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Register a new userOn the pulse-width statistics in radio pulsars. III. Importance of the conal profile components
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Krzysztof Maciesiak
Publication date
2012
fields
Physics
and research's language is
English
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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.
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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.
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.
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.
Timing noise in the data on accretion-powered millisecond pulsars (AMP) appears as irregular pulse phase jumps on timescales from hours to weeks. A large systematic phase drift is also observed in the first discovered AMP SAX J1808.4-3658. To study the origin of these timing features, we use here the data of the well studied 2002 outburst of SAX J1808.4-3658. We develop first a model for pulse profile formation accounting for the screening of the antipodal emitting spot by the accretion disk. We demonstrate that the variations of the visibility of the antipodal spot associated with the receding accretion disk cause a systematic shift in Fourier phases, observed together with the changes in the pulse form. We show that a strong secondary maximum can be observed only in a narrow intervals of inner disk radii, which explains the very short appearance of the double-peaked profiles in SAX J1808.4-3658. By directly fitting the pulse profile shapes with our model, we find that the main parameters of the emitting spot such as its mean latitude and longitude as well as the emissivity pattern change irregularly causing small shifts in pulse phase, and the strong profile variations are caused by the increasing inner disk radius. We finally notice that significant variations in the pulse profiles in the 2002 and 2008 outbursts of SAX J1808.4-3658 happen at fluxes differing by a factor of 2, which can be explained if the inner disk radius is not a simple function of the accretion rate, but depends on the previous history.
A detailed analysis of nulling was conducted for the pulsars studied in the Meterwavelength Single-pulse Polarimetric Emission Survey. We characterized nulling in 36 pulsars including 17 pulsars where the phenomena were reported for the first time. The most dominant nulls lasted for short durations, less than five periods. The longer duration nulls extending to hundreds of periods were also seen in some cases. A careful analysis showed the presence of periodicities in the transition from the null to the burst states in 11 pulsars. In our earlier work fluctuation spectrum analysis showed multiple periodicities in 6 of these 11 pulsars. We demonstrate that the longer periodicity in each case was associated with nulling. The shorter periodicities usually originate due to subpulse drifting. The nulling periodicities were more aligned with the periodic amplitude modulation indicating a possible common origin for both. Most prevalent nulling lasts for a single period and can be potentially explained using random variations affecting the plasma processes in the pulsar magnetosphere. On the other hand, the longer duration nulls require changes in the pair production processes that need an external triggering mechanism for the change. The presence of periodic nulling puts an added constrain on the triggering mechanism which also needs to be periodic.
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