Magnetic Pair Production Research Articles

On the Magnetic Field Screening in Strong Crossed Electromagnetic Fields

It has been shown that a rotating Black Hole (BH hereafter) immersed in a test background magnetic field, of initial strength $${{B}_{0}}$$ and aligned parallel to the BH rotation axis, generates an induced electric field, which strength is proportional to the background magnetic field. We consider the configuration of crossed fields: $${\mathbf{B}} = B\hat {z}$$ and $${\mathbf{E}} = E\hat {y}$$ . In this system, a huge number of $${{e}^{ + }}{{e}^{ - }}$$ pairs can be emitted and start to be accelerated to high energies, by means of the induced electric field, and emit synchrotron photons. These photons interact with the magnetic field via the magnetic pair production process (MPP hereafter), $$\gamma + B \to {{e}^{ + }} + {{e}^{ - }}$$ . The motion of all these pairs around the magnetic field lines generates also an induced magnetic field oriented in the opposite direction to the background one. This implies a reduction of the background magnetic field. The purpose of this study is to show if this reduction occurs, which implies a decreases the MPP efficiency and, consequently, the enhancement of the probability for the synchrotron photons to escape from the region and be detected.

Magnetic field screening in strong crossed electromagnetic fields

We consider crossed electric and a magnetic fields (B→=Bzˆ,E→=Eyˆ), with E/B<1, in presence of some initial number of e± pairs. We do not discuss here the mechanism of generation of these initial pairs. The electric field accelerates the pairs to high-energies thereby radiating high-energy synchrotron photons. These photons interact with the magnetic field via magnetic pair production process (MPP), i.e. γ+B→e++e−, producing additional pairs. We here show that the motion of all the pairs around the magnetic field lines generates a current that induces a magnetic field that shields the initial one. For instance, for an initial number of pairs N±,0=1010, an initial magnetic field of 1012 G can be reduced of a few percent. The screening occurs in the short timescales 10−21≤t≤10−15 s, i.e. before the particle acceleration timescale equals the synchrotron cooling timescale. The present simplified model indicates the physical conditions leading to the screening of strong magnetic fields. To assess the occurrence of this phenomenon in specific astrophysical sources, e.g. pulsars or gamma-ray bursts, the model can be extended to evaluate different geometries of the electric and magnetic fields, quantum effects in overcritical fields, and specific mechanisms for the production, distribution, and multiplicity of the e−e+ pairs.

Resonant Inverse Compton Scattering Spectra from Highly Magnetized Neutron Stars

Abstract Hard, nonthermal, persistent pulsed X-ray emission extending between 10 and ∼150 keV has been observed in nearly 10 magnetars. For inner-magnetospheric models of such emission, resonant inverse Compton scattering of soft thermal photons by ultrarelativistic charges is the most efficient production mechanism. We present angle-dependent upscattering spectra and pulsed intensity maps for uncooled, relativistic electrons injected in inner regions of magnetar magnetospheres, calculated using collisional integrals over field loops. Our computations employ a new formulation of the QED Compton scattering cross section in strong magnetic fields that is physically correct for treating important spin-dependent effects in the cyclotron resonance, thereby producing correct photon spectra. The spectral cutoff energies are sensitive to the choices of observer viewing geometry, electron Lorentz factor, and scattering kinematics. We find that electrons with energies ≲15 MeV will emit most of their radiation below 250 keV, consistent with inferred turnovers for magnetar hard X-ray tails. More energetic electrons still emit mostly below 1 MeV, except for viewing perspectives sampling field-line tangents. Pulse profiles may be singly or doubly peaked dependent on viewing geometry, emission locale, and observed energy band. Magnetic pair production and photon splitting will attenuate spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The resonant Compton spectra are strongly polarized, suggesting that hard X-ray polarimetry instruments such as X-Calibur, or a future Compton telescope, can prove central to constraining model geometry and physics.

Threshold singularities, dispersion relations and fixed-order perturbative calculations

We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.

Synchrotron X-ray emission from old pulsars

We study the synchrotron radiation as the observed non-thermal X-ray emission from old pulsars ($\gtrsim1-10$Myr) to investigate the particle acceleration in their magnetospheres. We assume that the power-law component of the observed X-ray spectra is caused by the synchrotron radiation from electrons and positrons in the magnetosphere. We consider two pair production mechanisms of X-ray emitting particles, the magnetic and the photon-photon pair productions. High-energy photons, which ignite the pair production, are emitted via the curvature radiation of the accelerated particles. We use the analytical description for the radiative transfer and estimate the luminosity of the synchrotron radiation. We find that for pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{33}$ erg s$^{-1}$, the locations of the particle acceleration and the non-thermal X-ray emission are within $\lesssim10^7$cm from the centre of the neutron star, where the magnetic pair production occurs. For pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{31}$ erg s$^{-1}$ such as J0108-1431, the synchrotron radiation is difficult to explain the observed non-thermal component even if we consider the existence of the strong and small-scale surface magnetic field structures.

Simulation of ultra-high energy photon propagation with PRESHOWER 2.0

In this paper we describe a new release of the PRESHOWER program, a tool for Monte Carlo simulation of propagation of ultra-high energy photons in the magnetic field of the Earth. The PRESHOWER program is designed to calculate magnetic pair production and bremsstrahlung and should be used together with other programs to simulate extensive air showers induced by photons. The main new features of the PRESHOWER code include a much faster algorithm applied in the procedures of simulating the processes of gamma conversion and bremsstrahlung, update of the geomagnetic field model, and a minor correction. The new simulation procedure increases the flexibility of the code so that it can also be applied to other magnetic field configurations such as, for example, encountered in the vicinity of the sun or neutron stars. Program summaryProgram title: PRESHOWER 2.0Catalog identifier: ADWG_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWG_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3968No. of bytes in distributed program, including test data, etc.: 37198Distribution format: tar.gzProgramming language: C, FORTRAN 77.Computer: Intel-Pentium based PC.Operating system: Linux or Unix.RAM:< 100 kBClassification: 1.1.Does the new version supercede the previous version?: YesCatalog identifier of previous version: ADWG_v1_0Journal reference of previous version: Comput. Phys. Comm. 173 (2005) 71Nature of problem:Simulation of a cascade of particles initiated by UHE photon in magnetic field.Solution method:The primary photon is tracked until its conversion into an e+ e− pair. If conversion occurs each individual particle in the resultant preshower is checked for either bremsstrahlung radiation (electrons) or secondary gamma conversion (photons).Reasons for new version:1.Slow and outdated algorithm in the old version (a significant speed up is possible);2.Extension of the program to allow simulations also for extraterrestrial magnetic field configurations (e.g. neutron stars) and very long path lengths.Summary of revisions:A veto algorithm was introduced in the gamma conversion and bremsstrahlung tracking procedures. The length of the tracking step is now variable along the track and depends on the probability of the process expected to occur. The new algorithm reduces significantly the number of tracking steps and speeds up the execution of the program. The geomagnetic field model has been updated to IGRF-11, allowing for interpolations up to the year 2015. Numerical Recipes procedures to calculate modified Bessel functions have been replaced with an open source CERN routine DBSKA. One minor bug has been fixed.Restrictions:Gamma conversion into particles other than an electron pair is not considered. Spatial structure of the cascade is neglected.Additional comments:The following routines are supplied in the package, IGRF [1, 2], DBSKA [3], ran2 [4]Running time:100 preshower events with primary energy 1020 eV require a 2.66 GHz CPU time of about 200 sec.; at the energy of 1021 eV, 600 sec.

ACCELERATING HIGH-ENERGY PULSAR RADIATION CODES

Curvature radiation (CR) is believed to be a dominant mechanism for creating gamma-ray emission from pulsars and is emitted by relativistic particles that are constrained to move along curved magnetic field lines. Additionally, synchrotron radiation (SR) is expected to be radiated by both relativistic primaries (involving cyclotron resonant absorption of radio photons and re-emission of SR photons), or secondary electron-positron pairs (created by magnetic or photon-photon pair production processes involving CR gamma rays in the pulsar magnetosphere). When calculating these high-energy spectra, especially in the context of pulsar population studies where several millions of CR and SR spectra have to be generated, it is profitable to consider approximations that would save computational time without sacrificing too much accuracy. This paper focuses on one such approximation technique, and we show that one may gain significantly in computational speed while preserving the accuracy of the spectral results.

Non-thermal pulsed X-ray emission from rotation-powered pulsars

We study the properties of the pulsed component of hard (>2 keV) X-ray emission from pulsars based on the new version of the outer-gap model proposed by Zhang et al. (2004). In this outer-gap model, high-energy photons emitted by relativistic charged particles produce e pairs through magnetic-pair production on their way from the outer gap to the neutron-star surface, and these pairs produce the bulk of pulsed X-rays by the synchrotron radiation. The X-ray luminosity of rotation-powered pulsars is a function not only of the period and magnetic field strength, but also of the magnetic inclination angle. Application of this model to the observed pulsed X-ray emission of normal pulsars by ASCA shows a better consistence. Further, the inclination angles of these pulsars are estimated using the observed X-ray data, and the predicted conversion efficiencies of high-energy γ-rays for seven confirmed γ-ray pulsars are consistent with the observed data.

High‐Energy Nonthermal Emission from High‐Field Pulsars

We study high-energy radiation properties of high-field (10(13)-10(14)G) pulsars in the framework of the outer-gap model. In this model, charged particles are accelerated inside the outer gap, which depends on the magnetic inclination angle and magnetic geometry. High-energy photons emitted by these relativistic charged particles produce electrons/positrons through magnetic pair production on their way from the outer gap to the neutron star surface, and these pairs produce nonthermal X-rays by synchrotron radiation. Applying this model to high- field pulsars, the characteristic gamma-ray energies, nonthermal X-ray luminosity, and gamma-ray luminosity are calculated. Furthermore, comparisons of the predicted gamma-ray fluxes for these high-field pulsars with the sensitivities of AGILE and GLAST are given. We discuss the possibility that some high-field pulsars with ages of similar to 10(4.9) to similar to 10(5.5) yr might be detected by AGILE.

Empirical Constraints on the General Relativistic Electric Field Associated with PSR J0437-4715

We simulate the magnetosphere of the nearby millisecond pulsar PSR J0437-4715, which is expected to have an unscreened electric potential due to the lack of magnetic pair production. We incorporate general relativistic (GR) effects and study curvature radiation (CR) by primary electrons but neglect inverse Compton scattering of thermal X-ray photons by these electrons. We find that the CR spectrum cuts off at energies below ~17 GeV, well below the threshold of the High Energy Stereoscopic System (H.E.S.S.) telescope (100 GeV), while other models predict a much higher cutoff of 100 GeV. GR theory also predicts a relatively narrow pulse (βo ~ 0.2 phase width) centered on the magnetic axis. EGRET observations above 100 MeV significantly constrain the application of the Muslimov & Harding model for γ-ray production as a result of GR frame dragging and ultimately its polar cap (PC) current and accelerating potential. Whereas the standard prediction of this pulsar's γ-ray luminosity due to GR frame dragging is ~10% of the spin-down power, a nondetection by forthcoming H.E.S.S. observations will constrain it to 0.3%, enforcing an even more severe revision of the accelerating electric field and PC current.

Charge Densities above Pulsar Polar Caps

The ability of the neutron star surface to supply all or only part of the charges filling the pulsar magnetosphere is crucial for the physics prevailing within it, with direct consequences for the possible formation of pair creation regions. We evaluate the conditions for $e^-$ emission from pulsar surfaces for a simple Goldreich-Julian geometry taking both thermal and field emission processes into account. Using recently published estimates for the equation of state at the neutron star's surface, we show, that for a large range of $T_{\rm surf}, B$ and $P$, the liberated charges will fully screen the accelerating B-parallel electric field ${\rm E_\|}$. For surface temperatures $T_{\rm surf}<2\cdot 10^5 $K a balance between field emission of electrons and shielding of the field will occur. Even in the overidealised case of $T_{\rm surf}=0$ one can expect a prodigious supply of electrons which will weaken the accelerating ${\rm E_\|}$. We calculated the motion of electrons along selected polar field lines numerically for the low temperature, field emission scenario yielding their Lorentz factors as well as the produced radiation densities. Inverse Compton and later curvature losses are seen to balance the acceleration by the residual electric fields. We found that the conditions for magnetic pair production are not met anywhere along the field lines up to a height of 1500 pulsar radii. We did not {\it a priori} assume an inner gap, and our calculations did not indicate the formation of one under realistic physical conditions without the introduction of further assumptions.

A Three-dimensional Outer-magnetospheric Gap Model for Gamma-ray Pulsars: I. The Crab Pulsar

We use a three-dimensional pulsar magnetosphere model to study the geometry of outer-magnetospheric gaps. The vertical size of the “outer gap” is first determined by a self-consistent model in which the outer gap size is limited by pair production from collisions between (1) thermal photons produced from polar cap heating by backflow “outer gap” current, and (2) the curvature photons emitted by gap-accelerated charged particles. The transverse size of the outer gap is also determined by local pair production limits. In principle, there are two topologically disconnected outer gaps in the magnetosphere of a pulsar. Both incoming and outgoing particle flows are allowed. However, the emission morphologies produced by incoming particle flow is severely restricted by local pair production in the gap and the absorption of magnetic pair production near the star. Double-peaked light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate the emission morphologies and phase-resolved spectra of gamma-ray pulsars. Applications to the Crab pulsar illustrate the model.

Electromagnetic showers in a strong magnetic field

We present the results concerning the main shower characteristics in a strong magnetic field obtained through shower simulation. The processes of magnetic bremsstrahlung and pair production were taken into account for values of the parameter >>1. We compare our simulation results with a recently developed cascade theory in a strong magnetic field.

Gamma-ray pulsars: polar cap or outer gap emission?

The power law spectra of the six knownγ-ray pulsars are seen to cut off at energies < 1 TeV so that no steady pulsed TeV component is observed from any knownγ-ray pulsar. In some cases we show that the cutoff is steeper than exponential, which is consistent with magnetic pair production above the polar cap region. The small upper limits on the ratio of TeV energy flux to optical - GeV energy flux is again consistent with the polar cap model, but appears to be inconsistent with inverse Compton controlled outer gaps.

Magnetic Compton-induced pair cascade model for gamma-ray pulsars

Electrons accelerated to relativistic energies in pulsar magnetospheres will Compton scatter surface thermal emission and nonthermal optical, UV, and soft X-ray emission to gamma-ray energies, thereby initiating a pair cascade through synchrotron radiation and magnetic pair production. This process is proposed as the origin of the high-energy radiation that has been detected from six isolated pulsars. We construct an analytic model of magnetic Compton scattering near the polar cap of isolated pulsar magnetospheres and present approximate analytic derivations for scattered spectra, electron energy-loss rates, and photon luminosities. A Monte Carlo simulation is used to model the pair cascade induced by relativistic electrons scattering photons through the cyclotron resonance. For simplicity, the primary electrons are assumed to be monoenergetic and the nonresonant emission is omitted. Assuming that the angle phi(sub B) between the magnetic and spin axes is approximately equal to the polar-cap angle theta(sub pc), this model can produce both double-peaked and broad single-peaked pulse profiles and account for the trend of harder gamma-ray spectra observed from older pulsars.

On the spectra and pulse profiles of gamma-ray pulsars

We model spectra and pulse profiles of gamma-ray pulsars assuming that the pulsar's magnetic axis is nearly aligned with its rotation axis. In this model, the nonthermal energy of electrons flowing outward along field lines connected to the light cylinder is efficiently converted to gamma rays via magnetic Compton scattering of optical and soft X-ray photons. The hard photons initiate a pair cascade in the pulsar magnetosphere through magnetic pair production followed by synchrotron emission. The calculated spectra are used to fit gamma-ray pulsar observations. This model produces a hollow cone of emission which can reproduce both the broad single-peaked and narrow double-peaked pulse profiles observed from gamma-ray pulsars.

TeV Gamma-Ray Observations of Compton Gamma-Ray Observatory Pulsars: Evidence against Inverse-Compton Controlled Outer Gaps

We present the first results of TeV γ-ray observations of the Compton Gamma-Ray Observatory γ-ray pulsar PSR 1706-44, indicating a spectral cutoff between ∼20 GeV and 600 GeV. Improved upper limits are also presented for the Vela pulsar and PSR 1509-58. These and other TeV results confirm similar cutoffs for these γ-ray pulsars as well as for Geminga. The polar cap model predicts such a spectral cutoff due to magnetic pair production, whereas the outer gap model for Vela-type pulsars predicts a similar cutoff resulting from the maximum synchrotron energy in the outer gap. The spectral flattening below a certain minimum energy, seen from all of these pulsars, is also consistent with the outer gap prediction

Magnetic field distribution in polar CAP models of gamma-ray bursters

The high-energy spectral cutoffs are discussed as a function of angle predicted by magnetized polar cap models of gamma-ray bursters, in the presence of magnetic pair production and general relativistic effects. The effect of the photon escape beam shape on the relative probability of detection as a function of energy is calculated for a range of model parameters. These predictions are compared to the burster cutoff upper limits observed with SMM and are used to derive constraints on the detectable magnetic field strength distribution among bursters from future observations. A method for determining the intrinsic magnetic field distribution among gamma-ray bursting neutron stars is discussed.

High-energy gamma-ray absorption in relativistic magnetospheres

Calculations are made of the propagation of gamma-rays around neutron stars with a dipole magnetic field, including the effects of general relativity and the absorption by the one-photon magnetic pair production process, as a model for the high-energy transport in gamma-ray burst sources and pulsars. The paper discusses the escaping photon beam characteristics as seen by distant observers at different angles with respect to the magnetic axis, for radiation arising from the polar caps of neutron stars of varying degrees of compactness and surface field strengths. The observed beaming depends strongly on the surface field only up to B of about 0.05 times the critical field value, being essentially constant above the value 0.1. The gravitational light bending contributes significantly to broaden the beam profiles especially at low energies above threshold, being sensitive to the stellar radius to mass ratio.

Synchro-Curvature Radiation and Magnetic Pair Production of Relativistic Electrons in Strong Curved Magnetic Fields

Most of common curved magnetic fields with axial symmetry in astrophysics can be expressed in a local cylindrical coordinate system (R, φ, Z) as where HO, RO and N are real constants. It has been known that the non-zero curvature of the magnetic field lines can impose an additional pitch angle on the electrons moving in the field (1).