Abstract
We show the spectral properties of 15 spin-powered X-ray pulsars, and the correlation between the average power-law photon index and spin-down rate. Generation order parameters (GOPs) based on polar-cap models are introduced to characterize the X-ray pulsars. We calculate three definitions of generation order parameters due to the different effects of magnetic and electric fields on photon absorption during cascade processes, and study the relations between the GOPs and spectral properties of X-ray pulsars. There exists a possible correlation between the photon index and GOP in our pulsar sample. Furthermore, we present a method due to the concept of GOPs to estimate the non-thermal X-ray luminosity for spin-powered pulsars. Then X-ray luminosity is calculated in the context of our polar-cap accelerator model which is well consistent with the most observed X-ray pulsar data. The ratio between X-ray luminosity estimated by our method and the pulsar's spin-down power is well consistent with the $L_{\rm X}\sim 10^{-3}L_{\rm sd}$ feature.
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