Abstract We present a case study of the relevance of the radially pulsational instability of a two-temperature accretion disk around a neutron star to anomalous X-ray pulsars(AXPs). Our estimates are based on the approximation that such a neutron star disk with mass in the range of 10-6--10-5M⊙ is formed by supernova fallback. We derive several peculiar properties of the accretion disk instability: a narrow interval of X-ray pulse periods; lower X-ray luminosities; a period derivative and an evolution time scale. All these results are in good agreement with the observations of the AXPs.
Keywords pulsars: general --- pulsars --- stars: neutron --- X-rays: stars --- accretion disk --- instability
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