Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz and Klu’zniak (2001). In a first paper (P'etri, 2005a, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. After a discussion on the magnitude of this deformation applied to neutron stars, we show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to {three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric resonance}. In a second part, we focus on the linear response of a thin accretion disk in the 2D limit. {Waves are launched at the aforementioned resonance positions and propagate in some permitted regions inside the disk, according to the dispersion relation obtained by a WKB analysis}. In a last part, these results are confirmed and extended via non linear hydrodynamical numerical simulations performed with a pseudo-spectral code solving Euler's equations in a 2D cylindrical coordinate frame. {We found that for a weak potential perturbation, the Lindblad resonance is the only effective mechanism producing a significant density fluctuation}. In a last step, we replaced the Newtonian potential by the so called logarithmically modified pseudo-Newtonian potential in order to take into account some general-relativistic effects like the innermost stable circular orbit (ISCO). The latter potential is better suited to describe the close vicinity of a neutron star or a black hole. However, from a qualitative point of view, the resonance conditions remain the same. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.     

巴颜喀拉山东段及其邻区大地电磁测深成果地质解释

本文主要依据青海省囊歉至大河坝大地电磁测深成果,并结合重力资料对巴颜喀拉及南北两侧地区的壳幔结构进行了地质解释。指出了该区壳幔存在4个明显的低阻层,并简述了它们的形态特征,推断了其地质含意。认为昆中断裂带与昆南断裂带间是一个巨大的构造混杂岩带,影响深度亦很大。推断该区可能存在太古代地层。划出了8条壳幔断裂带,认为昆中断裂应是塔里木—华北板块与华南板块的分界线。     

A numerical method for differential equations of second order

A new algorithm of order five is presented for the solution of the initial value problem where the system of ordinary differential equations is of second order and does not contain the first derivative.