Polar Cap Model Research Articles

Model of peak separation in the gamma light curve of the Vela pulsar

The separation Δpeak between two peaks in the gamma-ray pulse profile is calculated as a function of energy for several polar cap models with curvature-radiation induced cascades. The Monte Carlo results are interpreted with the help of analytical approximations and discussed in view of the recent data analysis for the Vela pulsar. We find that the behaviour of Δpeak as a function of photon energy ε depends primarily on local values of the magnetic field, Blocal, in the region where electromagnetic cascades develop. For low values of Blocal (<1012G), Δpeak(ε) is kept constant. However, for stronger magnetic fields (≳1012G) in the hollow-column model, Δpeak decreases with increasing photon energy at a rate dependent on the maximum energy of the beam particles, as well as on viewing geometry. There exists a critical photon energy εturn above which the relation Δpeak(ε) changes drastically: for , in hollow-column models the separation Δpeak increases (whereas in the filled-column model it decreases) rapidly with increasing ε, at a rate of ∼0.28 of the total phase per decade of photon energy. The existence of critical energy εturn is a direct consequence of one-photon magnetic absorption effects. In general, εturn is located close to the high-energy cut-off of the spectrum, thus photon statistics at εturn should be very low. This will make it difficult to verify the existence of εturn in real gamma-ray pulsars. Spectral properties of the Vela pulsar would favour those models that use low values of magnetic field in the emission region which in turn implies a constant value of the predicted Δpeak within the range of EGRET.

Model of peak separation in the gamma light curve of the Vela pulsar

The separation Δpeak between two peaks in the gamma-ray pulse profile is calculated as a function of energy for several polar cap models with curvature-radiation induced cascades. The Monte Carlo results are interpreted with the help of analytical approximations and discussed in view of the recent data analysis for the Vela pulsar. We find that the behaviour of Δpeak as a function of photon energy e depends primarily on local values of the magnetic field, Blocal, in the region where electromagnetic cascades develop. For low values of Blocal (<1012 G), Δpeak(e) is kept constant. However, for stronger magnetic fields (≳1012 G) in the hollow-column model, Δpeak decreases with increasing photon energy at a rate dependent on the maximum energy of the beam particles, as well as on viewing geometry. There exists a critical photon energy eturn above which the relation Δpeak(e) changes drastically: for , in hollow-column models the separation Δpeak increases (whereas in the filled-column model it decreases) rapidly with increasing e, at a rate of ∼0.28 of the total phase per decade of photon energy. The existence of critical energy eturn is a direct consequence of one-photon magnetic absorption effects. In general, eturn is located close to the high-energy cut-off of the spectrum, thus photon statistics at eturn should be very low. This will make it difficult to verify the existence of eturn in real gamma-ray pulsars. Spectral properties of the Vela pulsar would favour those models that use low values of magnetic field in the emission region which in turn implies a constant value of the predicted Δpeak within the range of EGRET.

Off-Beam Gamma-Ray Pulsars and Unidentified EGRET Sources in the Gould Belt

We investigate whether gamma-ray pulsars viewed at a large angle to the neutron star magnetic pole could contribute to the new population of Galactic unidentified EGRET sources associated with the Gould Belt. The faint, soft nature of these sources is distinctly different from both the properties of unidentified EGRET sources along the Galactic plane and the properties of the known gamma-ray pulsars. We explore the possibility, within the polar cap model, that some of these sources are emission from pulsars seen at lines of sight that miss both the bright gamma-ray cone beams and the radio beam. The off-beam gamma rays come from high-altitude curvature emission of primary particles, are radiated over a large solid angle and have a much softer spectrum than that of the main beams. We estimate that the relative detectability of such off-beam emission is about a factor of 4-5 higher than that of the on-beam emission. At least some of the radio-quiet Gould Belt sources detected by EGRET could therefore be such off-beam gamma-ray pulsars. The Gamma-ray Large Area Space Telescope should be able to detect pulsations in most of these sources.

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 ˆ 2ms and a surface magnetic field Bp ˆ 7:5 � 10 4 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.

Photon Splitting and Pair Creation in Highly Magnetized Pulsars

The absence of radio pulsars with long periods has lead to the popular notion of a high P ``death line.'' In the standard picture, beyond this boundary, pulsars with low spin rates cannot accelerate particles above the stellar surface to high enough energies to initiate pair cascades, and the pair creation needed for radio emission is strongly suppressed. In this paper we explore the possibility of another pulsar ``death line'' in the context of polar cap models, corresponding to high magnetic fields B in the upper portion of the period-period derivative diagram, a domain where few radio pulsars are observed. The origin of this high B boundary, which may occur when B becomes comparable to or exceeds $B_{\rm cr} = 4.4 \times 10^{13}$ Gauss, is also due to the suppression of magnetic pair creation, but primarily because of ineffective competition with magnetic photon splitting. Threshold pair creation also plays a prominent role in the suppression of cascades. We present Monte Carlo calculations of the pair yields in photon splitting/pair cascades which show that, in the absence of scattering effects, pair production is effectively suppressed, but only if all three modes of photon splitting allowed by QED are operating in high fields. This paper describes the probable shape and position of the new ``death line,'' above which pulsars are expected to be radio quiet, but perhaps still X-ray and gamma-ray bright. The hypothesized existence of radio-quiet sources finds dramatic support in the recent discovery of ultra-strong fields in Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars. Guidelines for moderate to high B pulsar searches at radio wavelengths and also in the soft and hard gamma-ray bands are presented.

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 ($\sim 10^9\G$) pulsars. We extend polar-cap model calculations of Rudak & Dyks (1999) by including inverse Compton scattering events in 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 due to curvature radiation of primary particles. Synchrotron component due to 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 $\sim 100\MeV$ all slopes converge to a unique value of 4/3 (in a $\nu {\cal F}_\nu$ convention). The thermal soft X-ray photons, which come either from the polar cap or from the surface, are Compton upscattered to a domain of the VHE and form a separate spectral component peaking at $\sim 1\TeV$. We discuss 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.

A new mechanism for pulsar gamma-ray emission

Gamma-ray emission in pulsar magnetospheres is attributed to synchrotron radiation, which tends to decrease the pitch angle of the particle, being balanced by plasma processes tending to increase the pitch angle. The plasma processes are non-resonant instabilities that drive non-resonant quasilinear diffusion (NQD), thereby pumping energy from waves and the parallel motion of the particle into the perpendicular motion of the particle. It is shown that NQD can maintain the pitch angles for particles near the light-cylinder such that they radiate synchrotron radiation at MeV energies. Compared to conventional emission mechanisms (such as polar cap or outer gap models), the resulting spectrum has a relatively low upper cut-off from about a few to 100 MeV. Possible observational consequences of this mechanism are discussed.

ICS as a Limiting Factor for Electron Energies in Pulsar Magnetospheres

AbstractBased on the polar cap model, we investigated in the energy loss of accelerated electrons in a neutron star magnetosphere by inverse Compton scattering of thermal photospheric radiation. An analytical treatment is presented, which turns out ranges in the magnetic field strength and thermal temperature where ultrarelativistic electrons can not survive.

Model of pulse separation in the gamma light curve of the Vela pulsar

AbstractWithin the framework of a single polar cap model we calculate the energy dependence of phase separation between two peaks in the gamma-ray lightcurve of the Vela pulsar. Results are confronted with EGRET data (Kanbach 1999).

Convective response to a transient increase in dayside reconnection

Measurements with five of the northern hemisphere Super Dual Auroral Radar Network (SuperDARN) radars have yielded a detailed temporal and spatial view of the evolution of a dayside convection enhancement, which we associate with a transient increase in dayside reconnection. The convection enhancement was located in and immediately poleward of the ionospheric footprint of the cusp. During the enhancement, both the cusp and the region of enhanced flow shifted equatorward by ∼2°. As the flow enhancement diminished, the cusp footprint moved poleward to its original position. The entire event had a duration of ∼18 min and was associated with a transient 29 kV increase in the cross polar cap potential. We estimate that ∼3.2×107 Wb of magnetic flux was opened at the dayside magnetopause during the most active 12 min of this event. The length of the reconnection line on the dayside magnetopause is estimated to have reached 19,000 km. The characteristics of the dayside ionospheric response are very similar to those predicted by Cowley and Lockwood [1992] in their expanding and contracting polar cap model. These are the first observations that have provided an extended spatial and temporal view of the responses of dayside convection and the cusp to a transient reconnection event.

High-energy emission from pulsars in polar-cap models with curvature-radiation-induced cascades

For a subclass of polar-cap models based on electromagnetic cascades induced by curvature radiation (CR) we calculate broad-band high-energy spectra of pulsed emission expected for classical and millisecond pulsars. The spectra are a combination of curvature and synchrotron components. The spectrum of the curvature component breaks at 150 MeV, and neither its slope nor the level below this energy is compatible with phase-averaged spectra of pulsed X-ray emission inferred from observations. Spectral properties in the combined energy range of ROSAT and ASCA (0.1--10 keV) depend upon the location of the cyclotron turnover energy ect = [h¯ (e B)/(mec) ]/sin ψ in the synchrotron component. Unlike in outer-gap models, the available range of pitch angles ψ is rather narrow and confined to low values. For classical pulsars, a gradual turnover begins at ∼ 1 MeV, and the level of the synchrotron spectrum decreases. At ∼ 10 keV the curvature component eventually takes over, but with photon index α = 2/3, which disagrees with observations. For millisecond pulsars, the X-ray spectra are dominated by the synchrotron component with α≃ 1.5, and a sharp turnover into α≃ -1 at ect∼ 100 eV. Relationships of pulsed luminosity LX to spin-down luminosity Lsd are presented for classical and millisecond pulsars. We conclude that spectral properties and fluxes of pulsed non-thermal X-ray emission of some objects, like the Crab or the millisecond pulsar B1821-24, pose a challenge to the subclass of polar-cap models based on curvature and synchrotron radiation alone.

The luminosity of γ-ray pulsars

We point out that in the polar cap model, the visible part is only part of the cap and this fact should be taken into account when calculating the pulsar luminosity. When this is done, the calculated luminosities are in basic agreement with the observed values. Based on our calculations we give a list of 12 possible γ-ray candidates.

Kinematics of Pulsar Beams

We have investigated in detail the geometry of the open magnetic field line structure of an oblique dipole rotator, with a view to attaining a better understanding of the geometry of pulsar beams in the polar cap model of pulsar emission. We find that the open field lines divide into two branches, both of which are required to describe the full polar cap. We have also investigated the possible changes in pulsar beams due to the spacetime curvature caused by the neutron star and the special relativistic aberration. Barring the light bending, which is treated numerically, we incorporate all other effects analytically. The formalism can be used for an arbitrary emission altitude and for all inclination angles between the magnetic and rotation axes. The combination of all these effects surprisingly leaves the Goldreich-Julian type beam essentially unaltered, owing to the mutually opposing nature of these effects. The general relativistic effects at most give a 4% beam squeeze. At a finer level, the possibility of seeing the resultant small effects in pulsar observations is indicated and briefly discussed.

Pulse profiles and spectra of gamma ray pulsars in the polar cap model

We investigate predictions for pulse profiles and spectra of gamma-ray pulsars in the polar cap curvature radiation-initiated cascade model. In this model, the gamma-ray beam is a hollow cone centered on the magnetic pole, producing either double-peaked or single-peaked pulse profiles depending on observer orientation. We have computed simulated distributions of pulse peak phase separation seen by observers at random orientation as a function of gamma-ray beam width and obliquity distribution. The observed distribution of pulse peak phase separation, which favors double-peaked pulses with phase separation near 0.4, can be matched assuming that most gamma-ray pulsars have obliquity < 45° and beam opening angles of around 30°. The gamma-ray spectra result from primary particle curvature radiation, softened by synchrotron radiation from one or more generations of electron-positron pairs. We have determined the generation number and predicted spectral index of gamma-ray pulsar cascades as a function of period and surface magnetic field. It is found that the spectral hardness should decrease with cascade generation number and increase with characteristic age, a trend observed for EGRET-detected pulsars.

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 possible acceleration of electron-positron pairs created in magnetospheres, and their subsequent contribution to gamma-ray luminosity L_\gamma. It also reproduces the empirical trend in L_\gamma for seven pulsars detected with Compton Gamma Ray Observatory (CGRO) experiments. At the same time it avoids basic difficulties (Nel et al. 1996, Arons 1996) faced by theoretical models when confronted with observational constraints. We show that the classical and millisecond pulsars form two distinct branches in the L_gamma - 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.

Magnetic Photon Splitting: Computations of Proper‐Time Rates and Spectra

The splitting of photons in the presence of an intense magnetic field has recently found astrophysical applications in polar cap models of gamma-ray pulsars and in magnetar scenarios for soft gamma repeaters. Numerical computation of the polarization-dependent rates of this third order QED process for arbitrary field strengths and energies below pair creation threshold is difficult: thus early analyses focused on analytic developments and simpler asymptotic forms. The recent astrophysical interest spurred the use of the S-matrix approach by Mentzel, Berg and Wunner to determine splitting rates. In this paper, we present numerical computations of a full proper-time expression for the rate of splitting that was obtained by Stoneham, and is exact up to the pair creation threshold. While the numerical results derived here are in accord with the earlier asymptotic forms due to Adler, our computed rates still differ by as much as factors of 3 from the S-matrix re-evaluation of Wilke and Wunner, reflecting the extreme difficulty of generating accurate S-matrix numerics for fields below about \teq{4.4\times 10^{13}}Gauss. We find that our proper-time rates appear very accurate, and exceed Adler's asymptotic specializations significantly only for photon energies just below pair threshold and for supercritical fields, but always by less than a factor of around 2.6. We also provide a useful analytic series expansion for the scattering amplitude valid at low energies.

A radio continuum study of the Magellanic Clouds. IVa. Catalogue of radio sources in the Large Magellanic Cloud at 2.30 GHz$^{\bf (\lambda=13 cm)}$

The pulsation of Geminga has been detected to date only at high energies (E greater than 0.1 keV). Since x-ray exposures are short and Geminga is at best only marginally detected in gamma-rays at E less than 30 MeV, the primary means of timing Geminga is with high-energy gamma-rays. The EGRET observations of Geminga now span 4 years. These data are analyzed to determine the 1995 ephemeris for Geminga which is provided here. We continue to count every revolution of Geminga during the GRO mission with a rotational phase resolution which improves with additional exposure. Proper motion is now apparent in gamma-ray timing, consistent with the optical measurement of Bignami et al. With improved statistics, two additional peaks are tentatively detected in the 'minor bridge' region. More exposure is required to confirm them. If found to be real, they are difficult to understand with polar cap models, but are expected for the outer gap model, and provide sorely needed constraints.

Gamma-Ray Pulsars: Emission from Extended Polar CAP Cascades

view Abstract Citations (346) References (52) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gamma-Ray Pulsars: Emission from Extended Polar CAP Cascades Daugherty, Joseph K. ; Harding, Alice K. Abstract We have used a Monte Carlo simulation of a polar cap (PC) model of γ-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 Earth. In this single polar cap (SPC) scenario, even sources whose light curves have two distinct peaks (Crab, Vela, Geminga, and PSR B1951+32) are due to emission concentrated near the rim of a single PC. If the inclination α is comparable to the half-width of the PC γ-beam, α ∼θb, 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 γ-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 that 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 beamwidths (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. Based on these assumptions, our model results for Vela reproduce key features of the light curves and phase-resolved spectra. We also consider the compatibility of the model with observations at X-ray, radio, and optical wavelengths. Publication: The Astrophysical Journal Pub Date: February 1996 DOI: 10.1086/176811 arXiv: arXiv:astro-ph/9508155 Bibcode: 1996ApJ...458..278D Keywords: GAMMA RAYS: THEORY; STARS: PULSARS: GENERAL; RADIATION MECHANISMS: NONTHERMAL; Astrophysics E-Print: 31 pages (AASTEX) + 9 figures (uuencoded, compressed ps), to be published in ApJ, Feb. 10 1996 full text sources arXiv | ADS | data products SIMBAD (8)

The Nightside Ionosphere: Ionospheric Convection during an Isolated Substorm on October 21, 1981

Substorms can occur in series such as during a geomagnetic storm or as isolated events. We have chosen an isolated substorm from the Dynamics Explorer-2 (DE-2) database and use the Expanding/Contracting Polar Cap Model to study the substorm-related ionospheric electric fields and polar cap dynamics. The isolated event of October 21, 1981 took place during several consecutive DE-2 passes which occur before the onset, just after the onset, during the substorm maximum, and during the recovery phase of the substorm. The polar cap expands during the growth and expansion phases and contracts little throughout the recovery phase. Tail reconnection, however, dominates the recovery phase. A total of 4 × 10 8 webers of open flux were reconnected during the recovery phase and removed from the polar cap.

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.