Electron-Positron Pair Production in the Electrosphere of Quark Stars

We study Schwinger pair creation of charged particles due to the inhomogeneous electric field created by the thin electron layer at the surface of quark stars (the electrosphere). As suggested earlier, due to the low photon emissivity of the quark-gluon plasma and of the electrosphere, electron-positron pair emission could be the main observational signature of quark stars. To obtain the electron-positron pair creation rate we use the tunneling approach. Explicit expressions for the fermion creation rate per unit time per unit volume are derived, which generalize the classical Schwinger result. The finite-size effects in pair production, due to the presence of a boundary (the surface of the quark star), are also considered in the framework of a simple approach. It is shown that the boundary effects induce large quantitative and qualitative deviations of the particle production rate from what one deduces with the Schwinger formula and its generalization for the electric field of the electrosphere. The electron-positron pair emissivity and flux of the electrosphere of quark stars due to pair creation is considered, and the magnitude of the boundary effects for these parameters is estimated. Due to the inhomogeneity of the electric field distribution in the electrosphere and to the presence of the boundary effects, at high temperatures (T ≥ Tcr ≈ 0.1 MeV) we find a lower electron-positron flux than previously estimated. The numerical value of the critical temperature Tcr depends on the surface potential of the star. We briefly consider the effect of the magnetic field on the pair creation process and show that the magnetic field can drastically enhance the pair creation rate.