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Register a new userOn the pulse--width statistics in radio pulsars. I. Importance of the interpulse emission
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Krzysztof Maciesiak
Publication date
2011
fields
Physics
and research's language is
English
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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.
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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.
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.
The Monte Carlo simulations of pulsar periods, pulse-widths and magnetic inclination angles are performed. Using the available observational data sets we study a possible trial parent distribution functions by means of the Kolmogorov-Smirnov significance tests. We also use an additional condition that the numbers of generated interpulses, whether from both magnetic poles or from single pole, are at the observed levels. We conclude that the parent distribution function of magnetic inclination angles is neither flat nor cosine but it is a more complicated function with a local maximum near alpha=25deg and another weaker one near alpha=90deg. The plausible distribution function of pulsar periods is represented by the gamma function. The beaming fraction describing the fraction of observable radio pulsars is about 0.12.
In the canonical picture of pulsars, radio emission arises from a narrow cone centered on the stars magnetic axis but many basic details remain unclear. We use high-quality polarization data taken with the Parkes radio telescope to constrain the geometry and emission heights of pulsars showing interpulse emission, and include the possibility that emission heights in the main and interpulse may be different. We show that emission heights are low in the centre of the beam, typically less than 3% of the light cylinder radius. The emission beams are under-filled in longitude, with an average profile width only 60% of the maximal beam width and there is a strong preference for the visible emission to be located on the trailing part of the beam. We show substantial evidence that the emission heights are larger at the beam edges than in the beam centre. There is some indication that a fan-like emission beam explains the data better than conal structures. Finally, there is a strong correlation between handedness of circular polarization in the main and interpulse profiles which implies that the hand of circular polarization is determined by the hemisphere of the visible emission.
We propose a new method to detect off-pulse (unpulsed and/or continuous) emission from pulsars, using the intensity modulations associated with interstellar scintillation. Our technique involves obtaining the dynamic spectra, separately for on-pulse window and off-pulse region, with time and frequency resolutions to properly sample the intensity variations due to diffractive scintillation, and then estimating their mutual correlation as a measure of off-pulse emission, if any. We describe and illustrate the essential details of this technique with the help of simulations, as well as real data. We also discuss advantages of this method over earlier approaches to detect off-pulse emission. In particular, we point out how certain non-idealities inherent to measurement set-ups could potentially affect estimations in earlier approaches, and argue that the present technique is immune to such non-idealities. We verify both of the above situations with relevant simulations. We apply this method to observation of PSR B0329+54 at frequencies 730 and 810 MHz, made with the Green Bank Telescope and present upper limits for the off-pulse intensity at the two frequencies. We expect this technique to pave way for extensive investigations of off-pulse emission with the help of even existing dynamic spectral data on pulsars and of course with more sensitive long-duration data from new observations.
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