Partially Screened Gap -- general approach and observational consequences

Abstract

Observations of the thermal X-ray emission from radio pulsars implicate that the size of hot spots is much smaller then the size of the polar cap that follows from the purely dipolar geometry of pulsar magnetic field. Most plausible explanation of this phenomena is an assumption that the magnetic field at the stellar surface differs essentially from the purely dipolar field. We can determine magnetic field at the surface by the conservation of the magnetic flux through the area bounded by open magnetic field lines. Then the value of the surface magnetic field can be estimated as of the order of $10^{14}$ G. On the other hand observations show that the temperature of the hot spot is about a few million Kelvins. Based on these observations the Partially Screened Gap (PSG) model was proposed which assumes that the temperature of the actual polar cap (hot spot) equals to the so called critical temperature. We discuss correlation between the temperature and corresponding area of the thermal X-ray emission for a number of pulsars. The results of our analysis show that the PSG model is suitable to explain both cases: when the hot spot is smaller and larger then conventional polar cap. We argue that in the second case structure and curvature of field lines allow pair creation in the closed field lines region thus the secondary particles can heat the stellar surface outside the actual polar cap. We have found that the Curvature Radiation (CR) plays dominant role in avalanche pair production in the PSG. We studied dependence of the PSG parameters on the pulsar period, the magnetic field strength and the curvature of field lines.