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 (IP) emission. We used recently available large data sets of the pulsar periods P, the pulse profile widths W and the magnetic inclination angle α. We also compiled the largest ever data base of pulsars with IP, divided into the double pole (DP-IP) and the single pole (SP-IP) cases. We identified 31 (about 2 per cent) and 13 (about 1 per cent) of the former and the latter, respectively, in the population of 1520 normal pulsars. Their distribution on the 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, α and IP), different models of pulsar radio beam ρ=ρ(P) as well as different trial distribution functions of pulsar period P and the inclination angles α. The best suited parent period distribution function is the lognormal distribution, although the gamma function distribution cannot be excluded. The strongest constraint on derived model distribution functions was the requirement that the numbers of IPs generated by means of Monte Carlo simulations (both DP-IP and SP-IP cases) were exactly (within 1σ 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 imply 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 f_b describing a fraction of the full sphere (called also beaming fraction) covered by a pulsar beam is about 10 per cent. This implies that the number of the neutron stars in the Galaxy might be underestimated.