Abstract
The appearance and time variability of accreting millisecond X-ray pulsars (hereafter AMXPs, e.g. Wijnands & van der Klis 1998) depends strongly on the accretion rate, the effective viscosity and the effective magnetic diffusivity of the disk-magnetosphere boundary. The accretion rate is the main parameter which determines the location of the magnetospheric radius of the star for a given stellar magnetic field. We introduce a classification of accreting neutron stars as a function of the accretion rate and show the corresponding stages obtained from our global 3D magnetohydrodynamic (MHD) simulations and from our axisymmetric MHD simulations. We discuss the expected variability features in each stage of accretion, both periodic and quasi-periodic (QPOs). We conclude that the periodicity may be suppressed at both very high and very low accretion rates. In addition the periodicity may disappear when ordered funnel flow accretion is replaced by disordered accretion through the interchange instability.
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