Abstract

According to standard theoretical interpretations, in neutron stars' magnetospheres particles are accelerated along the magnetic field lines where the highly-magnetized surrounding offers the ideal conditions to make them radiate high-energy gamma-rays (E ≥ 100 MeV) that bear the timing signature of their parent neutron star. Moreover, the accelerated particles (mostly electrons and positrons) can either move outward, to propagate into space, or be funnelled back, towards the star surface. While particles impinging on the neutron star surface generate hot spots, detectable in X-rays, outgoing ones could light-up the neutron star surroundings giving rise to extended features, visible both in X-and in Very-High-Energy (VHE) gamma-rays (E ≥ 100 GeV).By combining gamma-ray light curves and spectra with the X-ray emission, both thermal (from the hot spots) and non thermal (from somewhere in the magnetosphere) we can try to map the emission geography within the light cylinder. Moreover, we can trace the particles' propagation outside the neutron stars' magnetospheres through their synchrotron emission, responsible for X-ray extended features, and their VHE gamma-rays inverse Compton emission, which give rise to extended sources, whose shapes, however, appear different from that of the corresponding X-ray ones since they are produced by particles of different energies.

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