Null Charge Surface Research Articles

Comprehensive Analysis of Magnetospheric Gaps around Kerr Black Holes Using 1D GRPIC Simulations

Abstract Spark gaps are likely the source of plasma in active black hole (BH) magnetospheres. In this paper, we present results of 1D general relativistic particle-in-cell simulations of a starved BH magnetosphere with a realistic treatment of inverse-Compton scattering and pair production, for a broad range of conditions, run times longer than in previous studies, and different setups. We find that following the initial discharge, the system undergoes gradual evolution over prolonged time until either restoring the vacuum state or reaching a state of quasiperiodic oscillations, depending on the spectral shape and luminosity of the ambient radiation field. The oscillations occur near the null charge surface in cases where the global magnetospheric current is in the direction defined by the product of the asymptotic Goldreich–Julian charge density and the radial velocity, while they occur near the boundary of the simulation box when it is the opposite direction (return current). Their amplitude and the resultant luminosity of TeV photons emitted from the gap depend sensitively on the conditions; for the cases studied here the ratio of TeV luminosity to the Blandford–Znajek power ranges from 10−5 to 10−2, suggesting that strong flares may be generated by moderate changes in disk emission. We also examined the dependence of the solution on the initial number of particles per cell (PPC) and found convergence for PPC of about 50 for the cases examined. At lower PPC values the pair multiplicity is found to be artificially high, affecting the solution considerably.

ENERGETIC GAMMA RADIATION FROM RAPIDLY ROTATING BLACK HOLES

ABSTRACT Supermassive black holes (BHs) are believed to be the central powerhouse of active galactic nuclei. Applying the pulsar outer-magnetospheric particle accelerator theory to BH magnetospheres, we demonstrate that an electric field is exerted along the magnetic field lines near the event horizon of a rotating BH. In this particle accelerator (or a gap), electrons and positrons are created by photon–photon collisions and accelerated in the opposite directions by this electric field, efficiently emitting gamma-rays via curvature and inverse-Compton processes. It is shown that a gap arises around the null-charge surface formed by the frame-dragging effect, provided that there is no current injection across the gap boundaries. The gap is dissipating a part of the hole’s rotational energy, and the resultant gamma-ray luminosity increases with decreasing plasma accretion from the surroundings. Considering an extremely rotating supermassive BH, we show that such a gap reproduces the significant very-high-energy (VHE) gamma-ray flux observed from the radio galaxy IC 310, provided that the accretion rate becomes much less than the Eddington rate particularly during its flare phase. It is found that the curvature process dominates the inverse-Compton process in the magnetosphere of IC 310, and that the observed power-law-like spectrum in VHE gamma-rays can be explained to some extent by a superposition of the curvature emissions with varying curvature radius. It is predicted that the VHE spectrum extends into higher energies with increasing VHE photon flux.

Mechanism of the X-ray and Soft Gamma-ray Emissions from the High Magnetic Field Pulsar: PSR B1509-58

We use the outer gap model to explain the spectrum and the energy dependent light curves of the X-ray and soft -ray radiations of the spin-down powered pulsar PSR B1509-58. In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap`s electric field separates the opposite charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow current and that from the null charge surface to the star is dominated by the inflow current. We suggest that the viewing angle of PSR B1509-58 only receives the inflow radiation. The incoming curvature photons are converted to pairs by the strong magnetic field of the star. The X-rays and soft -rays of PSR B1509-58 result from the synchrotron radiation of these pairs. The magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and the second peak appearing at E > 10 MeV comes from the region near the star, where the stronger magnetic field allows the pair creation to happen with a smaller pitch angle.

PHASE-AVERAGED SPECTRA AND LUMINOSITIES OF GAMMA-RAY EMISSIONS FROM YOUNG ISOLATED PULSARS

We study the phase-averaged spectra and luminosities of gamma-ray emissions from young, isolated pulsars within a revised outer gap model. In the revised version of the outer gap, there are two possible cases for the outer gaps: the fractional size of the outer gap is estimated through the photon-photon pair process in the first case (Case I), and is limited by the critical field lines in the second case (Case II). The fractional size is described by Case I if the fractional size at the null charge surface in Case I is smaller than that in Case II, and vice versa. Such an outer gap can extend from the inner boundary, whose radial distance to the neutron star is less than that of the null charge surface to the light cylinder for a gamma-ray pulsar with a given magnetic inclination. When the shape of the outer gap is determined, assuming that high-energy emission at an averaged radius of the field line in the center of the outer gap, with a Gaussian distribution of the parallel electric field along the gap height, represents typical emission, the phase-averaged gamma-ray spectrum for a given pulsar can be estimated in the revised model with three model parameters. We apply the model to explain the phase-averaged spectra of the Vela (Case I) and Geminga (Case II) pulsars. We also use the model to fit the phase-averaged spectra of 54 young, isolated gamma-ray pulsars, and then calculate the gamma-ray luminosities and compare them with the observed data from Fermi-LAT.

MECHANISM OF THE X-RAY AND SOFT GAMMA-RAY EMISSIONS FROM HIGH MAGNETIC FIELD PULSAR: PSR B1509–58

We use the outer gap model to explain the spectrum and the energy-dependent light curves of the X-ray and soft γ-ray radiations of the spin-down powered pulsar PSR B1509-58. In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap's electric field separates the two charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow current while that from the null charge surface to the star is dominated by the inflow current. We suggest that the viewing angle of PSR B1509−58 only receives the inflow radiation. The incoming curvature photons are converted to pairs by the strong magnetic field of the star. The X-rays and soft γ-rays of PSR B1509−58 result from the synchrotron radiation of these pairs. Magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and that the second peak appearing at E > 10 MeV comes from the region near the star, where the stronger magnetic field allows pair creation to happen with a smaller pitch angle.

RADIO-TO-TeV PHASE-RESOLVED EMISSION FROM THE CRAB PULSAR: THE ANNULAR GAP MODEL

In the framework of the three-dimensional (3D) annular gap model with reasonable parameters (the magnetic inclination angle \alpha = 45 deg and the view angle \zeta = 63 deg), we first use the latest hight energy data to self-consistently calculate radio, X-ray, gamma-ray and TeV (MAGIC and VERITAS) light curves, phase-averaged spectrum and phase-resolved spectra for the Crab pulsar. It is found that the acceleration electric field and potential in the annular gap and core gap are huge enough in the several tens of neutron star radii. The pulsed emission of radio, X-ray, gamma-ray and TeV are mainly generated from the emission of primary particles or secondary particles with different emission mechanisms in the nearly similar region of the annular gap located in the only one magnetic pole, which leads to the nearly "phase-aligned" multi-wavelength light curves. The emission of peak 1 (P1) and peak 2 (P2) is originated from the annular gap region near the null charge surface, while the emission of bridge is mainly originated from the core gap region. The phase-averaged spectrum and phase-resolved spectra of the Crab pulsar from soft X-ray to TeV band are produced by four components: synchrotron radiation from CR-induced and ICS-induced pairs dominates the X-ray band to soft gamma-ray band (100 eV to 10 MeV); curvature radiation and synchrotron radiation from the primary particles mainly contribute to gamma-ray band (10 MeV to \sim 20 GeV); ICS from the pairs significantly contributes to the TeV gamma-ray band (\sim 20 GeV to 400 GeV). The multi-wavelength pulsed emission from the Crab pulsar has been well modeled with the annular gap and core gap model. To distinguish our single magnetic pole model from two-pole models, the convincing values of the magnetic inclination angle and the viewing angle will play a key role.

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.

GAMMA-RAY EMISSION FROM THE VELA PULSAR MODELED WITH THE ANNULAR GAP AND THE CORE GAP

The Vela pulsar represents a distinct group of {\gamma}-ray pulsars. Fermi {\gamma}-ray observations reveal that it has two sharp peaks (P1 and P2) in the light curve with a phase separation of 0.42 and a third peak (P3) in the bridge. The location and intensity of P3 are energy-dependent. We use the 3D magnetospheric model for the annular gap and core gap to simulate the {\gamma}-ray light curves, phase-averaged and phase-resolved spectra. We found that the acceleration electric field along a field line in the annular gap region decreases with heights. The emission at high energy GeV band is originated from the curvature radiation of accelerated primary particles, while the synchrotron radiation from secondary particles have some contributions to low energy {\gamma}-ray band (0.1 - 0.3 GeV). The {\gamma}-ray light curve peaks P1 and P2 are generated in the annular gap region near the altitude of null charge surface, whereas P3 and the bridge emission is generated in the core gap region. The intensity and location of P3 at different energy bands depend on the emission altitudes. The radio emission from the Vela pulsar should be generated in a high-altitude narrow regions of the annular gap, which leads to a radio phase lag of ~ 0.13 prior to the first {\gamma}-ray peak.

The annular gap model for γ-ray emission from young and millisecond pulsars

Pulsed high energy radiation from pulsars is not yet completely understood. In this paper, we use the 3D self-consistent annular gap model to study light curves for both young and millisecond pulsars observed by the Fermi Gamma-ray Space Telescope. The annular gap can generate high energy emission for short-period pulsars. The annular gap regions are so large that they have enough electric potential drop to accelerate charged particles to produce gamma-ray photons. For young pulsars, the emission region is from the neutron star surface to about half of the light cylinder radius, and the peak emissivity is in the vicinity of the null charge surface. The emission region for the millisecond pulsars is located much lower than that of the young pulsars. The higher energy gamma-ray emission comes from higher altitudes in the magnetosphere. We present the simulated light curves for three young pulsars (the Crab, the Vela, the Geminga) and three millisecond pulsars (PSR J0030+0451, PSR J0218+4232, PSR J0437-3715) using the annular gap model. Our simulations can reproduce the main properties of observed light curves.

WIDE RADIO BEAMS FROM γ-RAY PULSARS

We investigate the radio and gamma-ray beaming properties of normal and millisecond pulsars by selecting two samples from the known populations. The first, Sample G, contains pulsars which are detectable in blind searches of gamma-ray data from the Fermi Large Area Telescope. The second, Sample R, contains pulsars detectable in blind radio searches which have spin-down luminosities Edot > 10^{34} erg/s. We analyse the fraction of the gamma-ray-selected Sample G which have detectable radio pulses and the fraction of the radio-selected Sample R which have detectable gamma-ray pulses. Twenty of our 35 Sample G pulsars have already observed radio pulses. This rules out low-altitude polar-cap beaming models if, as is currently believed, gamma-ray beams are generated in the outer magnetosphere and are very wide. We further find that, for the highest-Edot pulsars, the radio and gamma-ray beams have comparable beaming factors, i.e., the beams cover similar regions of the sky as the star rotates. For lower-Edot gamma-ray emitting pulsars, the radio beams have about half of the gamma-ray sky coverage. These results suggest that, for high-Edot young and millisecond pulsars, the radio emission originates in wide beams from regions high in the pulsar magnetosphere, probably close to the null-charge surface and to the gamma-ray emitting regions. Furthermore, it suggests that for these high-Edot pulsars, as in the gamma-ray case, features in the radio profile represent caustics in the emission beam pattern.

PULSAR HIGH ENERGY EMISSIONS FROM OUTER GAP ACCELERATOR CLOSED BY A MAGNETIC PAIR-CREATION PROCESS

We discuss outer gap closure mechanism in the trans-field direction with the magnetic pair-creation process near the stellar surface. The gap closure by the magnetic pair creation is possible if some fraction of the pairs are produced with an outgoing momentum. By assuming that multiple magnetic field will affect the local field near the stellar surface, we show a specific magnetic field geometry near the stellar surface resulting in the outflow of the pairs. Together with the fact that the electric field is weak below null charge surface, the characteristic curvature photon energy emitted by incoming particles, which were accelerated in the outer gap, decreases drastically to ∼100 MeV near the stellar surface. We estimate the height measured from the last-open field line, above which 100 MeV photons are converted into pairs by the magnetic pair creation. We also show the resultant multiplicity due to the magnetic pair-creation process could acquire . In this model, the fractional outer gap size is proportional to P−1/2. The predicted γ-ray luminosity (Lγ) and the characteristic curvature photon energy (Ec) emitted from the outer gap are proportional to B2P−5/2 and B3/4P−1, respectively. This model also predicts that Lγ and Ec are related to the spin-down power (Lsd) or the spin-down age of pulsars (τ) as Lγ ∝ L5/8sd or Lγ ∝ τ−5/4 and Ec ∝ L1/4sd or Ec ∝ τ−1/2, respectively.

MODELING OF GAMMA-RAY PULSAR LIGHT CURVES USING THE FORCE-FREE MAGNETIC FIELD

(Abridged) Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light curve modeling using the more realistic field taken from 3D force-free magnetospheric simulations. Having the geometry of the field, we apply several prescriptions for the location of the emission zone, comparing the light curves to observations. We find that the conventional two-pole caustic model fails to produce double-peak pulse profiles, mainly because the size of the polar cap in force-free magnetosphere is larger than the vacuum field polar cap. The conventional outer-gap model is capable of producing only one peak under general conditions, because a large fraction of open field lines does not cross the null charge surface. We propose a novel "separatrix layer" model, where the high-energy emission originates from a thin layer on the open field lines just inside of the separatrix that bounds the open flux tube. The emission from this layer generates two strong caustics on the sky map due to the effect we term "Sky Map Stagnation" (SMS). It is related to the fact that force-free field asymptotically approaches the field of a rotating split monopole, and the photons emitted on such field lines in the outer magnetosphere arrive to the observer in phase. The double-peak light curve is a natural consequence of SMS. We show that most features of the currently available gamma-ray pulsar light curves can be reasonably well reproduced and explained with the sepatratrix model using the force-free field. Association of the emission region with the current sheet will guide more detailed future studies of the magnetospheric acceleration physics.

A REVISIT OF THE TWO-POLE CAUSTIC MODEL FOR GeV LIGHT CURVES OF GAMMA-RAY PULSARS

The GeV light curve of a pulsar is an important probe to detect acceleration regions in its magnetosphere. Motivated by the recent reports on the observations of pulsars by {\it Fermi} Large Area Telescope (LAT), we restudy the two-pole caustic model and revise it to investigate the properties of the light curves in the GeV band. In the revised model, although acceleration gaps can extend from the star surface to the light cylinder along near the last open field lines, the extension of the gaps along the azimuthal direction is limited because of photon-photon pair production process. In such gaps, high-energy photons are emitted uniformly and tangentially to the field lines but cannot be efficiently produced along these field lines where the distances to the null charge surface are larger than $\sim0.9$ times of the distance of the light cylinder, and the effective azimuth extension of the gaps is about $230^\circ$. The model is applied to the four pulsars Vela, PSR J1028-5819, PSR J0205+6449, and PSR J2021+3651 whose light curves obtained with {\it Fermi} have been recently released. The model is successful in reproducing the general feature of the light curves for the four pulsars, and the radial distances of the radio pulse for the four pulsars are estimated.

Studying the Fermi GeV light curve of Vela with the two-pole caustic model

An observation of the Vela pulsar with the Fermi Large Area Telescope has been recently reported and the GeV light curve shows two main peaks with a phase separation of ∼ 0.43. We study the GeV light curve using the two-pole caustic model in which the peaks of the light curves of the pulsar result from caustic effects. The results show that the two-pole caustic model can reproduce the observed emission pattern of the two peaks and the bridge emission between them well, but overestimates the flux outside the two peaks. After taking account of the pair production effect on the azimuthal angle, we find that the resulting light curve is more consistent with the observation. We excluded the emissions from the field lines for which the distance from the null charge surface, where the pairs can be significantly produced, is larger than the radius of the light cylinder.

ONE-DIMENSIONAL ACCELERATOR IN PULSAR OUTER MAGNETOSPHERE REVISITED

We re-examine the one-dimensional (1D) vacuum and nonvacuum accelerators in the outer magnetosphere of rotation-powered pulsars by considering the limit of trans-field height through pair-production process. In the original 1D nonvacuum outer gap model, both the Poisson equation for electrical potential and the Boltzmann equations of particles and γ-rays are solved self-consistently by assuming the trans-field height as a free parameter, usually resulting in a narrow outer gap (i.e., gap length along magnetic field lines is short). In the modified 1D nonvacuum outer gap model, two improvements have been made: the trans-field height is limited by photon-photon pair production process and the outer boundary of the outer gap can be extended outside the light cylinder. Under the above assumptions, we self-consistently solve the Poisson equation for electrical potential, and the Boltzmann equations of electrons/positrons and γ-rays in both vacuum and nonvacuum outer gaps for the parameters of both Vela and Geminga pulsars. We obtain an approximate geometry of the outer gap, i.e., the trans-field height is limited by the pair-production process and increases with the radial distance to the star, and the width of the outer gap starts at the inner boundary (near the null charge surface in the vacuum case) and ends at the outer boundary which is located inside or outside the light cylinder depending on the inclination angle. Our calculated results also indicate that γ-ray spectrum from a wide outer gap is flatter than the one from a narrow outer gap and the relation between the electric field and trans-field height has an important effect on the structure of the outer gap.

Vacuum Outer-Gap Structure in Pulsar Outer Magnetospheres

We study the vacuum outer-gap structure in the outer magnetosphere of rotation-powered pulsars by considering the limit of trans-field height through a pair production process. In this case, the trans-field height is limited by the photon-photon pair production process and the outer boundary of the outer gap can be extended outside the light cylinder. By solving self-consistently the Poisson equation for electrical potential and the Boltzmann equations of electrons/positrons and γ-rays in a vacuum outer gap for the parameters of Vela pulsar, we obtain an approximate geometry of the outer gap, i.e. the trans-field height is limited by the pair-production process and increases with the radial distance to the star and the width of the outer gap starts at the inner boundary (near the null charge surface) and ends at the outer boundary which locates inside or outside the light cylinder depending on the inclination angle.

An Annular Gap Acceleration Model for γ-ray Emission of Pulsars

If the binding energy of the pulsar's surface is not so high (the case of a neutron star), both the negative and positive charges will flow out freely from the surface of the star. The annular free flow model for $\gamma$-ray emission of pulsars is suggested in this paper. It is emphasized that: (1). Two kinds of acceleration regions (annular and core) need to be taken into account. The annular acceleration region is defined by the magnetic field lines that cross the null charge surface within the light cylinder. (2). If the potential drop in the annular region of a pulsar is high enough (normally the cases of young pulsars), charges in both the annular and the core regions could be accelerated and produce primary gamma-rays. Secondary pairs are generated in both regions and stream outwards to power the broadband radiations. (3). The potential drop in the annular region grows more rapidly than that in the core region. The annular acceleration process is a key point to produce wide emission beams as observed. (4). The advantages of both the polar cap and outer gap models are retained in this model. The geometric properties of the $\gamma$-ray emission from the annular flow is analogous to that presented in a previous work by Qiao et al., which match the observations well. (5). Since charges with different signs leave the pulsar through the annular and the core regions, respectively, the current closure problem can be partially solved.

Polarization of High‐Energy Emission from the Crab Pulsar

We investigate polarization of high-energy emissions from the Crab pulsar in the frame work of the outer gap accelerator, following previous works of Cheng and coworkers. The recent version of the outer gap, which extends from inside the null charge surface to the light cylinder, is used for examining the synchrotron radiations from the secondary and the tertiary pairs, which are produced outside the gap. We calculate the light curve, the spectrum and the polarization characteristics, simultaneously, by taking into account gyration motion of the particles. The polarization position angle curve and the polarization degree are calculated to compare with the Crab optical data. We demonstrate that the radiations from inside the null charge surface make outer-wing and off-pulse emissions in the light curve, and the tertiary pairs contribute to bridge emissions. The emissions from the secondary pairs explain the main features of the observed light curve and spectrum. On the other hand, both emissions from inside the null charge surface and from the tertiary pairs are required to explain the optical polarization behavior of the Crab pulsar. The energy dependence of the polarization features is expected by the present model. For the Crab pulsar, the polarization position angle curve indicates that the viewing angle of the observer measured from the rotational axis is greater than $90^{\circ}$.

Observational constraints on the radio and γ-ray emission regions of PSR B1055−52

Observational constraints on the radio and γ-ray emission regions of PSR B1055-52 seen through our line of sight are presented by analysing the position angle curves of radio linear polarization and fitting the observed pulse widths of radio and γ-ray pulses and the phase offsets between them. Aberration, retardation and magnetic field sweep back effects that can cause additional phase offset between the emissions from different locations are taken into account. The following conclusions are obtained. (i) The radio main pulse and γ-ray pulses are emitted from the same pole, while the radio interpulse is emitted from the opposite pole. (ii) The interpulse emission region locates on the open field lines much closer to the magnetic axis than those of the main pulse, and the emission altitudes are higher than those of the main pulse. (iii) At each pole, there are probably two groups of field lines where radio emission is generated, of which the outer one consists of open field lines near (or including) the last open field lines and the inner one consists of open field lines from very near the magnetic pole to approximately the midway between the magnetic axis and the last open field lines. (iv) The γ-ray pulse comes from inner open field lines rather than from the last open field lines, and the emission altitudes are beyond the null charge surface.

A study on emission geometry and the separation of peaks in the γ-ray pulse profiles of pulsar

In the inner annular gap (IAG) model the γ-ray radiation sources are suggested to be located close to the null charge surface (NCS). A method to explore two geometric parameters ( κ, λ) of the IAG model is given in this paper. Pulsar population statistics are proposed to test the radiation locations of γ-ray pulsars. Within the IAG model, predictions for the GLAST observation of γ-ray pulsars are also made.