Modelisation of relativistic winds and jets in Astrophysics

Winds and jets are one of most spectacular and enigmatic high energy phenomena in astrophysics. Such outflows are associated with objets ranging from newly born stars embedded in dense molecular clouds and binary systems in our galaxy to supermassive black holes in the center of active galactic nuclei. Nevertheless, despite the development of X-Ray and $\gamma$-Ray astronomy as the result of various spatial missions (ROSAT, ASCA, Chandra, XMM-Newton for X-Ray and INTEGRAL for $\gamma$ Ray), the problems of formation and acceleration of jet have not been fully resolved. In this thesis, we have study some dynamical mechanisms which can be responsible for the universality of the phenomenon and for the similarity of outflows that occur on vastly different scales. To this end, we used hydrodynamics and magnetohydrodynamics in general relativity to analyze as this is generally done in astrophysical plasmas characterised by large spatial and temporal scales. Initially, we started by studying hydrodynamic spherical winds in which we neglected the magnetic effects. We generalized the model of Parker to general relativity by introducing a new polytropic equation of state with a variable effective polytropic index, appropriate to describe relativistic temperatures close to the central object and non relativistic ones further away. Relativistic effects introduced by the Schwarzschild metric and the presence of relativistic temperatures in the corona are compared with previous results for a constant effective polytropic index and also with results of the classical wind theory. We showed with our new equation of state, that the thermal and gravity effects are coupled allowing an increase of the acceleration efficiency of the thermal wind. We also showed the necessity to use this new polytrope to study relativistic winds, because of the consistent treatment of flows near compact objects. Secondly, we worked on new analytical models of relativistic jets emitted by the central corona around a Schwarzschild black hole. The models were developed using meridional self-similar methods which are adequate in modelising the central jet. In, the first model we have neglected the light cylinder effects comparatively with thermal effects in the outflow. This allowed us to better appreciate the role of the thermal effects in the formation and acceleration of jets. We studied the evolution of solutions obtained with this model when gravity increases and found the application limits of this model. We have also check that the classification of the jets of active galactic nuclei proposed by Sauty et al. (2001) can be extended to the relativistic jets. In this classification the jet from FRII (active galaxies with a strong radio emission) are characterised by high luminosity with well collimated and powerful jets. These jets correspond in our model to solutions collimated by magnetic forces. Conversely, jets from FRI (active galaxies with a strong radio emission also and radio lobes instead of hot spots) are characterised by collimated jet and a rich environment. The collimation of these jets seems to be induced by the external medium. In our models, ther is a refocalisation of the jet characterized by a strong collimation and deceleration of the jet. To study these two types of jets we developed a new method to estimate the free parameters of the model. In this method, we have related the proprieties of the jet in the asymptotic region with the proprieties of the jet on to the disk corona. We found that a weak decrease on the rotation speed of the accretion disk allow to change the proprieties of the jet from FRII type to FRI type. On the other hand, we also found that relativistic thermal outflows are formed when the rotation speed of the corona is sub-keplerian. We developed also a second meridional self-similar model by taking into account effects of the light cylinder. To treat the problem of the light cylinder with the self-similar hypothesese, it is necessary to consider a jet which has a singularity on the polar axis and which is empty in the center. We started the study of this model for some specific solutions that are characterised by a light cylinder close to the Alfvén surface. This model allows us to examine the Poynting flux acceleration of jets, contrary to the previous model. We also studied the decollimation effects of the light cylinder on the jets. We found that the poloidal velocity in these jets remain weak, of the order of $0.6c$. This weak poloidal velocity is caused by the relativistic toroidal velocity in the jet which is of the order of $0.8c$. In fact, the proximity of the light cylinder to the Alfvén surface and the fast increase of the angular velocity towards the polar axis, induce the relativistic toroidal velocity near the polar axis where the acceleration is more efficient. Lastly, we began the development of a numerical code to solve steady and time-dependent MHD equations. The numerical code is developed by using the library LORENE in C++ which is based on spectral methods. It enabled us, in a first step, to treat the spherical hydrodynamic winds and to recover our analytical 1D solution. The code showed its robustness to cross the sonic transition - which is a strong singularity - and to treat the elliptic and hyperbolic domains simultaneously. We developed an algorithm that allows the treatment of the strong variations of the density close to the black hole.