No Arabic abstract
The X-ray spectra observed in the persistent emission of magnetars are evidence for the existence of a magnetosphere. The high-energy part of the spectra is explained by resonant cyclotron upscattering of soft thermal photons in a twisted magnetosphere, which has motivated an increasing number of efforts to improve and generalize existing magnetosphere models. We want to build more general configurations of twisted, force-free magnetospheres as a first step to understanding the role played by the magnetic field geometry in the observed spectra. First we reviewed and extended previous analytical works to assess the viability and limitations of semi-analytical approaches. Second, we built a numerical code able to relax an initial configuration of a nonrotating magnetosphere to a force-free geometry, provided any arbitrary form of the magnetic field at the star surface. The numerical code is based on a finite-difference time-domain, divergence-free, and conservative scheme, based of the magneto-frictional method used in other scenarios. We obtain new numerical configurations of twisted magnetospheres, with distributions of twist and currents that differ from previous analytical solutions. The range of global twist of the new family of solutions is similar to the existing semi-analytical models (up to some radians), but the achieved geometry may be quite different. The geometry of twisted, force-free magnetospheres shows a wider variety of possibilities than previously considered. This has implications for the observed spectra and opens the possibility of implementing alternative models in simulations of radiative transfer aiming at providing spectra to be compared with observations.
We present three-dimensional force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad-Shafranov equation. This result indicates the existence of an unstable branch of twisted magnetospheric solutions and allows to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30% of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of the mechanical stresses onto the stellar crust, which can potentially result in a global mechanical failure of a significant fraction of it. We find that the estimated energy release and the emission properties are compatible with the observed giant flare events. The newly identified instability is a candidate for recurrent energy dissipation, which could explain part of the phenomenology observed in magnetars.
We study the magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with $m=0,1$ are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode $(l,m)=(2,1)$, can be a factor $sim8$ larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface as small as $eta=0.05 Omega R$. The results obtained in this paper clarify the extent to which stellar oscillations are reflected in the time variation of the physical properties at the surface of the rotating neutron star, mainly by showing the existence of a relation between $Pdot{P}$ and the oscillation amplitude. Finally, we propose a qualitative model for the explanation of the phenomenology of intermittent pulsars in terms of stellar oscillations that are periodically excited by star glitches.
We discuss constraints that the observed brightness temperatures impose on coherent processes in pulsars and Fast Radio Bursts (FRBs), and in particular on the hypothesis of coherent curvature emission by bunches. We estimate the peak brightness temperature that a bunch of charge $Ze$ can produce via synchrotron and/or curvature emission as $k_B T sim (Z e)^2/lambda$, where $lambda$ is the typical emitted wavelength. We demonstrate that the bunchs electrostatic energy required to produce observed brightness temperature is prohibitively high, of the order of the total {it bulk } energy. We compare corresponding requirements for the Free Electron Laser mechanism (Lyutikov 2021) and find that in that case the constraints are much easier satisfied.
Instabilities in a neutron star can generate Alfven waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current $j_{rm A}$. We derive an analytic expression for the evolution of the wave vector $boldsymbol{k}$ and the growth of $j_{rm A}$. In the strongly sheared regime, $j_{rm A}$ may exceed the maximum current $j_{0}$ that can be supported by the background $e^{pm}$ plasma. We investigate these charge-starved waves, first using a simplified two-fluid analytic model, then with first-principles kinetic simulations. We find that the Alfven wave continues to propagate successfully even when $kappa equiv j_{rm A}/j_{0} gg 1$. It sustains $j_{rm A}$ by compressing and advecting the plasma along the magnetic field lines with particle Lorentz factors $sim kappa^{1/2}$. The simulations show how plasma instabilities lead to gradual dissipation of the wave energy, giving a dissipation power $L_{rm diss}sim 10^{35}(kappa/100)^{1/2} (B_w/10^{11},{rm G}),mathrm{erg/s}$, where $B_w$ is the wave amplitude. Our results imply that dissipation due to charge starvation is not sufficient to power observed fast radio bursts (FRBs), in contrast to recent proposals.
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure.