2007MNRAS.382.1833M

Recent calculations indicate that the cohesive energy of condensed matter increases with magnetic field strength and becomes very significant at magnetar-like fields (e.g. 10 keV at 3x10¹⁴ G for zero-pressure condensed iron). This implies that for sufficiently strong magnetic fields and/or low temperatures, the neutron star surface may be in a condensed state with little gas or plasma above it. Such surface condensation can significantly affect the thermal emission from isolated neutron stars, and may lead to the formation of a charge-depleted acceleration zone (`vacuum gap') in the magnetosphere above the stellar polar cap. Using the latest results on the cohesive property of magnetic condensed matter, we quantitatively determine the conditions for surface condensation and vacuum gap formation in magnetic neutron stars. We find that condensation can occur if the thermal energy kT of the neutron star surface is less than about 8 per cent of its cohesive energy Q_s, and that a vacuum gap can form if Ω ⋅ B_p< 0 (i.e. the neutron star's rotation axis and magnetic moment point in opposite directions) and kT is less than about 4 per cent of Q_s. For example, at B = 3x10¹⁴G, a condensed Fe surface forms when T ≲ 10⁷ K and a vacuum gap forms when T ≲ 5x10⁶ K. Thus, vacuum gap accelerators may exist for some neutron stars. Motivated by this result, we also study the physics of pair cascades in the (Ruderman-Sutherland type) vacuum gap model for photon emission by accelerating electrons and positrons due to both curvature radiation and resonant/non-resonant inverse-Compton scattering. Our calculations of the condition of cascade-induced vacuum breakdown and the related pulsar death line/boundary generalize previous works to the superstrong field regime. We find that inverse-Compton scatterings do not produce a sufficient number of high-energy photons in the gap (despite the fact that resonantly upscattered photons can immediately produce pairs for B ≳ 1.6x10¹⁴ G) and thus do not lead to pair cascades for most neutron star parameters (spin and magnetic field). We discuss the implications of our results for the recent observations of neutron star thermal radiation as well as for the detection/non-detection of radio emission from high-B pulsars and magnetars.