Detecting a tail effect in gravitational-wave experiments.
Detecting a tail effect in gravitational-wave experiments.
复制标题
检测引力波实验中的尾部效应。
DOI：
10.1103/physrevlett.74.1067
复制
发表时间：
1995
影响因子：
8.6
通讯作者：
B. Sathyaprakash
中科院分区：
文献类型：
--
作者：
L. Blanchet;B. Sathyaprakash
未来的引力波实验着眼于螺旋形的致密双星，可以探测到引力波尾部引起的非常小的相位调制效应。一旦已经识别出二进制信号，对数据的进一步分析将提供二进制的总质量-能量M的测量，其通过最佳信号处理作为该尾部效应中的因子进入。这种效应的检测将包括显示M的测量值和取决于双星的两个质量的其他参数的兼容性。这说明了引力波实验在检验广义相对论方面的巨大潜力。PACS编号：04.80.Nn、04.30.Db、97.60.Lf、97.80.- [4]引力辐射的首次直接探测可能会在未来的引力波实验中进行，如LIGO和VIRGO。目前，引力辐射的探测只是间接的，这要归功于对脉冲双星1913 + 16的非常精确的定时观测[1]。直接探测引力辐射的最佳候选源之一是致密天体（中子星或黑洞）的双星系统，它们处于演化的后期吸气阶段[2]。在100 Mpc的距离内，中子星合并的数量预计每年只有几个[3]（可能有相当数量的黑洞合并），在这个距离上，LIGO和VIRGO可能会观察到信噪比（SNR）为-10的波。这样的首次亮相将在天文学中开辟一个全新的领域，并将允许验证广义相对论的一些基本预测。经常引用的是验证波是纯螺旋度2的可能性，没有其他自旋状态的混合。我们的工作（这封信和详细的叙述[4]）的目的是，根据与所谓的引力波尾效应有关的一种特殊效应，表明对螺旋形致密双星的观测也将允许验证广义相对论的非线性结构的某些方面。现在已经认识到的事实[5]使得这种验证成为可能，即需要非常精确的广义相对论预测来达到测量双星参数的全部潜在准确性。尾部效应本质上是由于引力辐射在弯曲的背景时空上的传播，而背景时空是由它自己的源产生的。更具体地说，在最低阶，辐射的尾部是由源的时变四极矩（产生线性辐射）与其四极矩或总质能M（产生背景）之间的非线性相互作用产生的。尾辐射具有独特的性质（时间上的“非定域性”），它依赖于源在过去任意遥远时刻的动力学，在简单延迟时间t-r/c之前。这反映了重力不仅在光锥上传播（以光速c直接传播），而且在光锥内传播（所有速度小于c的平均传播）。(See[6]关于尾部和相关非线性效应的参考文献。在未来的引力波实验中，对尾部效应（或与之直接相关的效应）的探测将提供直接证据，证明引力在弯曲的时空中传播，而弯曲的时空是由引力源产生的。(Note来自脉冲双星观测的间接证据可能是遥不可及的。这将是对广义相对论在“引力动力学”理论中的非线性的一个有趣的测试，涉及快速变化的强引力场。这还将提供对源的总质量-能量M的独立测量。尾部效应在辐射中出现在所谓的1.5后牛顿（1.5-PN）近似下，即，在超出通常的四极辐射的相对阶数C3处。让我们考虑一个一般的孤立源发射的辐射，它离源有很大的距离r（忽略像1/r~这样消失的项）。更准确地说，我们用h（t）表示某些检测器直接感受到的波的分量的线性组合[例如，h（t）是激光干涉检测器的臂长的相对变化]。然后h（t）的表达式，包括后牛顿展开中直到c阶的所有项，可以写为[7]
Future gravitational-wave experiments looking at inspiralling compact binaries could achieve the detection of a very small effect of phase modulation induced by the tails of gravitational waves. Once a binary signal has been identified, further analysis of data will provide a measure of the total mass-energy M of the binary, which enters as a factor in this tail effect, by means of optimal signal processing. The detection of the effect will then consist in showing the compatibility of the measured values of M and of the other parameters depending on the two masses of the binary. This illustrates the high potentiality of gravitational-wave experiments for testing general relativity. PACS numbers: 04.80.Nn, 04.30.Db, 97.60.Lf, 97.80.— d The first direct detection of gravitational radiation will probably take place in future gravitational-wave experiments such as LIGO and VIRGO. For the moment, the detection of gravitational radiation has only been indirect, thanks to the very precise timing observations of the binary pulsar 1913 + 16 [1]. Among the best candidate sources for a direct detection of gravitational radiation are binary systems of compact objects (neutron stars or black holes) in their late inspiralling stages of evolution [2]. The number of neutron-star coalescences is expected to be a few per year out to a distance of 100 Mpc [3] (with maybe a comparable number of black-hole coalescences), at which distance LIGO and VIRGO might observe the waves with a signal-to-noise ratio (SNR) — 10. Such a premiere will open a totally new field in astronomy, and will permit verification of some fundamental predictions of general relativity. Often quoted is the possibility of verifying that the waves are of pure helicity two, with no admixture of other spin states. The purpose of our work (this Letter and the detailed account [4]) is to show, on the basis of a particular effect related to the so-called gravitational-wave tail effect, that the observations of inspiralling compact binaries will permit also verification of some aspects of the nonlinear structure of general relativity. This verification is made possible by the now recognized fact [5] that a very precise general relativity prediction is needed to reach full potential accuracy on the measurement of the binary's parameters. The tail effect is essentially due to the propagation of gravitational radiation on the curved background spacetime generated by its own source. More specifically, the tail of the radiation results, at lowest order, from the nonlinear interaction between the time-varying quadrupole moment of the source (which generates the linear radiation) and its monopole moment, or total mass-energy M (which generates the background). The tail radiation has the distinctive property ("nonlocality" in time) of depending on the source's dynamics at arbitrary remote instants in the past, anterior to the simply retarded time t — r/c. This reflects the fact that gravity propagates not only on the light cone (direct propagation with the speed of light c), but also within the light cone (averaged propagation with all velocities less than c). (See [6] for references on tails and related nonlinear effects. ) The detection of the tail effect (or of effects immediately related to it) in future gravitational-wave experiments will provide direct evidence that gravity propagates on a curved space-time — that generated by its own source. (Note that indirect evidence from the observations of the binary pulsar is probably out of reach [6].) This will represent an interesting test of the nonlinearity of general relativity in the "gravitodynamics" regime of the theory, involving rapidly varying and strong gravitational fields. This will also provide an independent measurement of the total mass-energy M of the source. The tail effect arises at the so called 1 5 postNewtonian (1.5-PN) approximation in the radiation, i.e., at the relative order c 3 beyond the usual quadrupole radiation. Let us consider the radiation emitted by a general isolated source, at a large distance r from the source (neglecting terms that die out like 1/r~). More precisely, we denote by h(t) that linear combination of the components of the wave which is directly felt by some detector [e.g. , h(t) is the relative variation of the arm's length of a laser interferometric detector]. Then the expression of h(t), including all terms in the post-Newtonian expansion up to the order c, can be written [7] as