评估瞬态轨道共振的影响
Assessing the impact of transient orbital resonances
摘要：
未来天基引力波探测器-激光干涉仪空间天线-的主要来源之一是小型致密物体进入星系中心大质量黑洞的螺旋。来自这种极端质量比Inspiral（EMRI）系统的重力波形将以前所未有的精度提供对其参数的测量，但前提是波形被精确建模。在这里，我们探讨的影响时发生的径向和极频率的比率是一个有理数的瞬态轨道共振。我们引入了一个新的有效共振模型，这是一个扩展的数字kludge EMRI波形近似，包括共振的影响，并使用它来探索共振对EMRI参数估计的影响。对于一年的吸气，我们发现，由3：2共振引起的几个周期的相位下降会导致参数估计的系统误差，这是几倍的典型测量精度的参数。在靠近中心黑洞的3：2共振中，偏差最大。通过将它们视为未知的模型参数，我们进一步表明，对于信噪比为20的典型的一年EMRI观测，观测将能够将整个共振的轨道参数变化的大小限制在10%的相对精度。通过将测量到的变化与广义相对论预测的变化进行比较，这种测量可以被视为基础物理学的测试。
英文摘要：
One of the primary sources for the future space-based gravitational wave detector, the Laser Interferometer Space Antenna, are the inspirals of small compact objects into massive black holes in the centres of galaxies. The gravitational waveforms from such Extreme Mass Ratio Inspiral (EMRI) systems will provide measurements of their parameters with unprecedented precision, but only if the waveforms are accurately modeled. Here we explore the impact of transient orbital resonances which occur when the ratio of radial and polar frequencies is a rational number. We introduce a new Effective Resonance Model, which is an extension of the numerical kludge EMRI waveform approximation to include the effect of resonances, and use it to explore the impact of resonances on EMRI parameter estimation. For one-year inspirals, we find that the few cycle dephasings induced by 3:2 resonances can lead to systematic errors in parameter estimates, that are up to several times the typical measurement precision of the parameters. The bias is greatest for 3:2 resonances that occur closer to the central black hole. By regarding them as unknown model parameters, we further show that observations will be able to constrain the size of the changes in the orbital parameters across the resonance to a relative precision of 10% for a typical one-year EMRI observation with signal-to-noise ratio of 20. Such measurements can be regarded as tests of fundamental physics, by comparing the measured changes to those predicted in general relativity.
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