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We report on the first self-consistent multidimensional particle-in-cell numerical simulations of non-homogeneous pair discharges in polar caps of rotation-powered pulsars. By introducing strong inhomogeneities in the initial plasma distribution in our simulations, we analyze the degree of self-consistently emerging coherence of discharges across magnetic field lines. In 2D, we study discharge evolution for a wide range of physical parameters and boundary conditions corresponding to both the absent and free escape of charged particles from the surface of a neutron star. We also present the results of the first 3D simulations of discharges in a polar cap with a distribution of the global magnetospheric current appropriate for a pulsar with $60^{\circ}$ inclination angle. For all parameters, we find the coherence scale of pair discharges across magnetic field lines to be of the order of gap height. We also demonstrate that the popular "spark" model of pair discharges is incompatible with the universally adopted force-free magnetosphere model: intermittent discharges fill the entire zone of the polar cap that allows pair cascades, leaving no space for discharge-free regions. Our findings disprove the key assumption of the spark model about the existence of isolated distinct discharge columns., Comment: 20 pages, 6 figures, accepted for publication in the ApJL

Pair cascades in polar cap regions of neutron stars are considered to be an essential process in various models of coherent radio emissions of pulsars. The cascades produce pair plasma bunch discharges in quasi-periodic spark events. The cascade properties, and therefore also the coherent radiation, depend strongly on the magnetospheric plasma properties and vary significantly across and along the polar cap. Importantly, where the radio emission emanates from in the polar cap region is still uncertain. We investigate the generation of electromagnetic waves by pair cascades and their propagation in the polar cap for three representative inclination angles of a magnetic dipole, $0^\circ$, $45^\circ$, and $90^\circ$. We use two-dimensional particle-in-cell simulations that include quantum-electrodynamic pair cascades in a charge-limited flow from the star surface. We find that the discharge properties are strongly dependent on the magnetospheric current profile in the polar cap and that transport channels for high intensity Poynting flux are formed along magnetic field lines where the magnetospheric currents approach zero and where the plasma cannot carry the magnetospheric currents. There, the parallel Poynting flux component is efficiently transported away from the star and may eventually escape the magnetosphere as coherent radio waves. The Poynting flux decreases with increasing distance from the star in regions of high magnetospheric currents. Our model shows that no process of energy conversion from particles to waves is necessary for the coherent radio wave emission. Moreover, the pulsar radio beam does not have a cone structure; rather, the radiation generated by the oscillating electric gap fields directly escapes along open magnetic field lines in which no pair creation occurs., Comment: 18 pages, 11 figures, 2 tables

Pulsar radio emission may be generated in pair discharges which fill the pulsar magnetosphere with plasma as an accelerating electric field is screened by freshly created pairs. In this Letter we develop a simplified analytic theory for the screening of the electric field in these pair discharges and use it to estimate total radio luminosity and spectrum. The discharge has three stages. First, the electric field is screened for the first time and starts to oscillate. Next, a nonlinear phase occurs. In this phase, the amplitude of the electric field experiences strong damping because the field dramatically changes the momenta of newly created pairs. This strong damping ceases, and the system enters a final linear phase, when the electric field can no longer dramatically change pair momenta. Applied to pulsars, this theory may explain several aspects of radio emission, including the observed luminosity, $L_{\rm{rad}} \sim 10^{28} \rm{erg} \, \rm{s}^{-1}$, and the observed spectrum, $S_\omega \sim \omega^{-1.4 \pm 1.0} $., Comment: Updated to accepted version

Since pulsars were discovered as emitters of bright coherent radio emission more than half a century ago, the cause of the emission has remained a mystery. In this Letter we demonstrate that coherent radiation can be directly generated in non-stationary pair plasma discharges which are responsible for filling the pulsar magnetosphere with plasma. By means of large-scale two-dimensional kinetic plasma simulations, we show that if pair creation is non-uniform across magnetic field lines, the screening of electric field by freshly produced pair plasma is accompanied by the emission of waves which are electromagnetic in nature. Using localized simulations of the screening process, we identify these waves as superluminal ordinary (O) modes, which should freely escape from the magnetosphere as the plasma density drops along the wave path. The spectrum of the waves is broadband and the frequency range is comparable to that of observed pulsar radio emission., Comment: 9 pages, 4 figures

We explore the burst energy distribution of fast radio bursts (FRBs) in the low-twist magnetar model of Wadiasingh and Timokhin (2019). Motivated by the power-law fluence distributions of FRB 121102, we propose an elementary model for the FRB luminosity function of individual repeaters with an inversion protocol which directly relates the power-law distribution index of magnetar short burst fluences to that for FRBs. The protocol indicates the FRB energy scales virtually linearly with crust/field dislocation amplitude, if magnetar short bursts prevail in the magnetoelastic regime. Charge starvation in the magnetosphere during bursts (required in WT19) for individual repeaters implies the predicted burst fluence distribution is narrow, $\lesssim 3$ decades for yielding strains and oscillation frequencies feasible in magnetar crusts. Requiring magnetic confinement and charge starvation, we obtain a death line for FRBs which segregates magnetars from the normal pulsar population, suggesting only the former will host recurrent FRBs. We convolve the burst energy distribution for individual magnetars to define the distribution of luminosities in evolved magnetar populations. The broken power-law luminosity function's low energy character depends on the population model, while the high energy index traces that of individual repeaters. Independent of the evolved population, the broken power-law isotropic-equivalent energy/luminosity function peaks at $\sim10^{37}-10^{40}$ erg with a low-energy cutoff at $\sim 10^{37}$ erg. Lastly, we consider the local fluence distribution of FRBs, and find that it can constrain the subset of FRB-producing magnetar progenitors. Our model suggests that improvements in sensitivity may reveal flattening of the global FRB fluence distribution and saturation in FRB rates., Comment: 23 pages, 3 figures, accepted to The Astrophysical Journal

We analyze the statistics of pulse arrival times in fast radio burst (FRB) 121102 and demonstrate that they are remarkably similar to statistics of magnetar high-energy short bursts. Motivated by this correspondence, we propose that repeating FRBs are generated during short bursts in the closed field line zone of magnetar magnetospheres via a pulsar-like emission mechanism. Crustal slippage events dislocate field line foot points, initiating intense particle acceleration and pair production, giving rise to coherent radio emission similar to that generated near pulsar polar caps. We argue that the energetics of FRB 121102 can be readily accounted for if the efficiency of the conversion of Poynting flux into coherent radio emission is $\sim10^{-4}-10^{-2}$, values consistent with empirical efficiencies of radio emission in pulsars and radio-loud magnetars. Such a mechanism could operate only in magnetars with preexisting low twist of the magnetosphere, so that the charge density in the closed zone is initially insufficient to screen the electric field provoked by the wiggling of magnetic field lines and is low enough to let $\sim 1$ GHz radio emission escape the magnetosphere, which can explain the absence of FRBs from known magnetars. The pair cascades crowd the closed flux tubes with plasma, screening the accelerating electric field, thus limiting the radio pulse duration to $\sim1$ ms. Within the framework of our model, the current dataset of the polarization angle variation in FRB 121102 suggests a magnetic obliquity $\alpha\lesssim40^\circ$ and viewing angle $\zeta$ with respect to the spin axis $\alpha<\zeta<180^\circ-\alpha$., Comment: 11 pages, 4 figures, accepted to ApJ, proofs corrected

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 different particle density distribution. In fact in the injection from the surface solution, electrons and positrons counterstream only along parts of the return current regions and most of the particles leave the magnetosphere without returning to the star. We also found that pair production in the outer magnetosphere is not critical for filling the whole magnetosphere with plasma. We study how the current density distribution supporting the global electromagnetic configuration is formed by analyzing particle trajectories. We found that electrons precipitate to the return current layer inside the light cylinder and positrons precipitate to the current sheet outside the light cylinder by crossing magnetic field lines contributing to the charge density distribution required by the global electrodynamics. Moreover, there is a population of electrons trapped in the region close to the Y-point. On the other hand the most energetic positrons are accelerated close to the Y-point. These processes can have observational signatures that, with further modeling efforts, would help to distinguish this particular magnetosphere configuration from others., Comment: 17 pages, 15 figures

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 to close to the Force-Free solution, respectively. For high particle injection rates (close to FF solutions) significant accelerating electric field components are confined only near the equatorial current sheet outside the light-cylinder. A judicious interpretation of our models allows the calculation of the particle emission and consequently the derivation of the corresponding realistic high-energy sky-maps and spectra. Using model parameters that cover the entire range of spin-down powers of Fermi young and millisecond pulsars, we compare the corresponding model $\gamma$-ray light-curves, cutoff energies, and total $\gamma$-ray luminosities with those observed by Fermi to discover a dependence of the particle injection-rate, $\mathcal{F}$, on the spin-down power, $\dot{\mathcal{E}}$, indicating an increase of $\mathcal{F}$ with $\dot{\mathcal{E}}$. Our models guided by Fermi observations provide field-structures and particle distributions that are not only consistent with each other but also able to reproduce a broad range of the observed $\gamma$-ray phenomenology of both young and millisecond pulsars., Comment: Accepted for publication in ApJ (24 pages, 22 figures). This version has some corrections and additions

In this paper we consider stationary force-free magnetosphere of an aligned rotator when plasma in the open field line region rotates differentially due to presence of a zone with the accelerating electric field in the polar cap of pulsar. We study the impact of differential rotation on the current density distribution in the magnetosphere. Using split-monopole approximation we obtain analytical expressions for physical parameters of differentially rotating magnetosphere. We find the range of admitted current density distributions under the requirement that the potential drop in the polar cap is less than the vacuum potential drop. We show that the current density distribution could deviate significantly from the ``classical'' Michel distribution and could be made almost constant over the polar cap even when the potential drop in the accelerating zone is of the order of 10 per cents of the vacuum potential drop. We argue that differential rotation of the open magnetic field lines could play an important role in adjusting between the magnetosphere and the polar cap cascade zone and could affect the value of pulsar breaking index., Comment: 15 pages, 15 figures; accepted for publication in MNRAS

Pulsar "standard model", that considers a pulsar as a rotating magnetized conducting sphere surrounded by plasma, is generalized to the case of oscillating star. We developed an algorithm for calculation of the Goldreich-Julian charge density for this case. We consider distortion of the accelerating zone in the polar cap of pulsar by neutron star oscillations. It is shown that for oscillation modes with high harmonic numbers (l,m) changes in the Goldreich-Julian charge density caused by pulsations of neutron star could lead to significant altering of an accelerating electric field in the polar cap of pulsar. In the moderately optimistic scenario, that assumes excitation of the neutron star oscillations by glitches, it could be possible to detect altering of the pulsar radioemission due to modulation of the accelerating field., Comment: 7 pages, 8 figures. Presented at the conference "Isolated Neutron Stars: from the Interior to the Surface", London, April 24-28, 2006; to appear in Astrophysics and Space Science

Here we briefly report on results of self-consistent numerical modeling of a differentially rotating force-free magnetosphere of an aligned rotator. We show that differential rotation of the open field line zone is significant for adjusting of the global structure of the magnetosphere to the current density flowing through the polar cap cascades. We argue that for most pulsars stationary cascades in the polar cap can not support stationary force-free configurations of the magnetosphere., Comment: 5 pages, 4 figures. Presented at the conference "Isolated Neutron Stars: from the Interior to the Surface", London, April 24-28, 2006; to appear in Astrophysics and Space Science. Significantly revised version, a mistake found by ourselfs in the numerical code was corrected, all presented results are obtained with the correct version of the code

We consider the force-free magnetosphere of an aligned rotator. Its structure is well described by a Grad-Shafranov equation for poloidal magnetic field, the so-called "pulsar equation". We solve this equation by a multigrid method with high numerical resolution. On the fine numerical grid current layer along the last closed field line could be accurately incorporated into the numerical procedure and all physical properties of the solution such as Goldreich-Julian charge density, drift velocity, energy losses etc. could be accurately calculated. Here we report results of the simulations. Among other interesting properties, the solution is not unique, i.e. the position of the last closed field line, and hence the pulsar energy losses, are not determined by the global magnetosphere structure and depend on kinetic of electromagnetic cascades. We discuss the properties of the solutions and their implications for pulsars. A model for pulsar magnetosphere evolution is proposed. In the frame of this model values of the pulsar braking index less than 3 have natural explanation., Comment: presented at the conference "Astrophysical Sources of High Energy Particles and Radiation", Torun, Poland, 20 - 24 June 2005 and at the conference "Physics of Neutron Stars - 2005", St. Petersburg, Russia, 27-29 June, 2005; corrected mistake in energy losses normalization

Current density determines the plasma flow regime. Cascades are non-stationary. ALWAYS. All flow regimes look different: multiple components (?) Return current regions should have particle accelerating zones in the outer magnetosphere: y-ray pulsars (?) Plasma oscillations in discharges: direct radio emission (?)