Influence Of R Modes On The Evolution Of Accreting Neutron Stars In LMXB

We enhance our understanding on neutron stars mainly via investigating their r-mode instabilities. R-mode evolution is determined by the competition between the viscous damping effect and the destabilizing effect due to gravitational radiation. Considering the temperature dependence of the viscosities, we would like to show the evolution equation of a NS first in the second chapter. The thermal evolution of a neutron star is actually the result of the competition between cooling and heating mechanisms. On one hand, the NS can be cooled by neutrino and photon energy release. On the other hand, the shear viscous dissipation of r-mode can convert part of the oscillation energy into heat energy gradually and in LMXB, we should also considering the accretion heating. Then we introduce the instability window and schematically illustrate the trajectory a system in LMXB would follow. According the observations, we modify the instability window by taking into account the presence of a viscous boundary layer. We introduce the first and second order r-mode equations obtained by solving the linear and non-linear fluid mechanics equations. Then we compared the results and analysed the differences. The differential rotation causes the fluid elements to large scale drift along the azimuthal direction. Magnetic field lines are "frozen" in the fluid and move entirely with it. The energy of this new field is coming from the r-mode, so this new field can be treated as a damping mechanism.In the third chapter, given the initial magnetic field interior the star, combine the second-order lagrangian displacement, we deduce the new toroidal magnetic field, the variation in the magnetic energy and magnetic damping under the second-order r-mode theory. On this basis, we reconsider the evolution of second-order r mode and spin evolution of the NS. The results show that the formation of toroidal magnetic field will shorten the duration of the r-mode instability, the spin-down of the neutron star is terminated and the viscous heating effects are also weakened. As the NS may looses significant spin angular momentum to GWs also through the induced magnetic deformation, We further considering this mechanism. We find that r-mode rapid growth and rapid reduction for about thousands years. It is quite different from the former result that r-mode oscillation for many years. This is because as we considering the magnetic deformation, it radiate gravitational waves and the accretion torque can not counter with gravitational radiation torque. So the NS will spin down rapidly. So we conclude that r mode instability is unlikely to play a role in accreting neutron star and the gravitational radiation may not be detected by the advanced laser interferometer detector LIGO. But the evolution of accretion neutron in LMXB is affected, the evolution of temperature,r mode and rotation are show prominent features, especially the rotation frequency limit could meet the observation data of the LMXB.