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 3 \times 10 ^ { 14 } 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 % of its cohesive energy Q _ { s } , and that a vacuum gap can form if \mathbf { \Omega } \cdot \mathbf { 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 % of Q _ { s } .
For example , at B = 3 \times 10 ^ { 14 } G , a condensed Fe surface forms when T \la 10 ^ { 7 } K and a vacuum gap forms when T \la 5 \times 10 ^ { 6 } 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/nonresonant 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 \ga 1.6 \times 10 ^ { 14 } 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 .