Electrodynamics of the Pulsar Magnetosphere: Equilibrium, Radiation and Reconnection – EMPERE

Our modelling is guided by the recent multi-wavelength observations of pulsed emission emanating from pulsars. We follow two approaches in order to accomplish our project: on one hand semi-analytical calculations and on the other hand numerical simulations with currently available codes such as AMRVAC (adaptive mesh refinement versatile advection code) or other codes obtained from international collaborators as well as self-developed methods at the Strasburg observatory. We indeed employed novel numerical algorithms like pseudo-spectral methods combined with high order finite volume methods of discontinuous Galerkin type. This new approach allows an efficient and accurate treatment in spherical geometry as well as an easy implementation of the parallelization of the code thanks to the MPI library (Message Passing Interface). Radiative signatures from our models are translated into radio and high-energy light curves deduced from post-processing the results of the numerical simulations.
Our objectives are therefore two-fold: first to understand the self-consistent structure of the pulsar magnetosphere and wind and second to understand the origin of the pulsed radio and high-energy emission emanating from the magnetospheric plasma. We hope two severely constrain the magnetospheric structure thanks to these observations.

First, we calculated the synchrotron spectrum emanating from the explosive magnetic reconnection event in the pulsar striped wind with application to gamma-ray flares from the Crab Nebula.

Second, the study of magnetospheric configurations have been materialized by a simulation software onto which additional modules of general relativity and quantum electrodynamics were added. This work was declined as publications formulating Maxwell's equations in general relativity with quantum electrodynamics corrections in the 3+1 formalism. A first application consisted to look for an approximate analytical solution to a static magnetic dipole. Extension to the rotating dipole required numerical simulations that we performed recently and showing that quantum electrodynamics has only a little impact on the global dynamics of the magnetosphere. General relativity effects were analysed in detail for an empty magnetosphere and one filled with an electron-positron plasma. A thorough quantitative analysis of the total power radiated by the neutron star surrounded by a plasma and taking into account the effects of general relativity showed that the braking index is not affected by gravity or by the plasma. It is very close to the theoretical value of 3 predicted by the vacuum model. However, the contribution of multipolar components significantly affects the estimate of its value at the surface and invalidates models based on estimates from a single magnetic dipole. We analysed the consequences of an off-centred dipole onto the radiative properties like pulse profiles and polarization. In a long term we can check our hypotheses by a careful analysis of the observations.

Thirdly, the calculation of pulsed radiation emanating from the wind was predicted at very high energies. We have demonstrated the ability to detect the Crab pulsar at TeV energies.

Our long lasting objective is to include the hydrodynamical part into our description of the electrodynamics of the magnetosphere. We hope to get soon quantitative and accurate results potentially important for the diagnose of observational signatures of the magnetosphere by including some dissipative effects like a resistive current or dissipation through radiation reaction. About high-energy emission, our aim is to compare our predictions of pulsar light curves with X-ray and gamma-ray observations. These data show indeed a phase lag between photon arrival time in both energy bands difficult to reconcile with current models. This should help us to constrain the pulsed emission mechanisms. A detailed study of the multi-wavelength light-curves related to this emission is under way. Fitting the polarization angle evolution in the radio domain represents another important aspect to decipher the magnetic field geometry and the to localize the emission sites in the low energy band. The too simplistic image of a rotating dipole located right at the centre of the perfectly spheric star is too naive and must be abandoned. Deviations from this picture a numerous. For example, we actually study the consequences of an off-centred dipole onto the pulsed emission and the structure of the wind. The star, due to its rotation and due to the anisotropic pressure exerted by the magnetic field, will deform and deviate from a perfect sphere. We will deduce the presence of such deformations in the multi-wavelength data.
On a longer timescale, our expertise will also serve to investigate the magnetosphere of black holes and their jets. Indeed, the tools at hand could be easily applied to such kind of problematic.

Our results have been communicated to the high-energy astrophysics and plasma physics communities through refereed publications in world leading journals of astrophysics and plasma physics. We also regularly participate actively to international conferences on related topics to disseminate our results.

Currently, we have published 20 papers in rank A journals. We have given 23 talks, some of them invited and 13 posters.

Our knowledge have also been disseminated to the general public via popularizing articles in dedicated science magazines and conferences.

Among the diversity of stellar populations observed in our galaxy, neutron stars remain the most enigmatic compact objects known so far. End product of stellar evolution, they concentrate a large amount of matter of the order the solar mass in a region of only a few kilometres in radius. Their density in the inner core therefore easily exceeds the nuclear density. Moreover, during the implosion of the progenitor, magnetic flux conservation drastically increases the strength of the magnetic field to such values that quantum electrodynamical processes become dominant, especially in the vicinity of the neutron star surface (electron/positron pair creation, quantum radiation mechanisms). In this project, we focus on a subclass of neutron stars known as pulsars. They emit pulsed radiation in the whole electromagnetic spectrum from radio, infra-red, through optical up to X-rays and gamma-rays. The overall complexity of these neutron stars is often underestimated. Indeed, the four fundamental interactions - strong, weak, gravitational and electromagnetic - are closely correlated in these stars in a strong field regime because of the presence of significant space-time curvature and very high magnetic fields. The quantitative interplay between these forces is not yet understood. Despite little progress made since their discovery more than forty years ago, pulsars are excellent laboratories for nuclear and particle physicists as well. They bring us to the limit of our current knowledge, a place where strong gravity meets quantum mechanics in an extremely entangled way. Moreover, pulsars have already shown their ability to test general relativity in the strong field regime to a precision unreachable at Earth by indirect observations of gravitational waves. Looking for the validity of our best theory of gravitation is indeed a major quest in modern astrophysics. However, to date, only electromagnetic radiation is detected at Earth, either thermal emission from their surface or high energies from their magnetosphere and/or wind.

Our project aims at investigating some aspects of pulsar fundamental physics related to the highly magnetized relativistic magnetohydrodynamical (RMHD) flows under different but complementary aspects. We will study the radiative and electrodynamical properties of the plasma present in both the magnetosphere and the wind up to the termination shock, i.e. the place where the flow enters the surrounding nebula. Different mechanisms within the plasma will be under scrutiny, namely
- stationary strongly magnetized plasma flows launched by the pulsar
- instabilities, particle acceleration and reconnection mechanisms
- properties of the emergent pulsed radiation
- confrontation with available and forthcoming high-energy X-ray and gamma ray observations, phase-resolved pulsed emission and polarization.

These points of focus will be approached by two mains tools: (semi-)analytical calculations and numerical simulations with currently available MHD codes such as the versatile advection code (VAC and adaptive mesh refinement version AMRVAC) and from collaborator as well as self-developed multi-fluid and particle in cell (PIC) methods. Radiative signatures will be deduced from post-processing the outputs of the simulations.