Spectral features in gamma-rays expected from millisecond pulsars

In the advent of next generation gamma-ray missions, we present general properties of spectral features of high-energy emission above 1 MeV expected for a class of millisecond, low magnetic field (∼10⁹ G) pulsars. We extend polar-cap model calculations of Rudak & Dyks by including inverse Compton scattering events in an ambient field of thermal X-ray photons and by allowing for two models of particle acceleration. In the range between 1 MeV and a few hundred GeV, the main spectral component is the result of curvature radiation of primary particles. The synchrotron component arising from secondary pairs becomes dominant only below 1 MeV. The slope of the curvature radiation spectrum in the energy range from 100 MeV to 10 GeV strongly depends on the model of longitudinal acceleration, whereas below ∼100 MeV all slopes converge to a unique value of 4/3 (in a ν ℱ _ν convention). The thermal soft X-ray photons, which come either from the polar cap or from the surface, are Compton upscattered to a very high energy domain and form a separate spectral component peaking at ∼1 TeV. We discuss the observability of millisecond pulsars by future high‐energy instruments and present two rankings relevant for GLAST and MAGIC. We point to the pulsar J0437−4715 as a promising candidate for observations.     

The role of multipolar magnetic fields in pulsar magnetospheres

We explore the role of complex multipolar magnetic fields in determining physical processes near the surface of rotation powered pulsars. We model the actual magnetic field as the sum of global dipolar and star-centred multipolar fields. In configurations involving axisymmetric and uniform multipolar fields, 'neutral points' and 'neutral lines' exist close to the stellar surface. Also, the curvature radii of magnetic field lines near the stellar surface can never be smaller than the stellar radius, even for very high-order multipoles. Consequently, such configurations are unable to provide an efficient pair-creation process above pulsar polar caps, necessary for plasma mechanisms of generation of pulsar radiation. In configurations involving axisymmetric and non-uniform multipoles, the periphery of the pulsar polar cap becomes fragmented into symmetrically distributed narrow subregions where curvature radii of complex magnetic field lines are less than the radius of the star. The pair-production process is only possible just above these 'favourable' subregions. As a result, the pair plasma flow is confined within narrow filaments regularly distributed around the margin of the open magnetic flux tube. Such a magnetic topology allows us to model the system of 20 isolated subbeams observed in PSR B0943+10 by Deshpande & Rankin. We suggest a physical mechanism for the generation of pulsar radio emission in the ensemble of finite subbeams, based on specific instabilities. We propose an explanation for the subpulse drift phenomenon observed in some long-period pulsars.     

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.     

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.     

Can the inner gap sparking take place in millisecond pulsars？

The inner vacuum gap model has become the foundation stone of most theories on pulsar radio emission. The fundamental picture of this model is the sparking, which was conjectured to be induced by magnetic absorption of background gamma photons. However, a question is, can the sparking be triggered in the millisecond pulsars (MSPs) with magnetic fields (B) only about 108 G? We investigate this problem by including the pair production above the inner gap. Under the assumption that the magnetic field is dipolar, our results show the background gamma-ray emission can not be the key factor that triggers the sparking, at least not in MSPs with B - 108 G, if the temperature in the polar cap region is only so high as is observed (< 4 × 106 K). Some other mechanisms are required.     

The terminal bulk Lorentz factor of relativistic electron–positron jets

We present a numerical simulation of the bulk Lorentz factor of a relativistic electron–positron jet driven by the Compton rocket effect from accretion disc radiation. The plasma is assumed to have a power-law distribution n _e(γ) ∝ γ^{− s} with 1 < γ < γ_max and is continuously reheated to compensate for radiation losses. We include the full Klein–Nishina (hereafter KN) cross-section, and study the role of the energy upper cut-off γ_max, spectral index s and source compactness. We determine the terminal bulk Lorentz factor in the cases of supermassive black holes, relevant to AGN, and stellar black holes, relevant to galactic microquasars. In the latter case, Klein–Nishina cross-section effects are more important and induce a terminal bulk Lorentz factor smaller than in the former case. Our result are in good agreement with bulk Lorentz factors observed in Galactic (GRS 1915+105, GRO J1655−40) and extragalactic sources. Differences in scattered radiation and acceleration mechanism efficiency in the AGN environment can be responsible for the variety of relativistic motion in those objects. We also take into account the influence of the size of the accretion disc; if the external radius is small enough, the bulk Lorentz factor can be as high as 60.     

The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.     

Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

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.     

One-dimensional electric field structure of an outer gap accelerator – III. Location of the gap and the gamma-ray spectrum

We investigate a stationary particle acceleration zone in the outer magnetosphere of an obliquely rotating neutron star. The charge depletion as a result of global current causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. As a result of this pair-production cascade, the replenished charges partially screen the electric field, which is self-consistently solved together with the distribution of particles and gamma-rays. If no current is injected at either of the boundaries of the accelerator, the gap is located around the so-called null surface, where the local Goldreich–Julian charge density vanishes. However, we find that the gap position shifts outwards (or inwards) when particles are injected at the inner (or outer) boundary. We apply the theory to the seven pulsars whose X-ray fields are known from observations. We show that the gap should be located near to or outside of the null surface for the Vela pulsar and PSR B1951+32, so that their expected GeV spectrum may be consistent with observations. We then demonstrate that the intrinsically large TeV flux from the outer gap of PSR B0540–69 is absorbed by the magnetospheric infrared photons, causing it to be undetectable. We also point out that the electrodynamic structure and the resultant GeV emission properties of millisecond pulsars are similar to young pulsars.     

Contribution to diffuse gamma-rays in the Galactic Centre region from unresolved millisecond pulsars

Diffuse gamma-rays in the Galactic Centre region have been studied. We propose that there exists a population of millisecond pulsars in the Galactic Centre, which emit GeV gamma-rays through synchrotron-curvature radiation as predicted by outer gap models. These GeV gamma-rays from unresolved millisecond pulsars probably contribute to the diffuse gamma-ray spectrum detected by EGRET which displays a break at a few GeV. We have used a Monte Carlo method to obtain simulated samples of millisecond pulsars in the Galactic Centre region covered by EGRET  (∼ 15)  according to the different period and magnetic field distributions from observed millisecond pulsars in the Galactic field and globular clusters, and superposed their synchrotron-curvature spectra to derive the total GeV flux. Our simulated results suggest that there probably exist about 6000 unresolved millisecond pulsars in the region of angular resolution of EGRET, the emissions of which could contribute significantly to the observed diffuse gamma-rays in the Galactic Centre.     

The Parkes Southern Pulsar Survey — II. Final results and population analysis

A survey of the entire southern sky for millisecond and low-luminosity pulsars using the ATNF Parkes radio telescope has now been completed. The survey detected 298 pulsars, of which 101 were previously unknown. The new pulsars include 17 millisecond pulsars. This is the largest sample of both normal and millisecond pulsars detected in any survey. Combining our sample with other recent surveys in the Northern Hemisphere, we present a statistical study of the populations of both normal and millisecond pulsars. We find that the improved statistics allow us to estimate the number and birth-rate of both types of pulsar down to a 400-MHz luminosity limit of 1 mJy kpc². The local surface densities of potentially observable normal pulsars and millisecond pulsars are both about 30 kpc⁻², corresponding to ∼ 30000 potentially observable pulsars of each type in the Galaxy. Once beaming effects are taken into consideration we estimate that the active population of normal pulsars is ∼ 160000. Although there is evidence for flattening of the luminosity function of normal pulsars, this is not evident for millisecond pulsars which probably have a substantial population with luminosities below 1 mJy kpc². After correcting for beaming effects, we estimate that a normal pulsar is born with a luminosity greater than 1 mJy kpc² between once every 60 and 330 yr in the Galaxy. The birth-rate of millisecond pulsars is at least 3 × 10⁻⁶ yr⁻¹ above the same luminosity limit. Modelling the observed transverse speeds of millisecond pulsars using a dynamical simulation, we find their mean birth velocity to be 130 ± 30 km s⁻¹, significantly lower than that of the normal pulsars.     

TeV neutrinos and gamma-rays from pulsars

Recent studies suggest that pulsars could be strong sources of TeV muon neutrinos provided positive ions are accelerated by pulsar polar caps to PeV energies. In such a situation, muon neutrinos are produced through the Δ-resonance in interactions of pulsar-accelerated ions with its thermal radiation field. High-energy gamma-rays should also be produced simultaneously in pulsar environment as both charged and neutral pions are generated in the interactions of energetic hadrons with the ambient photon fields. Here, we estimate TeV gamma-ray flux at the Earth from a few nearby young pulsars. When compared with the observations, we find that proper consideration of the effect of polar cap geometry in flux calculation is important. Incorporating such an effect, we obtain the (revised) event rates at the Earth due to a few potential nearby pulsars. The results suggest that pulsars are unlikely to be detected by the upcoming neutrino telescopes. We also estimate TeV gamma-ray and neutrino fluxes from pulsar nebulae for the adopted model of particle acceleration.     

Millisecond pulsar radiation properties

Two investigations of millisecond pulsar radiation are discussed: average total intensity pulse morphology and individual pulse to pulse fluctuations. The average emission profiles of millisecond pulsars are compared with those of slower pulsars in the context of polar cap models. In general the full widths of pulsar emission regions continue to widen inversely with periodP as P^-(0.30-0.5) as expected for dipole polar cap models. Many pulse components are very narrow. The period scaling of pulsar profiles -separations and widths -can tell us about the angular distribution of radiating currents. An investigation of individual pulses from two millisecond pulsars at 430 MHz shows erratic pulse to pulse variations similar to that seen in slow pulsars. PSR B1937+21 displays occasional strong pulses that are located in the trailing edge of the average profile with relative flux densities in the range of 100 to 400. These are similar to the giant pulses seen in the Crab pulsar.     

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.     

Pulsar Slot Gaps and Unidentified Egret Sources

A new picture of pulsar high-energy emission is proposed that is different from both the traditional polar cap and outer gap models, but combines elements of each. The slot gap model is based on electron acceleration along the edge of the open field region from the neutron star surface to near the light cylinder and thus could form a physical basis for the two-pole caustic model of Dyks and Rudak (2003). Along the last open field line, the pair formation front rises to very high altitude forming a slot gap, where the accelerating electric field is unscreened by pairs. The resulting radiation features both hollow cones from the lower-altitude pair cascades, seen at small viewing angles, as well as caustic emission on the trailing-edge field lines at high altitude, seen from both poles at large viewing angle. The combination of the small solid angle of slot gap emission (≪ 1 sr) with a high probability of viewing the emission predicts that more gamma-ray pulsars could be detected at larger distances. In this picture, many of the positional coincidences of radio pulsars with unidentified EGRET sources become plausible as real associations, as the flux predicted by the slot gap model for many of the pulsars would provide the observed EGRET source flux. The expected probability of seeing radio-quiet gamma-ray pulsars in this model will also be discussed.     

High-frequency cutoff and change of radio emission mechanism in pulsars

Pulsars are fast rotating neutron stars with a strong magnetic field, that emit over a wide frequency range. In spite of all efforts during the 40 years after the discovery of pulsars, the mechanism of their radio emission so far remains unknown. We propose a new approach to solving this problem for a subset of pulsars with a high-frequency cutoff of the spectrum from the Pushchino catalogue (the “Pushchino” sample). We provide a theoretical explanation of the observed dependence of the high-frequency cutoff on the pulsar period, and we predict the dependence of the cutoff position from the magnetic field. This explanation is based on a new mechanism for electron radio emission in pulsars. Namely, radiation occurs in the inner (polar) gap, when electrons are accelerated in the electric field that is increasing from zero level at the star surface. In this case the acceleration of electrons passes through a maximum and goes to zero when the electron velocity approaches the speed of light. All the radiated power is located within the radio frequency band. The averaging of radiation intensity over the polar cap, with some natural assumptions of the coherence of the radiation, leads to the observed spectra. It also leads to an acceptable estimate of the power of radio emission.     

类Crab脉冲星的三维磁层外隙模型

利用三维脉冲星磁层模型研究了磁层外隙的几何结构,首先用自治模型确定“外隙”的垂直尺度,在该模型中外隙尺度受回流的外隙流（带有隙加速的带电粒子发射的曲率光子）加热极帽而产生的热光子的碰撞而成对生成所限,外隙的横向尺度也受本地对生成所限,在脉冲星的磁层中,原则上有两个拓扑分离的外隙,允许同时进入和流出粒子,不过,流入粒子流产生的辐射形态受隙了本地对生成和恒星附近的磁对生成的严格制约,根据外隙及其本地结构的三维模型计算了类Crab脉冲星的辐射和相位分解谱。     

Precursors and e± pair loading from erupting fireballs

Recent observations suggest that long-duration γ -ray bursts and their afterglows are produced by highly relativistic jets emitted in core-collapse explosions. As the jet makes its way out of the stellar mantle, a bow shock runs ahead and a strong thermal precursor is produced as the shock breaks out. Such erupting fireballs produce a very bright γ -ray precursor as they interact with the thermal break-out emission. The prompt γ -ray emission propagates ahead of the fireball before it becomes optically thin, leading to e^± pair loading and radiative acceleration of the external medium. The detection of such precursors would offer the possibility of diagnosing not only the radius of the stellar progenitor and the initial Lorentz factor of the collimated fireball, but also the density of the external environment.     

The effective acceleration of plasma outflow in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for a paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric magnetohydrodynamic (MHD) flow. For the large Michel magnetization parameter σ it is possible to linearize the stream equation near the force-free solution and to solve the problem self-consistently as was done by Beskin, Kuznetsova & Rafikov for a monopole magnetic field. It is shown that, on the fast magnetosonic surface (FMS), the particle Lorentz factor γ does not exceed the standard value  σ^1/3  . On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as  γ≈ ( z / R _L)^1/2  up to the distance   z ≈σ² R _L  , where   R _L= c /Ω_F  is the radius of the light cylinder. Thus, the maximal Lorentz factor is  γ_max≈σ  , which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.