Magnetar spectra and twisted magnetospheres

The huge potential drop between the footpoints of the closed field lines in the twisted magnetospheres of magnetars may accelerate electrons up to very high energies, γ ≫ 10^6. On the other hand, the comparison between the observed spectra of magnetars and spectra obtained by accurate theoretical models seems to favor of a picture in which the magnetosphere is filled by “slow” electrons (v ≲ 0.8c), rather than by ultra-relativistic particles.Actually, two different processes may limit the effective velocity of charges in the innermost part of the magnetosphere, both related to the resonant behavior of the Compton scattering in strong magnetic field. Near the stellar surface, where the magnetic field B exceeds the quantum limit B_Q ≃ 4.4 × 10^13 G, scattering between fast electrons and ˜1 keV seed photons generates high-energy gamma rays that immediately convert to electron/positron pairs via one-photon pair production. This runaway process limits the value of γ to the threshold value for pair production γ ≈ 1000. At larger distance the magnetic field weakens, and pair creation is strongly depressed for the impossibility of resonant scattering to generate high-energy photons. We discuss the possibility that, in the intermediate region 5R∗ ≲ r ≲ 20R∗ (with R∗ = 10 km), intense Compton losses are effective in reducing the acceleration of electrons even in presence of a very high potential drop.