In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars （NSs） could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based ...In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars （NSs） could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based on a consideration of the coupling of the r-modes and the stellar spin and thermal evolution, we carefully investigate the influences of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects are taken into account. The numerical results show that, for both kinds of NSs, the differential rotation can significantly prolong the duration of the r-modes. As a result, the stars can keep nearly a constant temperature and constant angular velocity for over a thousand years. Moreover, the persistent radiation of a quasi-monochromatic gravitational wave would also be predicted due to the long-term steady r-mode oscillation and stellar rotation. This increases the detectability of gravitational waves from both young isolated and old accreting NSs.展开更多
A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In ...A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.10603002 and 10773004)
文摘In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars （NSs） could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based on a consideration of the coupling of the r-modes and the stellar spin and thermal evolution, we carefully investigate the influences of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects are taken into account. The numerical results show that, for both kinds of NSs, the differential rotation can significantly prolong the duration of the r-modes. As a result, the stars can keep nearly a constant temperature and constant angular velocity for over a thousand years. Moreover, the persistent radiation of a quasi-monochromatic gravitational wave would also be predicted due to the long-term steady r-mode oscillation and stellar rotation. This increases the detectability of gravitational waves from both young isolated and old accreting NSs.
文摘A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.
