On the pulse-width statistics in radio pulsars. III. Importance of the conal profile components

This work is a continuation of two previous papers of a series, in which we examined the pulse-width statistics of normal radio pulsars. In the first paper we compiled the largest ever database of pulsars with interpulses in their mean profiles. In the second one we confirmed the existence of the lower boundary in the scatter plot of core component pulse-widths versus pulsar period W50 sim 2.5 P^{-0.5}[deg], first discovered by Rankin using much smaller number of interpulse cases. In this paper we show that the same lower boundary also exists for conal profile components. Rankin proposed a very simple method of estimation of pulsar inclination angle based on comparing the width W50 of its core component with the period dependent value of the lower boundary. We claim that this method can be extended to conal components as well. To explain an existence of the lower boundary Rankin proposed that the core emission originates at or near the polar cap surface. We demonstrated clearly that no coherent pulsar radio emission can originate at altitudes lower than 10 stellar radii, irrespective of the actual mechanism of coherence. We argue that the lower boundary reflects the narrowest angular structures that can be distinguished in the average pulsar beam. These structures represent the core and the conal components in mean pulsar profiles. The P^{-0.5} dependence follows from the dipolar nature of magnetic field lines in the radio emission region, while the numerical factor of about 2.5 deg reflects the curvature radius of a non-dipolar surface magnetic field in the partially screened gap above the polar cap, where dense electron-positron plasma is created. Both core and conal emission should originate at altitudes of about 50 stellar radii in a typical pulsar, with a possibility that the core beam is emitted at a slightly lower heights than the conal ones.

On the pulse-width statistics in radio pulsars. II. Importance of the core profile components

We performed a statistical analysis of half-power pulse-widths of the core components in average pulsar profiles. We confirmed an existence of the lower bound of the distribution of half-power pulse-width versus the pulsar period W50~2.45deg P^(-0.5) found by Rankin (1990). Using our much larger database we found W50= (2.51 +/- 0.08)deg P^(-0.50 +/-0.02) for 21 pulsars with double-pole interpulses for which measurement of the core component width was possible. On the other hand, all single-pole interpulse cases lie in the swarm of pulsars above the boundary line. Using the Monte Carlo simulations based on exact geometrical calculations we found that the Rankins method of estimation of the inclination angle alpha ~ asin(2.45deg P^(-0.5)/W50) in pulsars with core components is quite good an approximation, except for very small angles alpha in almost aligned rotators.

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 alpha. 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. Their distribution on the P - Pdot 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, alpha and IP), different models of pulsar radio beam rho = rho(P) as well as different trial distribution functions of pulsar period 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 were exactly (within 1sigma 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 deg and the other near 90 deg. The former and the latter implies the right rates of IP occurrence. 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.