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We show that the r-mode instability can generate strong toroidal fields in the core of accreting millisecond quark stars by inducing differential rotation. We follow the spin frequency evolution on a long time scale taking into account the magnetic damping rate in the evolution equations of r-modes. The maximum spin frequency of the star is only marginally smaller than in the absence of the magnetic field. The late-time evolution of the stars which enter the r-mode instability region is instead rather different if the generated magnetic fields are taken into account: they leave the millisecond pulsar region and they become radio pulsars.
In millisecond pulsars the existence of the Coriolis force allows the development of the so-called Rossby oscillations (r-modes) which are know to be unstable to emission of gravitational waves. These instabilities are mainly damped by the viscosity
The flow of a matter, accreting onto a magnetized neutron star, is accompanied by an electric current. The closing of the electric current occurs in the crust of a neutron stars in the polar region across the magnetic field. But the conductivity of t
Pulsating ultra-luminous X-ray sources (PULXs) are characterised by an extremely large luminosity ($ > 10^{40} text{erg s}^{-1}$). While there is a general consensus that they host an accreting, magnetized neutron star (NS), the problem of how to pro
The large majority of neutron stars (NSs) in low mass X-ray binaries (LMXBs) have never shown detectable pulsations despite several decades of intense monitoring. The reason for this remains an unsolved problem that hampers our ability to measure the
The crust of accreting neutron stars plays a central role in many different observational phenomena. In these stars, heavy elements produced by H-He burning in the rapid proton capture (rp-) process continually freeze to form new crust. In this paper