The absorption of a high-energy photon from the external cosmic gamma-ray background in the inner neutron star magnetosphere triggers the generation of a secondary electron-positron plasma and gives rise to a lightning - a lengthening and simultaneously expanding plasma tube. It propagates along magnetic fields lines with a velocity close to the speed of light. The high electron-positron plasma generation rate leads to dynamical screening of the longitudinal electric field that is provided not by charge separation but by electric current growth in the lightning. The lightning radius is comparable to the polar cap radius of a radio pulsar. The number of electron-positron pairs produced in the lightning in its lifetime reaches 10^28. The density of the forming plasma is comparable to or even higher than that in the polar cap regions of ordinary pulsars. This suggests that the radio emission from individual lightnings can be observed. Since the formation time of the radio emission is limited by the lightning lifetime, the possible single short radio bursts may be associated with rotating radio transients (RRATs).
The connection between the radio emission from "lightnings" produced by the absorption of high-energy photons from the cosmic gamma-ray background in a neutron star magnetosphere and radio bursts from rotating radio transients (RRATs) is investigated. The lightning length reaches 1000 km; the lightning radius is 100 m and is comparable to the polar cap radius. If a closed magnetosphere is filled with a dense plasma, then lightnings are efficiently formed only in the region of open magnetic field lines. For the radio emission from a separate lightning to be observed, the polar cap of the neutro…
The production of electron-positron pairs in a vacuum neutron star magnetosphere is investigated for both low (compared to the Schwinger one) and high magnetic fields. The case of a strong longitudinal electric field where the produced electrons and positrons acquire a stationary Lorentz factor in a short time is considered. The source of electron-positron pairs has been calculated with allowance made for the pair production by curvature and synchrotron photons. Synchrotron photons are shown to make a major contribution to the total pair production rate in a weak magnetic field. At the same ti…
The motion of electrons and positrons in the vacuum magnetosphere of a neutron star with a surface magnetic field of B~10^12 G is considered. Particles created in the magnetosphere or falling into it from outside are virtually instantaneously accelerated to Lorentz factors gamma~10^8. After crossing the force-free surface, where the projection of the electric field onto the magnetic field vanishes, a particle begins to undergo ultra-relativistic oscillations. The particle experiences a regular drift along the force-free surface simultaneous with this oscillatory motion.
The accumulation of electrons and positrons in the vacuum magnetosphere of a neutron star with a surface magnetic field of B~10^12 G is considered. It is shown that particles created in the magnetosphere or falling into the magnetosphere from outside undergo ultra-relativistic oscillations with a frequency of 10-100 MHz. These oscillations decay due to energy losses to curvature radiation and bremsstrahlung, with their frequencies reaching 1-10 GHz. Simultaneously, the particles undergo regular motion along the force-free surface along closed trajectories. This leads to the gradual accumulatio…
We consider particle acceleration in vacuum gaps in magnetospheres of black holes powered through Blandford-Znajek mechanism and embedded into radiatively-inefficient accretion flow (RIAF) environment. In such situation the gap height is limited by the onset of gamma-gamma pair production on the infrared photons originating from the RIAF. We numerically calculate acceleration and propagation of charged particles taking into account the detailed structure of electric and magnetic field in the gap and in the entire black hole magnetosphere, radiative energy losses and interactions of gamma rays …
The current state of the art in the modeling of pulsar magnetospheres invokes either the vacuum or force-free limits for the magnetospheric plasma. Neither of these limits can simultaneously account for both the plasma currents and the accelerating electric fields that are needed to explain the morphology and spectra of high-energy emission from pulsars. To better understand the structure of such magnetospheres, we combine accelerating fields and force-free solutions by considering models of magnetospheres filled with resistive plasma. We formulate Ohm's Law in the minimal velocity fluid frame…
We study the transverse propagation of photons in a magnetized vacuum considering radiative corrections in the one-loop approximation. The dispersion equation is modified due to the magnetized photon self-energy in the transparency region ($0<ω<2m_e$). The aim of our study is to explore propagation of photons in a neutron star magnetosphere (described by magnetized vacuum). The solution of the dispersion equation is obtained in terms of analytic functions. The larger the magnetic field, the lower the phase velocity and the more the dispersion curve deviates from the light-cone. For fixed value…
We consider the motion of charged particles in the vacuum magnetospheres of rotating neutron stars with a strong surface magnetic field, B>10^(12) G. The electrons and positrons falling into the magnetosphere or produced in it are shown to be captured by the force-free surface EB=0. Using the Dirac-Lorentz equation, we investigate the dynamics of particle capture and subsequent motion near the force-free surface. The particle energy far from the force-free surface has been found to be determined by the balance between the power of the forces of an accelerating electric field and the intensity …
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to $40\%$ with respect to a vacuum model with t…
Relativistic effects of compact objects onto electromagnetic fields in their vicinity are investigated using the test-field approximation. In particular, we study the possible emergence of magnetic null points which are astrophysically relevant for the processes of magnetic reconnection. While the magnetic reconnection occurs in the presence of plasma and may lead to violent mass ejection, we show here that strong gravitation of the supermassive black hole may actively support the process by suitably entangling the field lines even in the electro-vacuum description. In this contribution we fur…
Pulsed, Polarized X-ray Emission from Neutron Star Surfaces: the Effects of Vacuum Birefringence in the Magnetosphere
Rice University（莱斯大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；George Washington University（乔治华盛顿大学）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）；Houston City College（休斯顿城市学院）
We construct hydromagnetic neutron star equilibria which allow for a non-zero electric current distribution in the exterior. The novelty of our models is that the neutron star's interior field is in equilibrium with its magnetosphere, thus bridging the gap between previous work in this area which either solves for the interior assuming a vacuum exterior or solves for the magnetosphere without modelling the star itself. We consider only non-rotating stars in this work, so our solutions are most immediately applicable to slowly-rotating systems such as magnetars. Nonetheless, we demonstrate that…
We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to $\sim 25\%$ more energy than the vacuum case, hel…
Pulsar magnetospheres admit non-stationary vacuum gaps that are characterized by non-vanishing ${\bf{E}} \cdot {\bf{B}}$. The vacuum gaps play an important role in plasma production and electromagnetic wave emission. We show that these gaps generate axions whose energy is set by the gap oscillation frequency. The density of axions produced in a gap can be several orders of magnitude greater than the ambient dark matter density. In the strong pulsar magnetic field, a fraction of these axions may convert to photons, giving rise to broadband radio signals. We show that dedicated observations of n…
We present a model of the magnetosphere around an oscillating neutron star. The electromagnetic fields are numerically solved by modeling electric charge and current induced by the stellar torsional mode, with particular emphasis on outgoing radiation passing through the magnetosphere. The current is modeled using Ohm's law, whereby an increase in conductivity results in an increase in the induced current. As a result, the fields are drastically modified, and energy flux is thereby enhanced. This behavior is however localized in the vicinity of the surface since the induced current disappears …
The rotational period of isolated pulsars increases over time due to the extraction of angular momentum by electromagnetic torques. These torques also change the obliquity angle $α$ between the magnetic and rotational axes. Although actual pulsar magnetospheres are plasma-filled, the time evolution of $α$ has mostly been studied for vacuum pulsar magnetospheres. In this work, we self-consistently account for the plasma effects for the first time by analysing the results of time-dependent 3D force-free and magnetohydrodynamic simulations of pulsar magnetospheres. We show that if a neutron star …
X-ray photons emitted from the surface or atmosphere of a magnetized neutron star is highly polarized. However, the observed polarization may be modified due to photon propagation through the star's magnetosphere. For photon frequencies much larger than the typical radio frequency, vacuum birefringence due to strong-field quantum electrodynamics dominates over the plasma effect. We study the evolution of photon polarization in the magnetized QED vacuum of a neutron star magnetosphere, paying particular attention to the propagation effect across the quasi-tangential (QT) point, where the photon…
In the magnetar model, the quiescent non-thermal soft X-ray emission from Anomalous X-ray Pulsars and Soft-Gamma Repeaters is thought to arise from resonant comptonization of thermal photons by charges moving in a twisted magnetosphere. Robust inference of physical quantities from observations is difficult, because the process depends strongly on geometry and current understanding of the magnetosphere is not very deep. The polarization of soft X-ray photons is an independent source of information, and its magnetospheric imprint remains only partially explored. In this paper we calculate how re…
Context: At the low accretion-rates typical for BL Lac-objects, magnetospheres of active galactic nuclei can develop vacuum gaps with strong electric fields accelerating charged seed particles parallel to the magnetic fields up to ultra-relativistic energies. The seed particles sustain electromagnetic cascades by inverse-Compton-scattering and subsequent pair-production in soft background-radiation-fields from the accretion-disk and/or photo-ionised clouds, along the direction of the primary particle beams. Method: The one-dimensional kinetic equation describing this linear inverse-Compton-Kle…
We review electrodynamics of rotating magnetized neutron stars, from the early vacuum model to recent numerical experiments with plasma-filled magnetospheres. Significant progress became possible due to the development of global particle-in-cell simulations which capture particle acceleration, emission of high-energy photons, and electron-positron pair creation. The numerical experiments show from first principles how and where electric gaps form, and promise to explain the observed pulsar activity from radio waves to gamma-rays.
We explore the structure of a dipole-type vacuum field of a slowly rotating magnetic star near the horizon of a supermassive black hole, where the structure of field lines becomes highly distorted by effects of strong gravity. Such a situation may occur near a neutron star in the final stages of a plunging trajectory into a galactic center. We solve Maxwell's equations in the Rindler approximation for the rotating conducting source of dipolar magnetic field arbitrarily inclined with respect to the axis of rotation. For the fixed inclination angle we calculate the field including the radiative …
We investigate the shapes of γ-ray pulsar light curves using 3D pulsar magnetosphere models of finite conductivity. These models, covering the entire spectrum of solutions between vacuum and force-free magnetospheres, for the first time afford mapping the GeV emission of more realistic, dissipative pulsar magnetospheres. To this end we generate model light curves following two different approaches: (a) We employ the emission patterns of the slot and outer gap models in the field geometries of magnetospheres with different conductivity σ. (b) We define realistic trajectories of radiating partic…
Pulsars are famous for their rotational stability. Most of them steadily spin down and display a highly repetitive pulse shape. But some pulsars experience timing irregularities such as nulling, intermittency, mode changing and timing noise. As changes in the pulse shape are often correlated with timing irregularities, precession is a possible cause of these phenomena. Whereas pulsar magnetospheres are filled with plasma, most pulsar precession studies were carried out within the vacuum approximation and neglected the effects of magnetospheric currents and charges. Recent numerical simulations…
An oblique pulsar magnetosphere with a plasma conductivity is studied by using a pseudo-spectral method. In the pseudo-spectral method, the time-dependent Maxwell equations are solved, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergencelessness of magnetic field is analytically enforced by a projection method. The pulsar magnetospheres in infinite (i. e., force-free approximation) and finite conductivities are simulated and a family of solutions that smoothly transition from the Deutsch vacuum solutio…
We reconsider pulsar electrodynamics for an obliquely rotating pulsar, and propose a way of synthesizing the vacuum dipole model (VDM) and the rotating magnetosphere model (RMM). We first modify the VDM by assuming that the parallel component of the inductive electric field is screened by charges. We refer to the resulting model as the minimal model. We calculate the screening charge density in the minimal model and compare it with the (Goldreich-Julian) charge density in the RMM. We identify the plasma velocity in the minimal model as the electric drift velocity due to the perpendicular compo…
The magnetospheres of magnetars are believed to be filled with electron-positron plasma generated by electric discharge. We present a first direct numerical experiment showing how the plasma is created in an axisymmetric closed magnetosphere. The $e^\pm$ discharge occurs in response to twisting of the magnetic field lines by a shear deformation of the magnetar surface, which launches electric currents into the magnetosphere. The simulation shows the formation of an electric "gap" with unscreened electric field ($\mathbf{E}\cdot \mathbf{B}\neq 0$) that continually accelerates particles along th…
The recently discovered rotationally powered pulsar PSR J1640-4631 is the first to have a braking index measured, with high enough precision, that is greater than three. An inclined magnetic rotator in vacuum or plasma would be subject not only to spin-down but also to an alignment torque. The vacuum model can address the braking index only for an almost orthogonal rotator that is incompatible with the single peaked pulse profile. The magnetic dipole model with the corotating plasma predicts braking indices between $3-3.25$. We find that the braking index of $3.15$ is consistent with two diffe…
We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated nonperturbatively and can be arbitrarily strong. This technique is particularly useful for examining non-linear effects in propagating waves. Waves travelling through such a medium typically form shocks; on the other hand we focus on the possible existence of waves that travel without evolving. Therefore, in order to examine the nonlinear effects, we make a travellin…
Recent studies have shown that gamma-ray pulsar light curves are very sensitive to the geometry of the pulsar magnetic field. Pulsar magnetic field geometries, such as the retarded vacuum dipole and force-free magnetospheres have distorted polar caps that are offset from the magnetic axis in the direction opposite to rotation. Since this effect is due to the sweepback of field lines near the light cylinder, offset polar caps are a generic property of pulsar magnetospheres and their effects should be included in gamma-ray pulsar light curve modeling. In slot gap models (having two-pole caustic …
Pulsars are thought to be highly magnetized rotating neutron stars accelerating charged particles along magnetic field lines in their magnetosphere and visible as pulsed emission from the radio wavelength up to high energy X-rays and gamma-rays. Being highly compact objects with compactness close to $Ξ= R_s/R\approx0.5$, where $\Rs=2\,G\,M/c^2$ is the Schwarzschild radius and $\{M,R\}$ the mass and radius of the neutron star, general-relativistic effects become important close to their surface. This is especially true for the polar caps where radio emission is supposed to emanate from, leading…
This is the second paper in a series where we examine the physics of pair producing gaps in low-luminosity accreting supermassive black hole systems. In this paper, we carry out time-dependent self-consistent fully general relativistic 1D PIC simulations of the gap, including full inverse Compton scattering and photon tracking. Similar to the previous paper, we find a highly time-dependent solution where a macroscopic vacuum gap can open quasi-periodically, producing bursts of $e^\pm$ pairs and high energy radiation. We present the light curve, particle and photon spectra from this process. Us…
We performed ab-initio Particle-In-Cell (PIC) simulations of a pulsar magnetosphere with electron-positron plasma produced only in the regions close to the neutron star surface. We study how the magnetosphere transitions from the vacuum to a nearly force-free configuration. We compare the resulting force-free like configuration with ones obtained in a PIC simulation where particles are injected everywhere as well as with macroscopic force-free simulations. We found that although both PIC solutions have similar structure of electromagnetic fields and current density distributions, they have dif…
Neutron star electromagnetic activity produces pairs that fill their magnetosphere represented to the zeroth order by the force-free approximation. Neither dissipation nor acceleration nor radiation from charged particles is expected from this simplified model. So far, only centred dipole magnetic fields have been studied in this limit. In this paper, we explore the consequences of a rotating off-centred dipole on the force-free magnetosphere, showing the new magnetic field geometry, its spin-down luminosity as well as the electromagnetic kick and torque felt by the neutron star. Solutions are…
We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long timescales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a …
We present the first self-consistent global simulations of pulsar magnetospheres with operating $e^\pm$ discharge. We focus on the simple configuration of an aligned or anti-aligned rotator. The star is spun up from zero (vacuum) state to a high angular velocity, and we follow the coupled evolution of its external electromagnetic field and plasma particles using the "particle-in-cell" method. A plasma magnetosphere begins to form through the extraction of particles from the star; these particles are accelerated by the rotation-induced electric field, producing curvature radiation and igniting …
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we addre…
The study of magnetars is of particular relevance since these objects are the only laboratories where the physics in ultra-strong magnetic fields can be directly tested. Until now, spectroscopic and timing measurements at X-ray energies in soft gamma-repeaters (SGRs) and anomalous X-ray pulsar (AXPs) have been the main source of information about the physical properties of a magnetar and of its magnetosphere. Spectral fitting in the ~ 0.5-10 keV range allowed to validate the "twisted magnetosphere" model, probing the structure of the external field and estimating the density and velocity of th…
Over the last four decades, persistent and flaring emission of magnetars observed by various telescopes has provided us with a suite of light curves and spectra in soft and hard X-rays, with no emission yet detected above around 1 MeV. Attenuation of such high-energy photons by magnetic pair creation and photon splitting is expected to be active in the magnetospheres of magnetars, possibly accounting for the paucity of gamma-rays in their signals. This paper explores polarization-dependent opacities for these two QED processes in static vacuum dipole magnetospheres of highly-magnetized neutron…
(abridged) Pulsar activity and its related radiation mechanism are usually explained by invoking some plasma processes occurring inside the magnetosphere. Despite many detailed local investigations, the global electrodynamics around those neutron stars remains poorly described. Better understanding of these compact objects requires a deep and accurate knowledge of their immediate electromagnetic surrounding within the magnetosphere and its link to the relativistic pulsar wind. The aim of this work is to present accurate solutions to the nearly stationary force-free pulsar magnetosphere and its…
Main sequence stars and compact objects like white dwarfs and neutron stars are usually embedded in magnetic fields that strongly deviate from a pure dipole located right at the stellar centre. An off-centred dipole can sometimes better adjust existing data and offer a simple geometric picture to include multipolar fields. However, such configurations are usually to restrictive, limiting multipolar components to strength less than the underlying dipole. In this paper, we consider the most general lowest order multipolar combination given by a dipole and a quadrupole magnetic field association …
Current models of pulsar gamma-ray emission use the magnetic field of a rotating dipole in vacuum as a first approximation to the shape of plasma-filled pulsar magnetosphere. In this paper we revisit the question of gamma-ray light-curve formation in pulsars in order to ascertain the robustness of the "two-pole caustic" (TPC) and "outer gap" (OG) models based on the vacuum magnetic field. We point out an inconsistency in the literature on the use of the relativistic aberration formula, where in several works the vacuum field was treated as known in the instantaneously corotating frame, rather …
Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axi…
Recently, it was claimed that accretion of electric charge by a black hole rotating in an aligned external magnetic field results in a "dead" vacuum magnetosphere, where the electric field is totally screened, no vacuum breakdown is possible, and the Blandford-Znajek mechanism cannot operate King & Pringle (2021). Here we study in details the properties of the Wald(1974) solution for electrically charged black holes discussed in that paper. Our results show that the claim is erroneous as in the solution with the critical charge $q_0=2aB_0$ there exists a drop of electrostatic potential along a…
We present 3D global kinetic pulsar magnetosphere models, where the charged particle trajectories and the corresponding electromagnetic fields are treated self-consistently. For our study, we have developed a cartesian 3D relativistic particle-in-cell code that incorporates the radiation reaction forces. We describe our code and discuss the related technical issues, treatments, and assumptions. Injecting particles up to large distances in the magnetosphere, we apply arbitrarily low to high particle injection rates and get an entire spectrum of solutions from close to the Vacuum-Retarded-Dipole…
We investigate the particle accelerator that arises in a rotating neutron-star magnetosphere. Solving the Poisson equation for the electro-static potential, the Boltzmann equations for relativistic electrons and positrons, and the radiative transfer equation simultaneously, we demonstrate that the electric field is substantially screened along the magnetic field lines by the pairs that are created and separated within the accelerator. As a result, the magnetic-field-aligned electric field is localized in the higher altitudes near the light cylinder and efficiently accelerates the positrons cre…
(abridged) The physics of the pulsar magnetosphere near the neutron star surface remains poorly constrained by observations. Nevertheless it is believed that large vacuum gaps exist in the magnetosphere, and a non-neutral plasma partially fills the neutron star surroundings to form an electrosphere. The equatorial disk in this electrosphere is diocotron and magnetron unstable. To better assess the long term evolution of these instabilities, we study the behavior of the non-neutral plasma with help on particle simulations. We designed a 2D electrostatic PIC code. In the diocotron regime, the eq…
The mechanism by which the radiation received from obliquely rotating neutron stars is generated remains an open question half a century after the discovery of pulsars. In contrast, considerable progress has recently been made in determining the structure of the magnetosphere that surrounds these objects: numerical computations based on the force-free, magnetohydrodynamic and particle-in-cell formalisms have now established that the magnetosphere of an oblique rotator entails a current sheet outside its light cylinder whose rotating distribution pattern moves with linear speeds exceeding the s…
The "no hair" theorem is not applicable to black holes formed from collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively "frozen-in" the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tub…
Magnetospheres of pulsars are thought to be filled with plasma, and variations in plasma supply can affect both pulsar emission properties and spin-down rates. A number of recently discovered "intermittent" pulsars switch between two distinct states: an "on", radio-loud state, and an "off", radio-quiet state. Spin-down rates in the two states differ by a large factor, $\sim 1.5-2.5$, which is not easily understood in the context of current models. In this Letter we present self-consistent numerical solutions of "on" and "off" states of intermittent pulsar magnetospheres. We model the "on" stat…
While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr--Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consid…
Aims. Many recent observations of pulsars and magnetars can be interpreted in terms of neutron stars (NS) with multipole electromagnetic fields. As a first approximation, we investigate the multipole magnetic and electric fields in the environment of a rotating star when this environment is deprived of plasma. Methods. We compute a multipole expansion of the electromagnetic field in vacuum for a given magnetic field on the conducting surface of the rotating star. Then, we consider a few consequences of multipole fields of pulsars. Results. We provide an explicit form of the solution. For each …
We compute the patterns of $γ$-ray emission due to curvature radiation in dissipative pulsar magnetospheres. Our ultimate goal is to construct macrophysical models that are able to reproduce the observed $γ$-ray light-curve phenomenology recently published in the Second Fermi Pulsar Catalog. We apply specific forms of Ohm's law on the open field lines using a broad range for the macroscopic conductivity values that result in solutions ranging, from near-vacuum to near Force-Free. Using these solutions, we generate model $γ$-ray light curves by calculating realistic trajectories and Lorentz fac…
