensler & Johnston (1995b). Our analysis has the main advantage that it is somewhat simpler and more model-free than the method described by Gaensler & Johnston (1995b).
For the purposes of the analysis it is useful to characterise each pair by the dimensionless parameter which is independent of distance, defined as the ratio of the angular separation between the pulsar and the remnant centroid to the angular radius of the remnant. Thus pairs in which the pulsar is within the boundary of the remnant occur if , whereas indicates that the pulsar lies outside the remnant (see also Shull et al. 1989; Frail et al. 1994; Gaensler & Johnston 1995 a & b).
We are interested in deriving the distribution of that occurs by chance and comparing this directly with the observed distribution. For completely unrelated sets of pulsars and supernova remnants, the number of pairs occupying an annulus between and is proportional to , regardless of the relative densities of pulsars and supernova remnants over the plane of the sky. To demonstrate this, we decoupled the respective pulsar and supernova remnant samples by applying a systematic shift to the Galactic longitude of each pulsar and then calculating the distribution of . To improve the statistics, we performed this procedure for shifts of and degrees in the Galactic longitudes of the pulsars. The shift sizes were chosen so that they are small compared to changes in the density of both types of objects on the sky, whilst being larger than the angular size of any supernova remnant in Green's (1996) catalogue. The shifted samples therefore contain only pairs which are truly unrelated, allowing us to deduce the expected distribution of chance remnants. This distribution is shown in Fig. 3 and is in excellent agreement with the theoretical prediction shown by the straight line fit through the origin. The slope of the best-fit straight line shown in Fig. 3 is .
We are now in a position to apply this relationship, which is based on a superposition of four longitude-shifted samples, to the observed distribution of shown in Fig. 4. The straight line shown in this case thus has a slope which is one quarter the value derived above. Comparing the observed distribution with this straight line we see a clear excess of pairs with in the observed sample, whilst the distribution with is in good agreement with the theoretical prediction. The pair excess is clearly due to the fact that many of these are genuine associations, not chance line-of-sight alignments. From Fig. 4, we infer that pairs are likely to be genuinely associated.
The difference between the shifted and observed samples can also be seen in the lower panels of Figs. 3 and 4, where we have plotted the median characteristic age of the pulsars as a function of . The shifted samples show no significant deviation from a flat distribution with respect to , and have a median age of Myr. The observed sample however is clearly more youthful for than for for which the median characteristic age is again 1 Myr.
From an inspection of the observed sample and the available literature, we have compiled a list of the most likely associations in Table 4. A critical appraisal of each of these and other proposed associations can be found in the original references and see also Gaensler & Johnston (1995b) and Kaspi (1996). Note that this list is concerned only with Galactic associations and therefore does not include PSR B0540-69 associated with the supernova remnant in the LMC (Seward et al. 1984). Based on the above analysis and the available statistics, which suggested a total of pairs, we expect anything from zero to nine further pairs to represent genuine associations. Examples of further candidates include recently discovered remnants around PSRs B1643-43 and B1706-44 (Frail et al. 1994), PSR B1930+22 and G57.3-1.2 (Routledge & Vaneldik 1988) and PSR J0538+2817 and G180.0-1.7 (Anderson et al. 1996). In the absence of further information to validate these associations, we list the 8 sources in Table 4.
Table 4. A compilation of the most likely genuine pulsar-supernova remnant pairs with . Our statistical analysis suggests that, at most, a further nine pairs may be real (see text).
As discussed in Sect. 5.1, both of the newly discovered pulsars in this survey, PSRs J0215+6218 and J1957+2831, have characteristic ages much larger than that expected for their target remnants. If they were to be genuinely associated with these remnants, then both the pulsars would have had to have been born with periods similar to the presently observed values, 0.5 and 0.3 seconds, in order to explain the large characteristic ages. In addition, the respective observed value of for these pulsars 0.7 and 0.8 does not place them in the group of pairs most likely to be genuinely associated. Based on the results of the above analysis, there is no strong statistical requirement for either of these pulsars to be associated with the remnants although they cannot be entirely ruled out.
Whether a significant number of radio pulsars were born with such long periods is controversial. Several authors, notably Vivekanand & Narayan (1981), Narayan (1987), Narayan & Ostriker (1990) and Deshpande et al. (1995) have found evidence for "injection" of pulsars into the population with periods ms, however other authors (Lyne et al. 1985; Stollman 1987; Lorimer et al. 1993) find no requirement for it. From an inspection of the pulse periods listed in Table 4, with the possible exception of PSR B2334+61, none of the pulsars listed in Table 4 are likely to have had such long periods at birth. Indeed Kulkarni et al. (1993) argue that PSR B2334+61 is the energy source to G114.3+0.3, which appears to be a Crab-like nebula. In this case, the initial period of B2334+61 must have been 100 ms. Thus the simplest, and most likely conclusion, to be drawn from the present sample of pulsar-supernova remnant pairs is that they support the notion that all pulsars are born with initial spin periods 100 ms.
Finally we wish to point out that, whilst our method is in principle sensitive to pairs over a large range in , the sample that we have used for our analysis is far from homogeneous. Therefore any real pairs with 1 are most likely to be underestimated in the present sample in comparison with those with 1 since many of the targeted searches for pulsars in remnants have concentrated mainly close to the remnant centre. Indeed, together with the searches by Gorham et al. (1996) and Kaspi et al. (1996), our search represents the first major effort to search the entire area, rather than just the centroid, of many of the more extended supernova remnants. Further searches with improved sensitivity to pulsars with 1 will improve the situation. New multibeam searches of the Galactic plane, presently underway at Parkes and Jodrell Bank, should provide a more homogeneous sample for further statistical studies.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998