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Register a new userParticle accelerator in pulsar magnetospheres: A hybrid solution of inner and outer gap models
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K. Hirotani
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A self-consistent electrodynamics of a particle accelerator in a rotating neutron-star magnetosphere is investigated on the two-dimensional poloidal plane. Solving the Poisson equation for the electrostatic potential together with the Boltzmann equations for electrons, positrons and gamma-rays, it is demonstrated that the created current density increases to be super-Goldreich-Julian if the trans-field thickness of the gap becomes thick enough. This new solution exists from the neutron-star surface to the outer magnetosphere with a small-amplitude positive acceleration field in the inner part, which works to extract ions from the stellar surface as a space-charge-limited flow. The acceleration field is highly unscreened in the outer magnetosphere, in the same manner as in traditional outer-gap models.
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We investigate a pair creation cascade in the magnetosphere of a rapidly rotating neutron star. We solve the set of the Poisson equation for the electro-static potential and the Boltzmann equations for electrons, positrons, and gamma-ray photons simultaneously. In this paper, we first examine the time-dependent nature of particle accelerators by solving the non-stationary Boltzmann equations on the two-dimensional poloidal plane in which both the rotational and magnetic axes reside. Evaluating the temperature of the heated polar cap surface, which is located near the magnetic pole, by the bombardment of gap-accelerated particles, and applying the scheme to millisecond pulsar parameters, we demonstrate that the solution converges to a stationary solution of which pair-creation cascade is maintained by the heated polar-cap emission, in a wide range of three-dimensional parameter space (period, period derivative, magnetic inclination angle). We also present the deathlines of millisecond pulsars.
A two-dimensional electrodynamic model is used to study particle acceleration and non-thermal emission mechanisms in the pulsar magnetospheres. We solve distribution of the accelerating electric field with the emission process and the pair-creation process in meridional plane, which includes the rotational axis and the magnetic axis. By solving the evolutions of the Lorentz factor, and of the pitch angle, we calculate spectrum in optical through $gamma$-ray bands with the curvature radiation, synchrotron radiation, and inverse-Compton process not only for outgoing particles, but also for ingoing particles, which were ignored in previous studies. We apply the theory to the Vela pulsar. We find that the curvature radiation from the outgoing particles is the major emission process above 10 MeV bands. In soft $gamma$-ray to hard X-ray bands, the synchrotron radiation from the ingoing primary particles in the gap dominates in the spectrum. Below hard X-ray bands, the synchrotron emissions from both outgoing and ingoing particles contribute to the calculated spectrum. The calculated spectrum is consistent with the observed phase-averaged spectrum of the Vela pulsar. We show that the observed five-peak pulse profile in the X-ray bands of the Vela pulsar is reproduced by the inward and outward emissions, and the observed double-peak pulse profile in $gamma$-ray bands is explained by the outward emissions.
We continue our investigation of particle acceleration in the pulsar equatorial current sheet (ECS) that began with Contopoulos (2019) and Contopoulos & Stefanou (2019). Our basic premise has been that the charge carriers in the current sheet originate in the polar caps as electron-positron pairs, and are carried along field lines that enter the equatorial current sheet beyond the magnetospheric Y-point. In this work we investigate further the charge replenishment of the ECS. We discovered that the flow of pairs from the rims of the polar caps cannot supply both the electric charge and the electric current of the ECS. The ECS must contain an extra amount of positronic (or electronic depending on orientation) electric current that originates in the stellar surface and flows outwards along the separatrices. We develop an iterative hybrid approach that self-consistently combines ideal force-free electrodynamics in the bulk of the magnetosphere with particle acceleration along the ECS. We derive analytic approximations for the orbits of the particles, and obtain the structure of the pulsar magnetosphere for various values of the pair-formation multiplicity parameter kappa. For realistic values kappa >> 1, the magnetosphere is practically indistinguishable from the ideal force-free one, and therefore, the calculation of the spectrum of high-energy radiation must be based on analytic approximations for the distribution of the accelerating electric field in the ECS.
We investigate the electrodynamics of an outer gap in the meridional plane of the aligned-rotator. The charge depletion from the Goldreich-Julian charge density causes a large electric field along the magnetic field line. The electrons or the positrons are accelerated by the field-aligned electric field and radiate the $gamma$-rays tangentially to the local magnetic field line. Some of such $gamma$-rays collide with $X$-rays to materialize as the electron-positron pairs on different field lines from the field line on which they were emitted. As a result, the electric field structure is expected to change across the field lines. Including these trans-field effects, we solve the formation of the electric field self-consistently with the curvature radiation and the pair creation processes. The $gamma$-ray emission and the pair creation are treated by use of Monte Carlo technique. We demonstrate that the distribution of the electric field along the field lines is affected by both the gap geometry and the external currents coming into the gap through the boundaries. In the electrodynamical model, it has been known that the solution disappears if the current density carried by the electron-positron pairs produced in the gap exceeds a critical value. We show that the critical current density is significantly increased when the trans-field structure is taken into account. We also find that the location of the inner boundary of the gap shifts toward the stellar surface from the conventional null surface as the current density increases. The reason for the shift is derived from the stability condition of the inner boundary. We also argue that the ideal-MHD condition holds outside of the gap only when the low energy particles coexist with the high energy particles migrating from the gap.
We consider magnetospheric structure of rotating neutron stars with internally twisted axisymmetric magnetic fields. The twist-induced and rotation-induced toroidal magnetic fields align/counter-align in different hemispheres. Using analytical and numerical calculations (with PHAEDRA code) we show that as a result the North-South symmetry is broken: the magnetosphere and the wind become angled, of conical shape. Angling of the magnetosphere affects the spindown (making it smaller for mild twists), makes the return current split unequally at the Y-point, produces anisotropic wind and linear acceleration that may dominate over gravitational acceleration in the Galactic potential and give a total kick up to $sim 100$ km/s. We also consider analytically the structure of the Y-point in the twisted magnetosphere, and provide estimate of the internal twist beyond which no stable solutions exist: over-twisted magnetospheres must produce plasma ejection events.
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