The main purpose of my thesis is to examine some electrodynamic properties of binary pulsars, trying to understand the peculiar physical processes that can happen in their magnetospheres; the ultimate aim is to discuss if such systems can be the source of the observed flux of cosmic rays between the knee and the ankle, since the mechanisms of acceleration for the cosmic rays in this range of energies are still unknown. Attention around binary pulsars has arisen after the recent discovery (December 2003) of the first double neutron star system in which both the stars are visible as pulsars (PSR J0737-3039); the inspection of the physical features of this binary pulsar has led to some intriguing possibilities up to now unexplored. In this thesis I will first of all review what is already known about the main properties of this binary system. I will describe in particular the possibility to go further in the verification of the predictions of general relativity with the so-called post-Keplerian parameters; I will discuss the possibility of studying the optical properties of the magnetospheres, since the inclination angle of the orbit is nearly 90° and some orbital phases show an eclipse of the light from one pulsar due to absorption by the magnetosphere of the companion; I will rapidly summarize how the discovery of that binary pulsar can enlarge our knowledge about the origin and evolution of double neutron star systems; lastly, I will examine the increase in the estimate of the Galactic double neutron star merger rate due to the discovery of PSR J0737-3039. I will then summarize the current knowledge about the magnetosphere of a single pulsar. After describing the Gold-Pacini model for the energy loss of the oblique rotator (in which the magnetic and rotational axes are not parallel), I will discuss the Goldreich-Julian model for the aligned axisymmetric rotator in the force-free approximation in which the inertial and gravitational forces are neglected with respect to the electromagnetic ones and the Lorentz force per unit volume is assumed to be zero outside the pulsar; after showing the main unsolved problems about this model, I will try to examine the origin of the leptons (positrons and electrons) which are expected to fill the pulsar magnetosphere and to continuously stream away from the star through the light cylinder (where co-rotation with the pulsar would mean traveling at the speed of light). Since even the magnetosphere of a single isolated pulsar is not well understood, my approach in considering some hitherto unexplored properties of the joint magnetosphere of a binary pulsar will mainly be qualitative, trying to understand through order-of-magnitude estimates the physical processes involved. First of all I will describe the possibility that, for binary pulsars in which the orbital separation is less than the sum of the light cylinder radii of the stars, the region at the center of the system could show a time-dependent distortion of the two co-rotating magnetospheres which could give origin to an induced electric field. I will then examine the possibility that such a field is quenched by a local production of pairs caused by the electric field itself. After showing that the electric field can not be switched-off by the pairs, I will discuss the possible observational consequences of the production of such a large number of leptons, which will be accelerated by the electric field along the magnetic field lines toward the pulsars and will then radiate their energy via curvature radiation; unfortunately, the small energy flux emitted, together with the rarity of double neutron star systems, will not likely allow us to detect the radiation emitted. Lastly, I will discuss the original idea that the strong induced electric fields could be responsible for the acceleration of cosmic rays whose energy lies between the knee and the ankle of the cosmic ray spectrum. In this case the unsolved problem is the origin for those ions, and I will examine three possibilities, comparing their respective predictions with the flux and power-law of the observed spectrum: they could come from the mass loss induced by the tidal heating caused by the strong gravitational fields of the two orbiting stars, or maybe they could fill the Goldreich-Julian magnetosphere as well as positrons and electrons, or they could even be extracted from the pulsar atmosphere which is continuously replenished by the evaporation of nuclei from the stellar surface, since the star is being heated by the flux of high energy leptons discussed above. The last hypothesis seems to be well confirmed by the observational constraints, even if we are not able to fully explain how to free the accelerated cosmic rays from the binary system and inject them in the interstellar medium; anyway, our qualitative approach could pave the way for further and more quantitative work on the electrodynamics of binary pulsars, in order to explain the details of the acceleration and escape of ions from such fascinating systems
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