Population statistics study of radio and gamma-ray pulsars in the Galactic plane

We present results of our pulsar population synthesis of normal and millisecond pulsars in the Galactic plane. Over the past several years, a program has been developed to simulate pulsar birth, evolution and emission using Monte Carlo techniques. We have added to the program the capability to simulate millisecond pulsars, which are old, recycled pulsars with extremely short periods. We model the spatial distribution of the simulated pulsars by assuming that they start with a random kick velocity and then evolve through the Galactic potential. We use a polar cap/slot gap model for γ-ray emission from both millisecond and normal pulsars. From our studies of radio pulsars that have clearly identifiable core and cone components, in which we fit the polarization sweep as well as the pulse profiles in order to constrain the viewing geometry, we develop a model describing the ratio of radio core-to-cone peak fluxes. In this model, short period pulsars are more cone-dominated than in our previous studies. We present the preliminary results of our recent study and the implications for observing these pulsars with GLAST and AGILE.      

High-energy emission from millisecond pulsars: polar cap models

The viability of polar cap models for high-energy emission from millisecond pulsars is discussed. It is shown that in millisecond pulsars, polar gap acceleration along the last open field lines is radiation-reaction limited, that is, the maximum energy to which particles can be accelerated is determined by balancing the energy-loss rate (due to curvature radiation) with the gap-acceleration rate. The maximum Lorentz factor is limited by curvature radiation and is not sensitive to the specific acceleration model. However, the distance (from the polar cap) at which the Lorentz factor achieves the limit is model dependent, and can be between one-hundredth (for the vacuum gap) and above one-tenth (for the space-charge limited gap) of a stellar radius distant from the polar cap for a pulsar period P =2 ms and a surface magnetic field B =7.510⁴ T. Because of the radiation reaction constraint and the relatively weak magnetic field, both the expected multiplicity (number of pairs per primary particle) and the Lorentz factor of the outflowing one-dimensional magnetospheric e^± plasma from the polar gap are considerably lower than those for normal pulsars. Assuming space-charge limited flow, the location of the pair production front (PPF) is estimated to occur at about one stellar radius above the polar cap, which is significantly higher than that for normal pulsars. If the observed X-ray emission originates in the region near or above the PPF, the wide hollow-cone can reproduce the observed wide double-peaked feature of the light curves without using the aligned rotator assumption.     

Studying millisecond pulsars in X-rays

Millisecond pulsars represent an evolutionarily distinct group among rotation-powered pulsars. Outside the radio band, the soft X-ray range (～0.1–10 keV) is most suitable for studying radiative mechanisms operating in these fascinating objects. X-ray observations revealed diverse properties of emission from millisecond pulsars. For the most of them, the bulk of radiation is of a thermal origin, emitted from small spots (polar caps) on the neutron star surface heated by relativistic particles produced in pulsar acceleration zones. On the other hand, a few other very fast rotating pulsars exhibit almost pure nonthermal emission generated, most probably, in pulsar magnetospheres. There are also examples of nonthermal emission detected from X-ray nebulae powered by millisecond pulsars, as well as from pulsar winds shocked in binary systems with millisecond pulsars as companions. These and other most important results obtained from X-ray observations of millisecond pulsars are reviewed in this paper, as well as results from the search for millisecond pulsations in X-ray flux of the radio-quite neutron star RX J1856.5-3754.     

The structure of integrated pulse profiles

We offer two possible explanations to account for the characteristics of integrated pulse profiles, in particular their degree of complexity, their variation from pulsar to pulsar, their stability, and the tendency of complex profiles to be associated with older pulsars. It is proposed that the pulse structure could be a reflection of surface irregularities at the polar caps, and it is shown how the surface relief can affect the number of positrons released into the magnetosphere which are subsequently responsible for the observed radio radiation. The electrons produced in the vacuum break-down in the gap carry enough energy to allow creating such a surface relief in ∼ 10⁶ years, and one way in which this could be achieved is discussed. Alternatively, the presence of multipole components in the magnetic fields of older pulsars could lead to significant variations in the curvature of the field lines across the gap, and hence to structure in the integrated pulse profiles. An assessment of the two hypotheses from observed pulse profiles seems to favour the polar cap relief picture. An erratum to this article is available at .     

Morphology and characteristics of radio pulsars

This review describes the observational properties of radio pulsars, fast rotating neutron stars, emitting radio waves. After the introduction we give a list of milestones in pulsar research. The following chapters concentrate on pulsar morphology: the characteristic pulsar parameters such as pulse shape, pulsar spectrum, polarization and time dependence. We give information on the evolution of pulsars with frequency since this has a direct connection with the emission heights, as postulated in the radius to frequency mapping (RFM) concept. We deal successively with the properties of normal (slow) pulsars and of millisecond (fast-recycled) pulsars. The final chapters give the distribution characteristics of the presently catalogued 1300 objects.Received: 5 December 2003, Published online: 15 April 2004 Correspondence to: Richard Wielebinski     

The efficiency of gamma-ray emission from pulsars

We present a modified scenario of gamma-ray emission from pulsars within the framework of polar cap models. Our model incorporates the possible acceleration of electron–positron pairs created in magnetospheres, and their subsequent contribution to the gamma-ray luminosity L _γ. It also reproduces the empirical trend in L _γ for seven pulsars detected with Compton Gamma-Ray Observatory ( CGRO ) experiments. At the same time it avoids basic difficulties faced by theoretical models when confronted with observational constraints.   We show that the classical and millisecond pulsars form two distinct branches in the L _γ— L _sd diagram (where L _sd is the spin-down luminosity). In particular, we explain why the millisecond pulsar J0437−4715 has not been detected with any of the CGRO instruments despite its very high position in the ranking list of spin-down fluxes (i.e. L _sd/ D ², where D is a distance). The gamma-ray luminosity predicted for this particular object is about one order of magnitude below the upper limit set by EGRET.     

Periodic nulls in the pulsar B1133+16

Numerous studies of the brightest Cambridge pulsar, B1133+16, have revealed little order in its individual pulses, apart from a weak 30-odd-rotation-period fluctuation feature and that some 15 per cent of the star's pulsars are 'nulls'. New Arecibo observations confirm this fluctuation feature and that it modulates all the emission, not simply the 'saddle' region. By replacing each pulse with a scaled version of the average profile, we were able to quench all subpulse modulation and thereby demonstrate that the star's 'null' pulses exhibit a similar periodicity. A subbeam carousel model with a sparse and irregular 'beamlet' population appears to be compatible with these characteristics.     

毫秒脉冲星定时研究进展

毫秒脉冲星守时的理论和方法研究己取得重要进展,利用现有2颗毫秒脉冲星约10yr的计时观测资料分析得到的 TAI-PT,其长期稳定度为 2×10－14。采用合适的长期稳定度算法,由多颗毫秒脉冲星计时观测可以建立综合脉冲星时间尺度。它可以成为与原子时系统比较的重要手段,并对原子时长期稳定度的改进做出贡献。介绍了该领域研究的基本状况,重点对毫秒脉冲星守时的理论方法,综合脉冲星时间及与原子时的关系等进行了讨论和评述。对由双星系统内毫秒脉冲星的轨道运动定义的双星脉冲星时也做了介绍。     

Spectral Constraints for Millisecond Pulsars Due to General Relativistic Frame Dragging

We develop a numerical code for simulating the magnetospheres of millisecond pulsars, which are expected to have unscreened electric potentials due to the lack of magnetic pair production. We incorporate General Relativistic (GR) expressions for the electric field and charge density and include curvature radiation (CR) due to primary electrons accelerated above the stellar surface, whereas inverse Compton scattering (ICS) of thermal X-ray photons by these electrons are neglected as a second-order effect. We apply the model to PSR J0437-4715, a prime candidate for testing the GR-Electrodynamic theory, and find that the curvature radiation spectrum cuts off at energies below 15 GeV, which are well below the threshold of the H.E.S.S. telescope, whereas Classical Electrodynamics predict a much higher cutoff near 100 GeV, which should be visible for H.E.S.S., if standard assumed Classical Electrodynamics apply. GR theory also predicts a relatively narrow pulse (2φ _L ∼ 0.2 phase width) centered on the magnetic axis, which sets the beaming solid angle to ∼0.5 sr per polar cap (PC) for a magnetic inclination angle of 35^∘ relative to the spin axis, given an observer which sweeps close to the magnetic axis. We also find that EGRET observations above 100 MeV of this pulsar constrain the polar magnetic field strength to B _pc < 4× 10⁸ G for a pulsar radius of 10 km and moment of inertia of 10⁴⁵ g cm². The field strength constraint becomes even tighter for a larger radius and moment of inertia. Furthermore, a reanalysis of the full EGRET data set of this pulsar, assuming the predicted pulse shape and position, should lead to even tighter constraints on neutron star and GR parameters, up to the point where the GR-derived potential and polar cap current may be questioned.     

Nulling,Mode-Changing and Drifting Subpulses in the Highly Asymmetric Conal Quadruple Radio Pulsar B2034$$$$19

Radio pulsar B2034\(+\)19 exhibits all three ‘canonical’ pulse-sequence phenomena—that is, pulse nulling, two distinct profile modes and subpulses with periodic modulation. Indeed, the bursts and nulls in the pulsar are short at several score pulses and quasi-periodic such that about 1/3 of the pulses are nulls. The pulsar’s two modes have very different characteristics, the first shows emission almost completely confined to the leading half of the profile and highly modulated in a 2-period odd–even manner; whereas the second mode illuminates both the leading and trailing parts of the star’s profile about equally with the appearance of drift bands at about a 3-period separation. The second mode occurs much less frequently than the first (about 15% of the time) and thus the leading part of the profile has a much larger average intensity than the trailing part. B2034\(+\)19 represents an interesting example of a pulsar with emission primarily in the leading part of its profile window with only occasional illumination in the trailing part. This suggests that there are pulsars that perhaps never emit in a part of their profile window, connecting with earlier work on pulsars with apparent ‘partial cone’ profiles.     

Pulse Width Measurements for Pulsars

There are a few methods of measuring pulse widths. Among the most often used pulse widths there are W_pp (the distance between two peak value points), W₅₀ (the width at the place of 50% of the highest peak intensity) and W10 (the width at the place of 10% of the highest peak intensity). In addition, there are also the width W_c50 at the place of 50% of their respective intensities and the width Wc10 at the place of 10% of the respective intensities of the two outermost components. The data of the pulse profiles of the sample of 16 double-cone peak pulsars and 7 core-cone triple peak pulsars at 1.4 GHz are utilized to measure 5 kinds of pulse widths. The pulsars with the data of the magnetic inclination α and impact angle β are employed to derive the corresponding radiation beam radius ρ, and the relation between ρ and the pulsar period P, ρ ∝ P^?0.5, is verified. Via a comparison between the qualities of the relation between ρ and P derived from the 5 kinds of pulse widths it is found that the width between the outermost components is better than any one of the first 3 kinds of widths, of which the correlative relation obtained from the W_c50 width is the best. From this it is considered that W_c50 is the measured value that can fully reflect the emission beam width. The symmetry of the pulse profile is also discussed and it is found that from the comparison with the preceding cone emission component the following cone emission component is much closer to the core emission component, and the widths of the two cone emission components are basically the same according to statistics.     

Searching for curvature pion radiation from protons in strongly magnetized pulsars

By using rather conservative estimates based on the simplest polar cap model, we search the ATNF Pulsar Catalogue for strongly magnetized stars that could accelerate relativistic protons up to the curvature pion production threshold. The best candidate turns out to be the 16 ms pulsar J0537-6910, but the corresponding characteristic parameter χ=a/m _p is yet too small to give origin to observable signals. We show that, for pulsars with period P≈1 ms, a surface polar magnetic field B≈10¹² G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered.     

Detection of giant radio pulses from the pulsar PSR B0656+14

Giant pulses (GPs) have been detected from the pulsar PSR B0656 + 14. A pulse that is more intense than the average pulse by a factor of 120 is encountered approximately once in 3000 observed periods of the pulsar. The peak flux density of the strongest pulse, 120 Jy, is a factor of 630 higher than that of the average pulse. The GP energy exceeds the energy of the average pulse by up to a factor of 110, which is comparable to that for other known pulsars with GPs, including the Crab pulsar and the millisecond pulsar PSR B1937+21. The giant pulses are a factor of ～6 narrower than the average pulse and are clustered at the head of the average pulse. PSR B0656+14 along with PSR B0031-07, PSR B1112+50, and PSR J1752+2359 belong to a distinctive group of pulsars in which GPs have been detected without any extremely strong magnetic field on the light cylinder.     

High-energy γ-rays from globular clusters

It is expected that specific globular clusters (GCs) can contain up to a hundred of millisecond pulsars. These pulsars can accelerate leptons at the shock waves originated in collisions of the pulsar winds and/or inside the pulsar magnetospheres. Energetic leptons diffuse gradually through the GC Comptonizing stellar and microwave background radiation. We calculate the GeV–TeV γ-ray spectra for different models of injection of leptons and parameters of the GCs assuming reasonable, of the order of 1 per cent, efficiency of energy conversion from the pulsar winds into the relativistic leptons. It is concluded that leptons accelerated in the GC cores should produce well localized γ-ray sources which are concentric with these GCs. The results are shown for four specific GCs (47 Tuc, Ter 5, M13 and M15), in which significant population of millisecond pulsars have been already discovered. We argue that the best candidates, which might be potentially detected by the present Cherenkov telescopes and the planned satellite telescopes (AGILE, GLAST), are 47 Tuc on the Southern hemisphere, and M13 on the Northern hemisphere. We conclude that detection (or non-detection) of GeV–TeV γ-ray emission from GCs by these instruments put important constraints on the models of acceleration of leptons by millisecond pulsars.     

The Geminga fraction

Radio-quiet γ-ray pulsars like Geminga may account for a number of the unidentified EGRET sources in the Galaxy. The number of Geminga-like pulsars is very sensitive to the geometry of both the γ-ray and radio beams. Recent studies of the shape and polarization of pulse profiles of young radio pulsars have provided evidence that their radio emission originates in wide cone beams at altitudes that are a significant fraction (1–10%) of their light cylinder radius. Such wide radio emission beams will be visible at a much larger range of observer angles than the narrow core components thought to originate at lower altitude. Using 3D geometrical modeling that includes relativistic effects from pulsar rotation, we study the visibility of such radio cone beams as well as that of the γ-ray beams predicted by slot gap and outer gap models. From the results of this study, one can obtain revised predictions for the fraction of Geminga-like, radio quiet pulsars present in the γ-ray pulsar population.      

The shape of pulsar beams

Observations of mean or average pulse profiles and their polarization give us much information on the shape of pulsar beams. The observed polarization variations, profile symmetry and frequency dependence of profile shape strongly suggest that the emission beam is conical and emitted from the vicinity of a magnetic pole. Central and outer parts of the beam have somewhat different properties, but the evidence is that they are emitted by the same basic mechanism. Recent observations suggest that the highly polarized pulse components seen in young pulsars may be emitted at a large angle to the magnetic axis.     

Polarization observations of 66 southern pulsars

Mean pulse profiles and polarization parameters at 435, 660 or 1500 MHz obtained using the ATNF Parkes radio telescope are presented for 66 southern pulsars. About half of these pulsars were discovered in the Parkes southern pulsar survey and most have no previously published polarization parameters. Where possible, beam impact parameters and inclination angles are computed assuming a circular beam geometry and the rotating-vector model. Implications of the results for models of the pulse emission mechanism are briefly discussed.     

Cyclotron absorption of radio emission within pulsar magnetospheres

Absorption of radio emission through normal cyclotron resonance within pulsar magnetospheres is considered. The optical depth for cyclotron damping is calculated using a plasma distribution with an intrinsically relativistic spread. We argue that such a broad distribution is plausible for pulsar plasmas and that it implies that a class of pulsars that should have cyclotron damping extends to include young pulsars with shorter periods and stronger magnetic fields. There is no obvious observational evidence for disruption of radio pulses, which implies that the optical depth cannot be too large. We propose that cyclotron resonance may cause marginal absorption of radio emission. It is shown that such marginal absorption produces potentially observable asymmetric features for double-peak pulse profiles with wide separation, with one peak tending to be suppressed.     

An empirical model for the beams of radio pulsars

Motivated by recent results on the location of the radio emission in pulsar magnetospheres, we have developed a model which can account for the large diversity found in the average profile shapes of pulsars. At the centre of our model lies the idea that radio emission at a particular frequency arises from a wide range of altitudes above the surface of the star, and that it is confined to a region close to the last open field lines. We assert that the radial height range over which emission occurs is responsible for the complex average pulse shapes rather than the transverse (longitudinal) range proposed in most current models. By implementing an abrupt change in the height range to discriminate between young, short-period, highly energetic pulsars and their older counterparts, we obtain the observed transition between the simple and complex average pulse profiles observed in each group respectively. Monte Carlo simulations are used to demonstrate the match of our model to real observations.     

Multifrequency integrated profiles of pulsars

We have observed a total of 67 pulsars at five frequencies ranging from 243 to 3100 MHz. Observations at the lower frequencies were made at the Giant Metre-Wave Telescope in India and those at higher frequencies at the Parkes Telescope in Australia. We present profiles from 34 of the sample with the best signal-to-noise ratio and the least scattering. The general 'rules' of pulsar profiles are seen in the data; profiles get narrower, the polarization fraction declines and outer components become more prominent as the frequency increases. Many counterexamples to these rules are also observed, and pulsars with complex profiles are especially prone to rule breaking. We hypothesize that the location of pulsar emission within the magnetosphere evolves with time as the pulsar spins down. In highly energetic pulsars, the emission comes from a confined range of high altitudes, in the middle range of spin down energies the emission occurs over a wide range of altitudes whereas in pulsars with low spin-down energies it is confined to low down in the magnetosphere.