On the pulse-width statistics in radio pulsars – I. Importance of the interpulse emission

We performed Monte Carlo simulations of different properties of pulsar radio emission, such as: pulsar periods, pulse–widths, inclination angles and rates of occurrence of interpulse emission (IP). We used recently available large data sets of the pulsar periods P, the pulse profile widths W and the magnetic inclination angle �. We also compiled the largest ever database of pulsars with interpulse emission, divided into the double–pole (DP–IP) and the single–pole (SP–IP) cases. We identified 31 (about 2%) and 13 (about 1%) of the former and the latter, respectively, in the population of 1520 normal pulsars. Their distribution on the P u P diagram strongly suggests a secular alignment of the magnetic axis from the originally random orientation. We derived possible parent distribution functions of important pulsar parameters by means of the Kolmogorov–Smirnov significance test using the available data sets (P, W, � and IP), different models of pulsar radio beam � = �(P) as well as different trial distribution functions of pulsar period P and the inclination angles �. The best suited parent period distribution function is the log–normal distribution, although the gamma function distribution cannot be excluded. The strongest constraint on derived model distribution functions was the requirement that the numbers of interpulses generated by means of Monte Carlo simulations (both DP–IP and SP–IP cases) were exactly (within 1� errors) at the observed level of occurrences. We found that a suitable model distribution function for the inclination angle is the complicated trigonometric function which has two local maxima, one near 0 � and the other near 90 � . The former and the latter implies the right rates of IP, occurrence, single–pole (almost aligned rotator) and double–pole (almost orthogonal rotator), respectively. It is very unlikely that the pulsar beam deviates significantly from the circular cross-section. We found that the upper limit for the average beaming factor fb describing a fraction of the full sphere (called also beaming fraction) covered by a pulsar beam is about 10%. This implies that the number of the neutron stars in the Galaxy might be underestimated.