Alice K. Harding

Physics of strongly magnetized neutron stars

There has recently been growing evidence for the existence of neutron stars possessing magnetic fields with strengths that exceed the quantum critical field strength of 4.4 × 1013 G, at which the cyclotron energy equals the electron rest mass. Such evidence has been provided by new discoveries of radio pulsars having very high spin-down rates and by observations of bursting gamma-ray sources termed magnetars. This paper will discuss the exotic physics of this high-field regime, where a new array of processes becomes possible and even dominant and where familiar processes acquire unusual properties. We review the physical processes that are important in neutron star interiors and magnetospheres, including the behaviour of free particles, atoms, molecules, plasma and condensed matter in strong magnetic fields, photon propagation in magnetized plasmas, free-particle radiative processes, the physics of neutron star interiors and field evolution and decay mechanisms. Application of such processes in astrophysical source models, including rotation-powered pulsars, soft gamma-ray repeaters, anomalous x-ray pulsars and accreting x-ray pulsars will also be discussed. Throughout this review, we will highlight the observational signatures of high magnetic field processes, as well as the theoretical issues that remain to be understood.

Electromagnetic cascades in pulsars

The development of pair photon cascades initiated by high energy electrons above a pulsar polar cap is simulated numerically. The calculation uses the energy of the primary electron, the magnetic field strength, and the period of rotation as parameters and follows the curvature radiation emitted by the primary, the conversion of this radiation e(+) - e(-) pairs in the intense fields, and the quantized synchrotron radiation by the secondary pairs. A recursive technique allows the tracing of an indefinite number of generations using a Monte Carlo method. Gamma ray and pair spectra are calculated for cascades in different parts of the polar cap and with different acceleration models. It is found that synchrotron radiation from secondary pairs makes an important contribution to the gamma ray spectrum above 25 MeV, and that the final gamma ray and pair spectra are insensitive to the height of the accelerating region, as long as the acceleration of the primary electrons is not limited by radiation reaction.

Gamma-ray pulsars: emission from extended polar cap cascades

We have used a Monte Carlo simulation of a Polar Cap (PC) model of gamma-ray pulsars to estimate light curves and phase-resolved spectra for sources whose rotational and magnetic axes are oriented so that only one of the magnetic poles produces emission directed at the Earth. In this Single Polar Cap (SPC) scenario, even sources whose light curves have two distinct peaks (Crab, Vela, Geminga, PSR B1951+32) are due to emission concentrated near the rim of a single PC. If the inclination alpha is comparable to the half-width of the PC gamma-beam, alpha ~ theta_{b}, the peak-to-peak phase separation can have the large values (0.4 - 0.5) observed from these sources. In the model presented here we attribute the observed interpeak emission to pair cascades above the PC interior. Our simulation assumes the physics of conventional PC models, in which the gamma rays are due to photon-pair cascades initiated by curvature radiation from the acceleration of electrons above the PCs. In this work we assume that the acceleration occurs over a finite region which may extend up to several radii above the neutron star surface. We find that the combined effects of moderately enlarged PC dimensions and extended acceleration zones resolve a major difficulty with earlier PC models, namely their small beam widths (and hence small detection probabilities). Our best fits to the observed light curves are obtained from models in which the accelerated electrons have a uniform surface density over the PC interior and a sharp density increase of 3 - 5 near the rim.

High-Altitude Particle Acceleration and Radiation in Pulsar Slot Gaps

We explore the pulsar slot gap (SG) electrodynamics up to very high altitudes, where for most relatively rapidly rotating pulsars both the standard small-angle approximation and the assumption that the magnetic field lines are ideal streamlines break down. We address the importance of the electrodynamic conditions at the SG boundaries and the occurrence of a steady state drift of charged particles across the SG field lines at very high altitudes. These boundary conditions and the deviation of particle trajectories from streamlines determine the asymptotic behavior of the scalar potential at all radii from the polar cap (PC) to near the light cylinder. As a result, we demonstrate that the steady state accelerating electric field, E∥, must approach a small and constant value at high altitude above the PC. This E∥ is capable of maintaining electrons moving with high Lorentz factors (~few × 107) and emitting curvature γ-ray photons up to nearly the light cylinder. By numerical simulations, we show that primary electrons accelerating from the PC surface to high altitude in the SG along the outer edge of the open field region will form caustic emission patterns on the trailing dipole field lines. Acceleration and emission in such an extended SG may form the physical basis of a model that can successfully reproduce some pulsar high-energy light curves.

Pulsar Polar Cap Heating and Surface Thermal X-Ray Emission. II. Inverse Compton Radiation Pair Fronts

We investigate the production of electron-positron pairs by inverse Compton scattered (ICS) photons above a pulsar polar cap (PC) and calculate surface heating by returning positrons. This paper is a continuation of our self-consistent treatment of acceleration, pair dynamics, and electric field screening above pulsar PCs. We calculate the altitude of the inverse Compton pair-formation fronts, the flux of returning positrons, and present the heating efficiencies and X-ray luminosities. We revise pulsar death lines implying cessation of pair formation, and present them in surface magnetic field-period space. We find that virtually all known radio pulsars are capable of producing pairs by resonant and nonresonant ICS photons radiated by particles accelerated above the PC in a pure star-centered dipole field, so that our ICS pair death line coincides with empirical radio pulsar death. Our calculations show that ICS pairs are able to screen the accelerating electric field only for high PC surface temperatures and magnetic fields. We argue that such screening at ICS pair fronts occurs locally, slowing but not turning off acceleration of particles until screening can occur at a curvature radiation (CR) pair front at higher altitude. In the case where no screening occurs above the PC surface, we anticipate that the pulsar γ-ray luminosity will be a substantial fraction of its spin-down luminosity. The X-ray luminosity resulting from PC heating by ICS pair fronts is significantly lower than the PC heating luminosity from CR pair fronts, which dominates for most pulsars. PC heating from ICS pair fronts is highest in millisecond pulsars, which cannot produce CR pairs, and may account for observed thermal X-ray components in the spectra of these old pulsars.

Particle Acceleration Zones above Pulsar Polar Caps: Electron and Positron Pair Formation Fronts

We investigate self-consistent particle acceleration near a pulsar polar cap (PC) by the electrostatic field due to the effect of inertial frame dragging. Test particles gain energy from the electric field parallel to the open magnetic field lines and lose energy by both curvature radiation (CR) and resonant and nonresonant inverse Compton scattering (ICS) with soft thermal X-rays from the neutron star (NS) surface. Gamma rays radiated by electrons accelerated from the stellar surface produce pairs in the strong magnetic field, which screen the electric field beyond a pair formation front (PFF). Some of the created positrons can be accelerated back toward the surface and produce γ-rays and pairs that create another PFF above the surface. We find that ICS photons control PFF formation near the surface, but because of the different angles at which the electron and positron scatter the soft photons, positron-initiated cascades develop above the surface and may screen the accelerating electric field. Stable acceleration from the NS surface is therefore not possible in the presence of dominant ICS energy losses. However, we find that stable acceleration zones may occur at some distance above the surface, where CR dominates the electron and positron energy losses and there is up-down symmetry between the electron and positron PFFs. We examine the dependence of CR-controlled acceleration zone voltage, width, and height above the surface on parameters of the pulsar and its soft X-ray emission. For most pulsars, we find that acceleration will start at a height of 0.5-1 stellar radii above the NS surface.

Relativistic Effects and Polarization in Three High-Energy Pulsar Models

We present the influence of the special relativistic effects of aberration and light-travel time delay on pulsar high-energy light curves and polarization characteristics predicted by three models: the two-pole caustic model, the outer gap model, and the polar cap model. Position angle curves and degree of polarization are calculated for the models and compared with the optical data on the Crab pulsar. The relative positions of peaks in gamma-ray and radio light curves are discussed in detail for the models. We find that the two-pole caustic model can qualitatively reproduce the optical polarization characteristics of the Crab pulsar: fast swings of the position angle and minima in polarization degree, associated with both peaks. The anticorrelation between the observed flux and the polarization degree (observed in the optical band also for B0656+14) naturally results from the caustic nature of the peaks, which are produced in the model because of the superposition of radiation from many different altitudes, i.e., polarized at different angles. The two-pole caustic model also provides an acceptable interpretation of the main features in the Crabs radio profile. Neither the outer gap model nor the polar cap model is able to reproduce the optical polarization data on the Crab. Although the outer gap model is very successful in reproducing the relative positions of gamma-ray and radio peaks in pulse profiles, it can reproduce the high-energy light curves only when photon emission from regions very close to the light cylinder is included.

FULL POLAR CAP CASCADE SCENARIO: GAMMA-RAY AND X-RAY LUMINOSITIES FROM SPIN-POWERED PULSARS

Canonical polar cap cascade models involve curvature radiation (CR) or inverse Compton scattering (ICS) of the primary particles and synchrotron radiation (SR) of the higher generation pairs. Here we modify such a cascade picture to include the ICS of the higher generation pairs. In such a ii full-cascade ˇˇ scenario, not only the perpendicular portion of the energy of the pairs goes to high-energy radiation via SR, but the parallel portion of the energy of the pairs can also contribute to high-energy emission via ICS with the soft thermal photons from either the full neutron star surface or the hot polar cap. The efficiency of converting particleskinetic energy to radiation by ICS is very high if the scatterings occur in the ii resonant ˇˇ regime. As a result, almost 100% of the energy input from the pulsar inner acceler- ators could be converted to high-energy emission. An important output of such a scenario is that the soft tail of the ICS spectrum can naturally result in a nonthermal X-ray component that can contribute to the luminosities observed by ROSAT and ASCA. Here we present an analytic description of such a full polar cap cascade scenario using the recursion relationships between adjacent generations following the approach —rst proposed by Lu et al., but we develop it to be able to delineate the complex full- cascade process. The acceleration model we adopted is the space-chargelimited —ow model proposed by Harding & Muslimov. We present the theoretical predictions of the c-ray luminosities, the thermal and nonthermal X-ray luminosities for the known spin-powered X-ray pulsars (eight of them are also c-ray pulsars) and compare them with the observations from CGRO, ROSAT , and ASCA. We estimate the nonthermal X-ray luminosity by including all the possible ICS branches contributing to a certain energy band and estimate both the full surface and hot polar cap thermal X-ray luminosities by adopting a standard neutron star cooling scenario, and by treating self-consistent polar cap heating in the Harding & Muslimov model, respectively. Our results show that the observed diUerent dependences of the high- energy luminosities on the pulsar spin-down luminosities, i.e., and are well L c P (L sd )1@2 L X D 10~3L sd , reproduced. We found that, for normal pulsars, both the hard (ASCA band) and the soft (ROSAT band) X-ray luminosities are dominated by the nonthermal X-rays of ICS origin, although for some pulsars, thermal components due to either neutron star cooling or polar cap heating can have comparable lumi- nosities so that they are detectable. For the millisecond pulsars, our predicted upper limits of the thermal luminosities due to polar cap heating are usually higher than the ICS-origin nonthermal components if there are no strong multipolar magnetic —eld components near the neutron star surface; thus, the pulsed soft X-rays in the ROSAT band from most of the millisecond pulsars might be of thermal origin. Subject headings: gamma rays: theorypulsars: generalradiation mechanisms: nonthermal ¨ X-rays: stars

High-Altitude Emission from Pulsar Slot Gaps: The Crab Pulsar

We present results of a 3D model of optical-to-?-ray emission from the slot gap accelerator of a rotation-powered pulsar. Primary electrons accelerating to high altitudes in the unscreened electric field of the slot gap reach radiation reaction limited Lorentz factors of ~ -->2 ? 107, while electron-positron pairs from lower altitude cascades flow along field lines interior to the slot gap. The curvature, synchrotron, and inverse Compton radiation of both primary electrons and pairs produce a broad spectrum of emission from infrared to GeV energies. Both primaries and pairs undergo cyclotron resonant absorption of radio photons, allowing them to maintain significant pitch angles. Synchrotron radiation from pairs with a power-law energy spectrum from -->? = 102 to 105, dominate the spectrum up to ~10 MeV. Synchrotron and curvature radiation of primaries dominates from 10 MeV up to a few GeV. We examine the energy-dependent pulse profiles and phase-resolved spectra for parameters of the Crab pulsar as a function of magnetic inclination ? and viewing angle ?, comparing to broadband data. In most cases, the pulse profiles are dominated by caustics on trailing field lines. We also explore the relation of the high-energy and the radio profiles, as well as the possibility of caustic formation in the radio cone emission. We find that the Crab pulsar profiles and spectrum can be reasonably well reproduced by a model with -->? = 45? and -->? ~ 100? or 80?. This model predicts that the slot gap emission below 200 MeV will exhibit correlations in time and phase with the radio emission.

Pulsar Polar Cap Heating and Surface Thermal X-Ray Emission. I. Curvature Radiation Pair Fronts

We investigate the effect of pulsar polar cap (PC) heating produced by positrons returning from the upper pair formation front. Our calculations are based on a self-consistent treatment of the pair dynamics and the effect of electric field screening by the returning positrons. We calculate the resultant X-ray luminosities and discuss the dependence of the PC heating efficiencies on pulsar parameters, such as characteristic spin-down age, spin period, and surface magnetic field strength. In this study we concentrate on the regime where the pairs are produced in a magnetic field by curvature photons emitted by accelerating electrons. Our theoretical results are not in conflict with the available observational X-ray data and suggest that the effect of PC heating should significantly contribute to the thermal X-ray fluxes from middle-aged and old pulsars. The implications for current and future X-ray observations of pulsars are briefly outlined.