1、1引力波官方论文中英对照【机器翻译】10?5 10?4 10?3 10?2 10?1 100 101 102 Number of events ?/ / GW150914 Generic transient search Search Result (C3) Search Background (C3) Search Result (C2+C3) Search Background (C2+C3) 2x 3x 4x 5.1x 5.1x 2x 3x 4x 5.1x 5.1x 8 10 12 14 16 18 20 22 24 Detection statistic ?vc 10?8 10?7 1
2、0?6 10?5 10?4 10?3 10?2 10?1 100 101 102 Number of events GW150914 Binary coalescence search 210?5 10?4 10?3 10?2 10?1 一百 一百零一 一百零二 事件数 ?/ / gw150914 通用暂态搜索 搜索结果（C3） 研究背景（C3） 搜索结果（C2 + C3 ） 研究背景（C2 + C3） 2X 3X 4X 5.1倍 5.1 倍 2X 3X 4X 5.1 倍 5.1 倍 10 12 14 16 18 20 22 24 8 检测统计 ?VC 10?8 10?7 10?6 10?5
3、10?4 10?3 10?2 10?1 一百 一百零一 一百零二 事件数 gw150914 二元聚结 Search Result Search Background Background excluding GW150914 FIG. 4. Search results from the generic transient search (left) and the binary coalescence search (right). These histograms show the number of candidate events (orange markers) and the me
4、an number of background events (black lines) in the search class where GW150914 was found as a function of the search detection statistic and with a bin width of 0:2. The 搜索结果 搜索背景 背景 gw150914 除外 图 4。搜索结果从通用的瞬态搜索（左）和二元聚结搜索（右） 。这些直方图显示 3在搜索类中的候选事件（橙色标记）和背景事件的平均数（黑线） gw150914 发现作为一个搜索检测统计功能以 0:2 bin 宽
5、度。上面的鳞片给 scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background . The significance of GW150914 is greater than 5:1 _ and 4:6 _ for the binary coalescence and the generic transient searches, respectively. Left: Along with the pr
6、imary search (C3) we also show the results (blue markers) and background (green curve) for an alternative search that treats events independently of their frequency evolution (C2+C3). The classes C2 and C3 are defined in the text. Right: The tail in the blackline background of the binary coalescence
7、 search is due to random coincidences of GW150914 in one detector with noise in the other detector. (This type of event is practically absent in the generic transient search background because they do not pass the time-frequency 4consistency requirements used in that search.) The purple curve is the
8、 background excluding those coincidences, which is used to assess the significance of the second strongest event. subtracted from the data. The statistic _c thus quantifies the SNR of the event and the consistency of the data between the two detectors. Based on their time-frequency morphology, the e
9、vents are divided into three mutually exclusive search classes, as described in 41: events with time-frequency morphology of known populations of noise transients (class C1); events with frequency that increases with time (class C3); and all remaining events (class C2). Detected with _c = 20:0, GW15
10、0914 is the strongest 了 一种基于相应噪声背景的高斯标准偏差事件的意义。gw150914 的意义 大于 5:1 _和 4:6 _为二进制聚结和一般的瞬时搜索，分别。左：随着 元搜索引擎（C3）我们也显示结果（蓝色标记）和背景（绿色曲线）寻找替代治疗事件 独立的频率演变（C2 + C3 ） 。类 C2 和 C3 在文本的定义。5右：在黑色的尾巴 的二进制搜索的背景是一个检测器，并对 gw150914 随机的巧合由于与其他噪声 探测器。 （这种类型的事件实际上是不存在的，在一般的瞬态搜索背景，因为他们不通过时频 一致性要求用于搜索。 ）紫色曲线的背景排除巧合，这是用来评估 第
11、二个最强事件的意义。 从数据中减去。统计_c 从而量化 事件信噪比与数据的一致性 双检测器。 基于它们的时频形态学特征 分为三个相互排斥的搜索类，作为 描述在 41 ：事件与时间-频率形态 已知的瞬态噪声的人群（C1 类） ；事件 频率随时间增加（C3） ；和 剩余的事件（C2 类） 。 与_c = 20:0 的检测，gw150914 是最强的 event of the entire search. Consistent with its coalescence signal signature, it is found in the search class C3 of events wit
12、h increasing time-frequency evolution. Measured on a background equivalent to over 67 400 years of data and including a trials factor of 3 to account for the search classes, its false alarm rate is lower than 1 in 22 500 years. This corresponds to a probability The selection criteria that 6define th
13、e search class C3 reduce the background by introducing a constraint on the signal morphology. In order to illustrate the significance of GW150914 against a background of events with arbitrary shapes, we also show the results of a search that uses the same set of events as the one described above but
14、 without this constraint. Specifically we use only two search classes: the C1 class and the union of C2 and C3 classes (C2+C3). In this two-class search the GW150914 event is found in the C2+C3 class. The left panel of Fig. 4 shows the C2+C3 class results and background. In the background of this cl
15、ass there are four events with _c _ 32:1, yielding a false alarm rate for GW150914 of 1 in 8 400 years. This corresponds to a false alarm probability of 5 _ 10”,6 equivalent to 4:4 _. For robustness and validation, we also use other generic transient search algorithms 41. A different search 73 and a
16、 parameter estimation follow-up 74 detected GW150914 with consistent significance and signal parameters. Binary coalescence search This search targets gravitational-wave emission from binary systems with 7individual masses from 1M_ to 99M_, total mass less than 100M_ and dimensionless spins up to 0.
17、99 45. To model systems with total mass larger than 4M_, we use 事件的整个搜索。与它的合并 信号，它是在事件的搜索类 C3 发现 随着时频演化。测量的 背景相当于 400 年以上 67 年的数据 一个 3 到搜索类的实验因子， 其误报率低于 22，500 年 1。这 对应于概率小于 2 _ 10”,6 观察 以上的噪声事件 gw150914 强在 分析时间，相当于 6 _。图 4 左面板 显示 C3 类结果和背景。 定义搜索类 C3 的选择标准降低 背景通过引入一个约束的信号 形态。为了说明的意义 对一个事件的 gw150914
18、任意背景 形状，我们也显示搜索的结果，使用 同一组事件，正如上面所描述的那样 这个约束。具体地说，我们只使用 2 个搜索类：C1 级和C2 和 C3 类联盟（C2 + C3） 。 在这两类搜索发现是gw150914 事件 C2 + C3 类。图 4 左面板显示 C2 + C3 班级成绩及背景。在此背景下 班上有四个事件与_c _ 32:1，产生一个错误 在 8 个 400年的 1 gw150914 报警率。这相当于到 5 _ 10”,6 等效虚警概率 来 4:4 _。 8对于鲁棒性和验证，我们也使用其他通用 瞬态搜索算法 41 。不同的搜索 73 和一个参数估计后续行动 74 gw150914
19、 一致的意义和信号参数。 二进制合并搜索-搜索目标 二元系统的引力波发射 从 1m_到 99m_群众，总质量小于 100m_和无量纲转动了 0.99 45 。以 总质量大于 4m_模型系统，我们使用 the effective-one-body (EOB) formalism 75, which combines results from the Post-Newtonian approach 11, 76 with results from black hole perturbation theory and numerical relativity. The waveform model
20、77, 78 assumes that the spins of the merging objects are aligned with the orbital angular momentum, but the resulting templates can 6 LIGO-P150914-v13 nonetheless effectively recover systems with misaligned spins in the parameter region of GW150914 45. Approximately 250,000 template waveforms are us
21、ed to cover this parameter space. The search calculates the matched-filter signal-to-noise ratio _(t) for each template in each detector and identifies 9maxima of _(t) with respect to the time of arrival of the signal 7981. For each maximum we calculate a chi-squared statistic _2r to test whether th
22、e data in several different frequency bands are consistent with the matching template 82. Values of _2r near unity indicate that the signal is consistent wit. To produce background data for this search the SNR maxima of one detector are time-shifted and a new set of 有效单体（EOB）形式 75 ，它结合 后牛顿法的结果 76，11
23、 从黑洞的扰动理论和数值计算结果 相对论。波形模型 77，78 假设 合并对象的旋转与该 轨道角动量，但由此产生的模板可以 六 ligo-p150914-v13 this procedure _ 107 times produces a noise background analysis time equivalent to 608 000 years. To account for the search background noise varying across the target signal space, candidate and background events are di
24、vided into three seced on its false alarm rate. Across the three search classes this bound is 1 in 203 000 yrs. This translates to a false alarm probability A second, independent matched-filter analysis that uses a different 10method for estimating the significance of its events 85, 86, also detecte
25、d GW150914 with identical signal parameters and consistent significance. When an event is confidently identified as a real gravitational wave signal, as for GW150914, the background used to determine the significance of other events is reestimated without the contribution of this event. This is the
26、background distribution shown as a purple line in the right panel of Fig. 4. Based on this, the second most significant event has a false alarm rate of 1 per 2.3 years and corresponding Poissonian false alarm probability of 0.02. Waveform analysis of this event indicates that if it is astrophysical
27、in origin it is also a binary black hole 45. Source discussion The matched filter search is optimized for detecting signals, but it provides only approximate estimates of the source parameters. To refine them we use general relativity-based models 77, 78, 89, 90, some of which include spin precessio
28、n, and for each model perform a coherent Bayesian analysis to derive posterior dis- TABLE I. Source parameters for GW150914. We report median 计算重合事件。重复这个过程 _ 107 次产生的背景噪声11分析 相当于 000 年 608 年。 为搜索背景噪声变化 在目标信号空间，候选人和背景 事件被分为三个搜索类基于模板 长度。图 4 的右边面板显示了背景 为 gw150914献。这是 背景分布显示为紫色线在 图 4 右面板。基于此，二最重要 事件的误报率
29、为 1 每2.3 年和 相应的泊松虚警概率 0.02。 这一事件波形的分析表明，如果是天体物理学 它也是一个二进制黑洞 45 。 源讨论- 匹配滤波器搜索优化 用于检测信号，但它仅提供近似 源参数估计。来完善他们 使用广义相对论为基础的模型 77，78，89，90 ，一些其中包括旋进，并为每个模型执行 一个连贯的贝叶斯分析，以获得后验分布 表一gw150914 源参数。我们报告中位 百度搜索“就爱阅读”,专业资料、生活学习,尽在就爱阅读网 ,您的在线图书馆! Observation of GravitationalWaves from a Binary Black Hole Merger Th
30、e LIGO Scientific Collaboration and The Virgo Collaboration On September 14, 2015 at 09:50:45 UTC the two detectors 12of the Laser Interferometer Gravitationalwave Observatory (LIGO) simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 Hz to 2
31、50 Hz with a peak gravitational-wave strain of 1:0 _ 10”,21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black 从一个黑洞的合并 gravitationalwaves 观察 LIGO 科学合作和处女座的合作 在 09:50:45 UTC 两探测器的激光干涉引力波 2015 年 9月 14 日 天文台（LIGO）同时观察到一个短暂的引力波信号。信号 把以上的频率从 35 赫兹到 25
32、0 赫兹以 1:0 _ 10”,21 峰引力波应变。 它与波形的灵感和一对广义相对论所预言的黑洞合并 holes and the ringdown of the resulting single black hole. The signal was observed with a matched filter signalto- noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to 13a significance greater t
33、han 5:1 _. The source lies at a luminosity distance of 410+160 “,180 Mpc corresponding to a redshift z = 0:09+0:03 “,0:04. In the source frame, the initial black hole masses are 36+5 “,4M_ and 29+4 “,4M_, and the final black hole mass is 62+4 “,4M_, with 3:0+0:5 “,0:5M_c2 radiated in gravitational w
34、aves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. PACS numbers: 04.80.Nn, 04.25.dg, 95.85.Sz
35、, 97.80.-d Introduction In 1916, the year after the final formulation of the field equations of general relativity, Albert Einstein predicted the existence of gravitational waves. He found that the linearized weak-field equations had wave solutions: transverse waves of spatial strain that travel at
36、the 14speed of light, generated by time variations of the mass quadrupole moment of the source 1, 2. Einstein understood 和由此产生的单一黑洞的响铃。一个匹配滤波器的信号，观察信号 噪音之比为 24 和假警报率估计为小于 1 事件每 000 203年，相当于 一个意义大于 5:1 _。源位于 160 + 410 的亮度距离 “,180 MPC 相应 一个红移 z = + 0:03 0:09 “,0:04。在源框架，初始黑洞群众 36 + 5 “,4m_和 29 + 4 “,4
37、m_， 而最终黑洞质量为 624 “,4m_，以 3:0 + 0:5 “,0:5m_c2 辐射引力波。所有不确定因素 定义 90%可信区间。这些观察表明存在的二进制恒星质量 黑洞系统。这是第一个直接探测引力波和第一个观察的 二元黑洞合并。 PACS 编号：04.80.nn，04.25.dg，95.85.sz ，D 97.80。 介绍-在 1916，年后的最后制定 广义相对论的场方程，爱因斯坦艾伯特 预测引力波的存在。他 发现线性化的弱场方程有波 解决方案：横向波的空间应变，旅行 光的速度，所产生15的时间变化的质量 四极矩的来源 1，2 。爱因斯坦明白 that gravitational-w
38、ave amplitudes would be remarkably small; moreover, until the Chapel Hill conference in 1957 there was significant debate about the physical reality of gravitational waves 3. Also in 1916, Schwarzschild published a solution for the field equations 4 that was later understood to describe a black hole
39、 5, 6, and in 1963 Kerr generalized the solution to rotating black holes 7. Starting in the 1970s theoretical work led to the understanding of black hole quasinormal modes 810, and in the 1990s higher-order post- Newtonian calculations 11 preceded extensive analytical studies of relativistic two-bod
40、y dynamics 12, 13. In the past decade these analytical advances, together with breakthroughs in numerical relativity 1416, have enabled accurate simulations of binary black hole mergers. While numerous black hole candidates have now been identified through electromagnetic observations 1719, black ho
41、le mergers have not previously been observed. The discovery of the binary pulsar system PSR B1913+16 by Hulse and Taylor 20 and subsequent observations of its energy loss by Taylor and 16Weisberg 21 demonstrated the existence of gravitational waves. This discovery, along with emerging astrophysical
42、understanding 22, led to the recognition that direct observations of the amplitude and phase of gravitational waves would enable studies of additional relativistic systems and provide new tests of general relativity, especially in the dynamic strong-field regime. Experiments to detect gravitational
43、waves began with Weber and his resonant mass detectors in the 1960s 23, followed by an international network of cryogenic resonant detectors 24. Interferometric detectors were first suggested in the early 1960s 25 and the 1970s 26. A study of the noise and performance of such detectors 27, 这种引力波的振幅将
44、非常明显 小；而且，直到教堂山会议在 1957 关于物理现实的重大辩论 引力波 3 。 在 1916 出版的，史瓦西解 场方程 4 ，后来被理解为描述 黑洞 5，6 ，并在 1963 克尔广义的解决方案 旋转黑洞 7 。从 20 世纪 70 年代开始的理论 工作导致黑洞似的理解 模式 8，10 ，并在 20 世纪 90 年代高阶 牛顿计算 11 之前广泛的分析 17相对论双体动力学研究 12，13 。在 过去的十年中，这些分析的进步，与突破 在数值相对论 14，16 ，使精确 二元黑洞合并的模拟。而 现在已经确定了许多黑洞候选 通过电磁观测 17，19 ，黑洞 合并以前没有被观察到。 双星系统
45、的发现 PSR b1913 + 16 哈尔斯和泰勒 20 和随后的 泰勒对其能量损失的观测 韦斯伯格 21 证明引力的存在 波。这一发现，随着新兴天体物理学 理解 22 ，导致认识到直接观察 引力波的振幅和相位 将使额外的相对论系统的研究和 提供新的广义相对论，特别是在 动力强场。 探测引力波的实验开始了 在 20 世纪 60 年代，韦伯和他的共振质谱检测器 23 ， 其次是一个国际低温共振网络 探测器 24 。干涉探测器 建议在 20 世纪 60 年代初 25 和 20 世纪 70 年代 26 。一这种探测器的噪声和性能的研究 27 ， and further concepts to imp
46、rove them 28, led to proposals for long-baseline broadband laser interferometers with the potential for significantly increased sensitivity 2932. By the early 2000s, a set of initial detectors was completed, including TAMA300 in Japan, GEO600 in 18Germany, the Laser Interferometer Gravitational-wave
47、 Observatory (LIGO) in the United States, and Virgo in Italy. Combinations of these detectors made joint observations from 2002 through 2011, setting upper limits on a variety of gravitational-wave sources while evolving into a global network. In 2015 Advanced LIGO became the first of a significantl
48、y more sensitive network of advanced detectors to begin observations 3336. A century after the fundamental predictions of Einstein and Schwarzschild, we report the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging to form a single bl
49、ack hole. Our observations provide unique access to the properties of space-time in the strong-field, high velocity regime and confirm predictions of general relativity for the nonlinear dynamics of highly disturbed black holes. Observation On September 14, 2015 at 09:50:45 UTC the LIGO Hanford, WA, and Livingston, LA, observatories detected the coincident signal GW150914 shown in Fig. 1. The initial detection was made by low-latency se
