OJ287双黑洞轨道计算:3.5阶后牛顿近似

大质量双黑洞OJ287是一个强引力辐射源.为了探测其引力波信号,需要知道波形,而这主要是由轨道运动所决定.为此,从广义相对论3.5阶后牛顿近似的运动方程出发对OJ287的轨道进行仔细研究,取大黑洞位置固定作为近似,给出了后牛顿近似下3.5阶的次黑洞轨道解,比他人2.5阶的工作高了一阶.次黑洞撞击吸积盘面到光学爆发存在时间延迟,这对于确定轨道参数有很大影响.利用径向距离与爆发时间关系的线性模型,对最近7次爆发时刻的观测值拟合,给出了更精确的OJ287双黑洞的轨道参数及其运动轨道.分析了计算结果,研究运动特征,并且发现了两个新性质:次黑洞进动在初期增加,在晚期接近并和时,进动达到最大值,然后减小并越过0而趋于负值.尚不能确定晚期的这个行为是否由3.5阶近似不够准确所造成.运动方程中耗散性的辐射项,后牛顿2.5阶和3.5阶的系数具有相反的符号.这意味着3.5阶项反而是从外界吸收能量.但2.5阶与3.5阶之和仍然是向外辐射引力波的,体系能量变化率为负.这个工作的计算结果可以用来更精确地计算OJ287的引力辐射.

The Orbit of Binary Black Hole OJ287: A 3.5th Post-Newtonian Order Calculation

Supermassive binary black hole OJ287 is a strong gravitational radiation source.To detect the signal of its gravitational wave,the knowledge of the waveform will be of great help,which is mainly determined by the orbital motion of the binary.For this purpose,we carry out a detailed calculation of the orbital motion of OJ287,using the postNewtonian (PN)approximation up to 3.5th order within the framework of general relativity. Our result is one order higher than the previous work made by others.As a radiation process, there is a time delay from the instance when the secondary black hole impacts on the accretion disk of the primary to the moment of the optical outburst.This time delay has to be taken into account when we try to fit the calculated orbit to the observed outburst times.Adopting a linear relation between the time delay and the impact distance as an empirical model,we fit the calculated orbit to the observed data of the recent seven outbursts of OJ287,obtain the solution of its orbital motion,and give the important orbital properties,including the averaged orbital parameters.By analyzing the result of 3.5PN order calculation of the binary system,we find some interesting features.The precession rate of secondary black hole is shown to increase to a maximum,and then to decrease at late stages,and to eventually turn into a negative value.This result might indicate the breakdown of 3.5PN approximation at late stages when a more accurate calculation is needed. More interestingly,as a main finding of this paper,we discover that the dissipative terms of 2.5th order and 3.5th order have opposite signs.This implies that the 3.5th order term itself does not radiate,but absorbs energy.However,the sum of the two terms still radiates gravitational waves outward.This is confirmed by the change rate of the energy of the system.Our results of the orbit of binary black hole OJ287 up to 3.5PN can be further used to calculate its radiated gravitational waves.