General-relativistic force-free pulsar magnetospheres

Abstract

Pulsar magnetospheres are shaped by ultra-relativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio R/r L and on frame-dragging through the spin parameter a s , R is the neutron star radius and r L the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to 2 depending on the rotation rate. Moreover we retrieve the sin 2 χ dependence of this luminosity, χ being the obliquity of the pulsar, as well as a braking index close to n = 3. We also show that the angular dependence of the Poynting flux scales like sin 2 ϑ for the aligned rotator but like sin 4 ϑ for the orthogonal rotator, ϑ being the colatitude.

Theory of pulsar magnetosphere and wind

“…Morozova, Ahmedov & Zanotti (2010) studied the influence of neutron star oscillations in general relativity on the corotation density in the magnetosphere for a aligned rotator. Pétri (2016a) made an extensive study of force-free pulsar magnetospheres in general relativity. General relativity seems to play a decisive role for efficient pair creation at the surface (Philippov et al 2015a;Belyaev & Parfrey 2016).…”

“…Vacuum solution are of the Deutsch kind but in general relativity are discussed in Pétri (2013a). The numerical simulations based on a pseudo-spectral code are described in Pétri (2014) and extended to a discontinuous Galerkin approach in Pétri (2015cPétri ( , 2016a. The conclusions drawn from special-relativistic force-free (SRFFE) simulations remain valid and the physics is not changed.…”

Strongly magnetized rotating dipole in general relativity

“…For a pure dipole rotating in vacuum, this should be very close to n = 3, see for instance Roberts & Sturrock (1973) for the dipole and the general case of a multipole of order being n = 2 + 1 as given in Krolik (1991), see also Pétri (2015c) for the exact expression taking into account the finite size of the star. For the dipole, Pétri (2016a) showed that this result is not affected by the presence of a plasma in the magnetosphere in general relativity. Hamil et al (2015) summarized the current knowledge in measuring pulsar braking indices.…”

Atmospheres and radiating surfaces of neutron stars

“…A real pulsar strongly differs from a rotating magnetic dipole, because its magnetosphere is filled with plasma, carrying electric charges and currents (see reviews [25][26][27][28] and recent papers [29][30][31]). According to the model by Beskin et al [32,33], the magnetodipole radiation is absent beyond the magnetosphere, while the slowdown of rotation is provided by the current energy losses.…”

“…For hydrostatic and energy balance, we can keep Eqs. (28), (29), and (32), if we put I ω = 2 j=1 I ω,j by definition. The diffusion equation for the normal modes in these approximations was derived in [261,361].…”