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Radiation of X-ray bursts and of accretion shocks in weakly magnetized neutron stars in low-mass X-ray binaries is produced in plane-parallel atmospheres dominated by electron scattering. We first discuss polarization produced by single (non-magnetic) Compton scattering, in particular the depolarizing effect of high electron temperature, and then the polarization due to multiply electron scattering in a slab. We further predict the X-ray pulse profiles and polarization properties of nuclear- and accretion-powered millisecond pulsars. We introduce a relativistic rotation vector model, which includes the effect of rotation of polarization plane due to the rapid motion of the hot spot as well as the light bending. Future observations of the X-ray polarization will provide a valuable tool to test the geometry of the emission region in pulsars and its physical characteristics.
Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen kn
Nuclear-powered X-ray millisecond pulsars are the third type of millisecond pulsars, which are powered by thermonuclear fusion processes. The corresponding brightness oscillations, known as burst oscillations, are observed during some thermonuclear X
Neutron Stars are among the most exotic objects in the Universe. A neutron star, with a mass of 1.4-2 Solar masses within a radius of about 10-15 km, is the most compact stable configuration of matter in which degeneracy pressure can still balance gr
Compact binary millisecond pulsars with main-sequence donors, often referred to as redbacks, constitute the long-sought link between low-mass X-ray binaries and millisecond radio pulsars, and offer a unique probe of the interaction between pulsar win
The X-ray radiation produced on the surface of accreting magnetised neutron stars is expected to be strongly polarised. A swing of the polarisation vector with the pulsar phase gives a direct measure of the source inclination and magnetic obliquity.