Polar Cap Model Research Articles

Magnetic local time variation and scaling of poleward auroral boundary dynamics

AbstractThe balance of dayside and nightside reconnection processes within the Earth's magnetosphere and its effect on the amount of open magnetic flux threading the ionosphere is well understood in terms of the expanding‐contracting polar cap model. However, the nature and character of the consequential fluctuations in the polar cap boundary are poorly understood. By using the poleward auroral luminosity boundary (PALB), as measured by the FUV instrument of the IMAGE spacecraft, as a proxy for the polar cap boundary, we have studied the motion of this boundary for more than 2 years across the complete range of magnetic local time. Our results show that the dayside PALB dynamics are broadly self‐similar on timescales of 12 min to 6 h and appear to be monofractal. Similarity with the characteristics of solar wind and interplanetary magnetic field variability suggests that this dayside monofractal behavior is predominantly inherited from the solar wind via the reconnection process. The nightside PALB dynamics exhibit scale‐free behavior at intermediate time scales (12–90 min) and appear to be multifractal. We propose that this character is a result of the intermittent multifractal structure of magnetotail reconnection.

MODELING THE X-RAYS FROM THE CENTRAL COMPACT OBJECT PSR J1852+0040 IN KESTEVEN 79: EVIDENCE FOR A STRONGLY MAGNETIZED NEUTRON STAR

I present modeling of the X-ray pulsations from the central compact object (CCO) PSR J1852+0040 in the Galactic supernova remnant Kesteven 79. In the context of thermal surface radiation from a rotating neutron star, a conventional polar cap model can reproduce the broad, large-amplitude X-ray pulse only with a "pencil plus fan" beam emission pattern, which is characteristic of strongly magnetized ($\gtrsim$10^12 Gauss) neutron star atmospheres, substantially stronger than the ~10^10 Gauss external dipole field inferred from the pulsar spin-down rate. This discrepancy can be explained by an axially displaced dipole. For other beaming patterns, it is necessary to invoke high-aspect-ratio emitting regions that are greatly longitudinally elongated, possibly due to an extremely offset dipole. For all assumed emission models, the existence of strong internal magnetic fields ($\gtrsim$10^14} Gauss) that preferentially channel internal heat to only a portion of the exterior is required to account for the implied high-temperature contrast across the stellar surface. This lends further observational evidence in support of the "hidden" strong magnetic field scenario, in which CCOs possess strong submerged magnetic fields that are substantially stronger than the external dipole field, presumably due to burial by fallback of supernova ejecta. I also conduct phase-resolved X-ray spectroscopy and find no evidence for prominent spin-phase-dependent absorption features that could be produced by cyclotron absorption/scattering.

MAGNETIC PAIR CREATION TRANSPARENCY IN GAMMA-RAY PULSARS

Magnetic pair creation $\gamma \to e^+e^-$ has been at the core of radio pulsar paradigms and central to polar cap models of gamma-ray pulsars for over three decades. The Fermi gamma-ray pulsar population now exceeds 140 sources and has defined an important part of Fermi's science legacy. Among the population characteristics well established is the common occurrence of exponential turnovers in their spectra in the 1--10 GeV range. These turnovers are too gradual to arise from magnetic pair creation in the strong magnetic fields of pulsar inner magnetospheres. By demanding insignificant photon attenuation precipitated by such single-photon pair creation, the energies of these turnovers for Fermi pulsars can be used to compute lower bounds for the typical altitude of GeV band emission. This paper explores such pair transparency constraints below the turnover energy, and updates earlier altitude bound determinations of that have been deployed in various Fermi pulsar papers. For low altitude emission locales, general relativistic influences are found to be important. Rotational aberration influences are also explored, and are found to be small at low altitudes, except near the magnetic pole. The altitude bounds are typically in the range of 2-7 stellar radii for the young Fermi pulsar population, and provide key information on the emission altitude in radio quiet pulsars that do not possess double-peaked pulse profiles. The bound for the Crab pulsar is at a much higher altitude, with the putative detection by MAGIC out to 350-400 GeV implying a lower bound of 310km to the emission region, i.e., approximately 20% of the light cylinder radius. These results are also extended to the super-critical field domain, where it is found that emission in magnetars originating below around 10 stellar radii will not appear in the Fermi-LAT band.

CONSTRAINTS ON THE EMISSION GEOMETRIES AND SPIN EVOLUTION OF GAMMA-RAY MILLISECOND PULSARS

Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using a maximum likelihood technique. We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II) or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed.

REALISTIC MODELING OF THE PULSE PROFILE OF PSR J0737-3039A

The Double Pulsar, PSR J$0737$$-$$3039$A/B, is a unique system in which both neutron stars have been detected as radio pulsars. As shown in Ferdman et al., there is no evidence for pulse profile evolution of the A pulsar, and the geometry of the pulsar was fit well with a double-pole circular radio beam model. Assuming a more realistic polar cap model with a vacuum retarded dipole magnetosphere configuration including special relativistic effects, we create synthesized pulse profiles for A given the best-fit geometry from the simple circular beam model. By fitting synthesized pulse profiles to those observed from pulsar A, we constrain the geometry of the radio beam, namely the half-opening angle and the emission altitude, to be $30^\circ$ and $10$ neutron star radii, respectively. Combining the observational constraints of PSR J$0737$$-$$3039$A/B, we are able to construct the full three-dimensional orbital geometry of the Double Pulsar. The relative angle between the spin axes of the two pulsars ($\Delta_S$) is estimated to be ($138^\circ \pm 5^\circ$) at the current epoch and will likely remain constant until tidal interactions become important in $\sim$$85$ Myr, at merger.

The influence of small scale magnetic field on the polar cap X-ray luminosity of old radio pulsars

The influence of small-scale magnetic field on the polar cap heating by returning positrons is considered. The returning positron current is calculated in the framework of two models of rapid and gradual screening. To calculate the electron-positron pair production rate we take into account only the curvature radiation of primary electrons and its absorption in magnetic field. We use the polar cap model with steady space charge limited electron flow. It is shown that the rapid screening model is in the better agreement with observations of old (age > 106 years) radio pulsars. The gradual screening model usually leads to too strong heating and too large X-ray luminosities.

Numerical modelling of -ray emission produced by electrons originating from the magnetospheres of millisecond pulsars in globular clusters

Globular clusters are source of gamma-ray radiation. At GeV energies, their emission is attributed to magnetospheric activity of millisecond pulsars residing in the clusters. Inverse Compton scattering of ambient photon fields on relativistic particles diffusing through cluster environment is thought to be the source of GeV-TeV emission of globular clusters. Using pair starved polar cap model gamma-ray emission from synthetic millisecond pulsar was modelled. In addition to pulsar emission characteristics, the synthetic pulsar model yielded spectra of electrons escaping pulsar magnetosphere. To simulate gamma-ray emission of globular cluster, both products of synthetic millisecond pulsar modelling were used. Gamma-ray spectra of synthetic millisecond pulsars residing in the cluster were summed to produce the magnetospheric component of cluster emission. Electrons ejected by these pulsars were injected into synthetic globular cluster environment. Their diffusion and interaction, both, with cluster magnetic field and ambient photon fields, were performed with Bednarek & Sitarek (2007) model yielding ICS component of cluster emission. The sum of the magnetospheric and ICS components gives the synthetic gamma-ray spectrum of globular cluster. The synthetic cluster spectrum stretches from GeV to TeV energies. Detailed modelling was preformed for two globular clusters: Ter 5 and 47 Tuc. Simulations are able to reproduce (within errors) the shape and the flux level of the GeV part of the spectrum observed for both clusters with the Fermi/LAT instrument. The synthetic flux level obtained in the TeV part of the clusters' spectrum is in agreement with a H.E.S.S. upper limit determined for 47 Tuc, and with emission level recently detected for Ter 5 with H.E.S.S. telescope. The synthetic globular cluster model, however, is not able to reproduce the exact shape of the TeV spectrum observed for Ter 5.

THE ANNULAR GAP: GAMMA-RAY & RADIO EMISSION OF PULSARS

Pulsars have been found more than 40 years. Observations from radio to gamma-rays present abundant information. However, the radiation mechanism is still an open question. It is found that the annular gap could be formed in the magnetosphere of pulsars (neutron stars or quark stars), which combines the advantages of the polar cap, slot gap and outer gap models. It is emphasized that observations of some radio pulsars, normal and millisecond gamma-ray pulsars (MSGPs) show that the annular gap would play a very important role. Here we show some observational and theoretical evidences about the annular gap. For example, bi-drifting sub-pulses; radio and gamma-ray millisecond pulsars and so on.

A Particle Simulation for the Pulsar Magnetosphere: Relationship of Polar Cap, Slot Gap, and Outer Gap

Abstract To explain the pulsed emission of the rotation powered pulsars from radio to gamma-ray, polar cap models, slot gap models, and outer gap models are proposed. Recent observations suggest that these models are likely to co-exist in the same magnetosphere. If so, their mutual relation is known to be troublesome (Harding 2009), due to the boundary conditions and the direction of the current, which are properly assumed in each acceleration model. We performed a particle simulation for the global magnetospheric structure. Based on this simulation, we present a new picture of the global structure of the pulsar magnetosphere. It is found that a new dead zone is formed along the current neutral line that separates the oppositely directed current. We shall call this the current-neutral zone. We suggest that the polar cap accelerators and the slot gaps locate above the current-neutral zone, and the outer gap exist between the current neutral zone and the traditional dead zone. We also give an estimate of the super-rotation region.

MODELING PHASE-ALIGNED GAMMA-RAY AND RADIO MILLISECOND PULSAR LIGHT CURVES

Since the discovery of the first eight gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope, this population has been steadily expanding. Four of the more recent detections, PSR J00340534, PSR J1939+2134 (B1937+21; the first MSP ever discovered), PSR J1959+2048 (B1957+20; the first discovery of a black widow system), and PSR J2214+3000, exhibit a phenomenon not present in the original discoveries: nearly phase-aligned radio and gamma-ray light curves (LCs). To account for the phase alignment, we explore models where both the radio and gamma-ray emission originate either in the outer magnetosphere near the light cylinder or near the polar caps. Using a Markov Chain Monte Carlo technique to search for best-fit model parameters, we obtain reasonable LC fits for the first three of these MSPs in the context of altitude-limited outer gap (alOG) and two-pole caustic (alTPC) geometries (for both gamma-ray and radio emission). These models differ from the standard outer gap (OG)/two-pole caustic (TPC) models in two respects: the radio emission originates in caustics at relatively high altitudes compared to the usual conal radio beams, and we allow both the minimum and maximum altitudes of the gamma-ray and radio emission regions to vary within a limited range (excluding the minimum gamma-ray altitude of the alTPC model, which is kept constant at the stellar radius, and that of the alOG model, which is set to the position-dependent null charge surface altitude). Alternatively, phase-aligned solutions also exist for emission originating near the stellar surface in a slot gap scenario (low-altitude slot gap (laSG) models). We find that the alTPC models provide slightly better LC fits than the alOG models, and both of these give better fits than the laSG models (for the limited range of parameters considered in the case of the laSG models). Thus, our fits imply that the phase-aligned LCs are likely of caustic origin, produced in the outer magnetosphere, and that the radio emission for these pulsars may come from close to the light cylinder. In addition, we were able to constrain the minimum and maximum emission altitudes with typical uncertainties of 30% of the light cylinder radius. Our results therefore describe a third gamma-ray MSP subclass, in addition to the two previously found by Venter et al.: those with LCs fit by standard OG/TPC models and those with LCs fit by pair-starved polar cap models.

The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W10, since the broadening of the observed pulses due to the transition to the full width W0 and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β1 are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β1〉 = 18° at λ = 10 cm and 〈β1〉 = 14° at λ = 20 cm). The angle β2 is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β2 at 10 cm is found to be 〈β2〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β2〉 = 52.1° ifC 0 and 〈β2〉 = 54.1° ifC 0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β2〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.

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 $\chi=a/m_p$ is yet too small to give origin to observable signals. We show that, for pulsars with period $P\approx 1\,$ms, a surface polar magnetic field $B \approx 10^{12}$G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered.

A unified polar cap/striped wind model for pulsed radio and gamma-ray emission in pulsars

(abridged) Thanks to the recent discovery by Fermi of about fifty new gamma-ray pulsars, it becomes possible to look for statistical properties of their pulsed high-energy emission, especially their light-curves and phase-resolved spectra. These pulsars emit by definition mostly gamma-ray photons but some of them are also detected in the radio band. For those seen in these two extreme energies, the relation between time lag of radio/gamma-ray pulses and gamma-ray peak separation, in case both high-energy pulses are seen, helps to put some constrain on the magnetospheric emission mechanisms and location. This idea is analyzed in detail in this paper, assuming a polar cap model for the radio pulses and the striped wind geometry for the pulsed high-energy counterpart. Combining the time-dependent emissivity in the wind, supposed to be inverse Compton radiation, with a simple polar cap emission model along and around the magnetic axis, we compute the radio and gamma-ray light-curves, summarizing the results in several phase plots. The phase lag as well as the gamma-ray peak separation dependence on the pulsar inclination angle and on the viewing angle are studied. Using the gamma-ray pulsar catalog compiled from the Fermi data, we are able to predict the radio lag/peak separation relation and compare it with available observations taken from this catalog.

AGILEOBSERVATIONS OF THE “SOFT” GAMMA-RAY PULSAR PSR B1509 – 58

We present the results of new AGILE observations of PSR B1509 − 58 performed over a period of ∼2.5 years following the detection obtained with a subset of the present data. The modulation significance of the light curve above 30 MeV is at a 5σ confidence level and the light curve is similar to those found earlier by COMPTEL up to 30 MeV: a broad asymmetric first peak reaching its maximum 0.39 ± 0.02 cycles after the radio peak plus a second peak at 0.94 ± 0.03. The gamma-ray spectral energy distribution of the pulsed flux detected by COMPTEL and AGILE is well described by a power law (photon index α = 1.87 ± 0.09) with a remarkable cutoff at Ec = 81 ± 20 MeV, representing the softest spectrum observed among gamma-ray pulsars so far. The pulsar luminosity at E > 1 MeV is Lγ = 4.2+0.5−0.2 × 1035 erg s−1, assuming a distance of 5.2 kpc, which implies a spin-down conversion efficiency to gamma rays of ∼0.03. The unusual soft break in the spectrum of PSR B1509 − 58 has been interpreted in the framework of polar cap models as a signature of the exotic photon-splitting process in the strong magnetic field of this pulsar. In this interpretation, our spectrum constrains the magnetic altitude of the emission point(s) at 3 km above the neutron star surface, implying that the attenuation may not be as strong as formerly suggested because pair production can substitute photon splitting into regions of the magnetosphere where the magnetic field becomes too low to sustain photon splitting. In the case of an outer-gap scenario or the two-pole caustic model, better constraints on the geometry of the emission would be needed from the radio band in order to establish whether the conditions required by the models to reproduce AGILE light curves and spectra match the polarization measurements.

PROBING MILLISECOND PULSAR EMISSION GEOMETRY USING LIGHT CURVES FROM THEFERMI/LARGE AREA TELESCOPE

An interesting new high-energy pulsar sub-population is emerging following early discoveries of gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope (LAT). We present results from 3D emission modeling, including the Special Relativistic effects of aberration and time-of-flight delays and also rotational sweepback of B-field lines, in the geometric context of polar cap (PC), outer gap (OG), and two-pole caustic (TPC) pulsar models. In contrast to the general belief that these very old, rapidly-rotating neutron stars (NSs) should have largely pair-starved magnetospheres due to the absence of significant pair production, we find that most of the light curves are best fit by TPC and OG models, which indicates the presence of narrow accelerating gaps limited by robust pair production -- even in these pulsars with very low spin-down luminosities. The gamma-ray pulse shapes and relative phase lags with respect to the radio pulses point to high-altitude emission being dominant for all geometries. We also find exclusive differentiation of the current gamma-ray MSP population into two MSP sub-classes: light curve shapes and lags across wavebands impose either pair-starved PC (PSPC) or TPC / OG-type geometries. In the first case, the radio pulse has a small lag with respect to the single gamma-ray pulse, while the (first) gamma-ray peak usually trails the radio by a large phase offset in the latter case. Finally, we find that the flux correction factor as a function of magnetic inclination and observer angles is typically of order unity for all models. Our calculation of light curves and flux correction factor for the case of MSPs is therefore complementary to the "ATLAS paper" of Watters et al. for younger pulsars.

Aspect angle for interstellar magnetic field in SN 1006

A number of important processes taking place around strong shocks in supernova remnants (SNRs) depend on the shock obliquity. The measured synchrotron flux is a function of the aspect angle between interstellar magnetic field (ISMF) and the line of sight. Thus a model of non-thermal emission from SNRs should account for the orientation of the ambient magnetic field. We develop a new method for the estimation of the aspect angle, based on the comparison between observed and synthesized radio maps of SNRs, making different assumptions about the dependence of electron injection efficiency on the shock obliquity. The method uses the azimuthal profile of radio surface brightness as a probe for orientation of ambient magnetic field because it is almost insensitive to the downstream distribution of magnetic field and emitting electrons. We apply our method to a new radio image of SN 1006 produced on the basis of archival VLA and Parkes data. The image recovers emission from all spatial structures with angular scales from few arcseconds to 15 arcmin. We explore different models of injection efficiency and find the following best-fitting values for the aspect angle of SN 1006: phi=70 +/- 4.2 deg if the injection is isotropic, phi=64 +/- 2.8 deg for quasi-perpendicular injection (SNR has an equatorial belt in both cases) and phi=11 +/- 0.8 deg for quasi-parallel injection (polar-cap model of SNR). In the last case, SN 1006 is expected to have a centrally-peaked morphology contrary to what is observed. Therefore, our analysis provides some indication against the quasi-parallel injection model.

Effect of the pulsar-tube radius on the gamma-ray curvature radiation from the polar regions of radio pulsars with non-dipolar magnetic fields

The effect of the radius of the tube of open magnetic-field lines on the gamma-ray curvature radiation from the polar regions of a radio pulsar with a non-dipolar magnetic field is analyzed. The pulsar is considered in a polar-cap model with free electron emission from the neutron-star surface. The effect of the non-dipolar magnetic field on the radius of curvature of the field lines and the field intensity is taken into account. In connection with the creation of electron-positron pairs, we take into account only the birth of pairs by curvature radiation in the magnetic field. The small non-dipolarity of the field enables the radio pulsar not to turn off, even after a considerable decrease in the pulsar-tube radius. For instance, with a 20% non-dipolarity (ν = 0.2), a pulsar with B = 1013 G and P = 0.5 s can still operate even for a fivefold decrease in the pulsar-tube radius. A maximum is observed in the dependence of the electrostatic potential in the diode on the non-dipolarity parameter ν at ν ∼ 0.5–0.7. The pulse profile in non-thermal X-ray emission for ν ∼ 0.5–0.7 may look virtually the same as for ν ∼ 0.1–0.2. Decreases in the pulsar-tube radius could be due to a structure of currents in the magnetosphere that results in the pulsar diode on the neutron-star surface occupying only a small fraction of the pulsar tube, with the remainder of the tube containing an outer annular gap. The pulsar-tube size is also affected by the presence of a circum-pulsar disk. A change in the pulsar-tube radius could also be due to an external magnetic field, associated with either a magnetic white dwarf or a circum-pulsar disk.

Transpolar voltage and polar cap flux during the substorm cycle and steady convection events

Transpolar voltages observed during traversals of the polar cap by the Defense Meteorological Satellite Program (DMSP) F‐13 spacecraft during 2001 are analyzed using the expanding‐contracting polar cap model of ionospheric convection. Each of the 10,216 passes is classified by its substorm phase or as a steady convection event (SCE) by inspection of the AE indices. For all phases, we detect a contribution to the transpolar voltage by reconnection in both the dayside magnetopause and in the cross‐tail current sheet. Detection of the IMF influence is 97% certain during quiet intervals and &gt;99% certain during substorm/SCE growth phases but falls to 75% in substorm expansion phases: It is only 27% during SCEs. Detection of the influence of the nightside voltage is only 19% certain during growth phases, rising during expansion phases to a peak of 96% in recovery phases: During SCEs, it is &gt;99%. The voltage during SCEs is dominated by the nightside, not the dayside, reconnection. On average, substorm expansion phases halt the growth phase rise in polar cap flux rather than reversing it. The main destruction of the excess open flux takes place during the 6‐ to 10‐hour interval after the recovery phase (as seen in AE) and at a rate which is relatively independent of polar cap flux because the NENL has by then retreated to the far tail. The best estimate of the voltage associated with viscous‐like transfer of closed field lines into the tail is around 10 kV.

Electrodynamics of Magnetars. IV. Self‐Consistent Model of the Inner Accelerator with Implications for Pulsed Radio Emission

We consider the voltage structure in the open-field circuit and outer magnetosphere of a magnetar. The standard polar cap model for radio pulsars is modified significantly when the polar magnetic field exceeds 1.8 × 1014 G. Then a surface gap is effectively screened, because resonantly scattered X-rays can convert almost instantaneously to electron-positron pairs. We point out a second possible voltage distribution, in which backflowing charges spawn just enough pairs to compensate the gradient in the corotation charge density. We also examine the gap structure when the magnetic field is somewhat weaker and deduce a voltage 10-30 times larger over a range of surface temperatures. We examine carefully how the flow of charge back to the star above the gap depends on the magnitude of the current, on the curvature of the magnetic field lines, and on resonant drag. The rates of different channels of pair creation are determined self-consistently, including the nonresonant scattering of X-rays and collisions between gamma rays and X-rays. Both circuit solutions are subject to a two-stream instability due to a spatially extended return charge flow. The voltage is high enough to sustain the radio output of strongly magnetic pulsars, but not of the two radio magnetars with active magnetospheres, unless the gap is also present on the closed magnetic field lines. Several properties of the radio magnetars—their rapid variability, broad pulses, and unusually hard radio spectra—are consistent with a third possibility, that the current in the outer magnetosphere is strongly variable and a very high rate of pair creation is sustained by a turbulent cascade.

Contributions from nearby pulsars to the local cosmic ray electron spectrum

PSR J0437-4715 is one of the closest millisecond pulsars (MSPs) to Earth, lying at a distance of ∼140 pc. This pulsar has a characteristic age of 4.9 Gyr and a relatively low spindown power of ∼10 34 ergs/s. During its rather long lifetime, a large fraction of the energy output has been in the form of multi-TeV electrons. In this paper, we investigate the possible contribution of this nearby MSP to the local interstellar electron spectrum (LIS). The old age of the system justifies a steady-state evaluation of the contribution from this pulsar to the LIS. We calculate the electron spectrum at the light cylinder in the framework of a General Relativistic polar cap (PC) model, and use this as an injection spectrum in a diffusion model. The younger Geminga pulsar is also very close to Earth and warrants investigation. A steady-state approach is however no longer justified, so we use an impulsive injection model. We will present results of a study of the contribution from these pulsars to the cosmic ray (CR) LIS. Our calculations show that pulsars like Geminga can make a non-negligible contribution to the LIS.