引力波官方论文中英对照【机器翻译】.doc

Observation of GravitationalWaves from a Binary Black Hole MergerThe LIGO Scientific Collaboration and The Virgo CollaborationOn September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer GravitationalwaveObservatory (LIGO) simultaneously observed a transient gravitational-wave signal. The signalsweeps upwards in frequency from 35 Hz to 250 Hz with a peak gravitational-wave strain of 1:0 _ 1021.It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holesand 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 toa significance greater than 5:1 _. The source lies at a luminosity distance of 410+160180 Mpc correspondingto a redshift z = 0:09+0:030:04. In the source frame, the initial black hole masses are 36+54M_ and 29+44M_,and the final black hole mass is 62+44M_, with 3:0+0:50:5M_c2 radiated in gravitational waves. All uncertaintiesdefine 90% credible intervals. These observations demonstrate the existence of binary stellar-massblack hole systems. This is the first direct detection of gravitational waves and the first observation of abinary black hole merger.PACS numbers: 04.80.Nn, 04.25.dg, 95.85.Sz, 97.80.-dIntroduction In 1916, the year after the final formulationof the field equations of general relativity, Albert Einsteinpredicted the existence of gravitational waves. Hefound that the linearized weak-field equations had wavesolutions: transverse waves of spatial strain that travel atthe speed of light, generated by time variations of the massquadrupole moment of the source 1, 2. Einstein understood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250赫兹以1:0 _ 1021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 0:090:04。在源框架，初始黑洞群众36 + 54m_和29 + 44m_，而最终黑洞质量为6244m_，以3:0 + 0:50:5m_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，所产生的时间变化的质量四极矩的来源 1，2 。爱因斯坦明白that gravitational-wave amplitudes would be remarkablysmall; moreover, until the Chapel Hill conference in1957 there was significant debate about the physical realityof gravitational waves 3.Also in 1916, Schwarzschild published a solution for thefield equations 4 that was later understood to describe ablack hole 5, 6, and in 1963 Kerr generalized the solutionto rotating black holes 7. Starting in the 1970s theoreticalwork led to the understanding of black hole quasinormalmodes 810, and in the 1990s higher-order post-Newtonian calculations 11 preceded extensive analyticalstudies of relativistic two-body dynamics 12, 13. In thepast decade these analytical advances, together with breakthroughsin numerical relativity 1416, have enabled accuratesimulations of binary black hole mergers. Whilenumerous black hole candidates have now been identifiedthrough electromagnetic observations 1719, black holemergers have not previously been observed.The discovery of the binary pulsar systemPSR B1913+16 by Hulse and Taylor 20 and subsequentobservations of its energy loss by Taylor andWeisberg 21 demonstrated the existence of gravitationalwaves. This discovery, along with emerging astrophysicalunderstanding 22, led to the recognition that direct observationsof the amplitude and phase of gravitational waveswould enable studies of additional relativistic systems andprovide new tests of general relativity, especially in thedynamic strong-field regime.Experiments to detect gravitational waves began withWeber and his resonant mass detectors in the 1960s 23,followed by an international network of cryogenic resonantdetectors 24. Interferometric detectors were firstsuggested in the early 1960s 25 and the 1970s 26. Astudy of the noise and performance of such detectors 27,这种引力波的振幅将非常明显小；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 improve them 28, led to proposalsfor long-baseline broadband laser interferometers withthe potential for significantly increased sensitivity 2932.By the early 2000s, a set of initial detectors was completed,including TAMA300 in Japan, GEO600 in Germany,the Laser Interferometer Gravitational-wave Observatory(LIGO) in the United States, and Virgo in Italy.Combinations of these detectors made joint observationsfrom 2002 through 2011, setting upper limits on a varietyof gravitational-wave sources while evolving into a globalnetwork. In 2015 Advanced LIGO became the first of asignificantly more sensitive network of advanced detectorsto begin observations 3336.A century after the fundamental predictions of Einsteinand Schwarzschild, we report the first direct detection ofgravitational waves and the first direct observation of a binaryblack hole system merging to form a single black hole.Our observations provide unique access to the propertiesof space-time in the strong-field, high velocity regime andconfirm predictions of general relativity for the nonlineardynamics of highly disturbed black holes.Observation On September 14, 2015 at 09:50:45 UTCthe LIGO Hanford, WA, and Livingston, LA, observatoriesdetected the coincident signal GW150914 shown inFig. 1. The initial detection was made by low-latencysearches for generic gravitational wave transients 41 andwas reported within three minutes of data acquisition 43.Subsequently, matched-filter analyses that use relativisticmodels of compact binary waveforms 44, 45 recoveredGW150914 as the most significant event from each detectorfor the observations reported here. Occuring within the10 ms inter-site propagation time, the events have a combinedsignal-to-noise ratio (SNR) of 24.LIGO-P150914-v13和进一步的概念，以提高他们 28 ，导致建议长基线宽带激光干涉仪潜在的显着增加的敏感性 29，32 。在本世纪初，一组初始探测器完成，包括在日本的TAMA300，GEO600在德国，激光干涉引力波天文台（LIGO）在美国，意大利和处女座。这些探测器的组合进行联合观测从2002到2011，设定上限引力波的来源，同时发展成为一个全球性的网络。2015高级LIGO成为第一先进探测器的更灵敏的网络开始观察 33，36 。一个世纪后，爱因斯坦的基本预测和史瓦西，我们报告的第一个直接的检测引力波和二元的直接观测黑洞系统合并形成一个黑洞。我们的观察提供了独特的访问属性在强场，高速度的制度和确定非线性广义相对论的预测高度不安的黑洞动力学。在09:50:45 UTC 2015年9月14日观测LIGO汉福德，WA，和利文斯顿，La，天文台检测到的信号gw150914表现一致图1。初始检测是由低延迟搜索一般的引力波瞬变 41 和据报道，三分钟内的数据采集 43 。随后，匹配滤波器的分析，使用相对论紧凑的二进制波形模型 44，45 恢复gw150914从每个探测器的最重大的事件这里的观测报告。发生在10毫秒站点间的传播时间，事件有一个组合信噪比（信噪比）为24。ligo-p150914-v13-1.0-0.50.00.51.0H1 observedL1 observedH1 observed (shifted, inverted)Hanford, Washington (H1) Livingston, Louisiana (L1)-1.0-0.50.00.51.0Strain (10 21)Numerical relativityReconstructed (wavelet)Reconstructed (template)Numerical relativityReconstructed (wavelet)Reconstructed (template)-0.50.00.5Residual Residual0.30 0.35 0.40 0.45Time (s)3264128256512Frequency (Hz)0.30 0.35 0.40 0.4510.5零零点五一H1的观察L1观察H1观察（移，倒）恒福利文斯顿，华盛顿（H1），路易斯安那（L1）10.5零零点五一应变（21 - 10）数值相对论重构（小波）重构（模板）数值相对论重构（小波）重构（模板）0.5零零点五残留残留0.35 0.40 0.45 0.30时间（秒）三十二六十四一百二十八二百五十六五百一十二频率（赫兹）0.35 0.40 0.45 0.30Time (s)02468Normalized amplitudeFIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1,right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time seriesare filtered with a 35350 Hz band-pass filter to suppress large fluctuations outside the detectors most sensitive frequency band, andband-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right:L1 strain. GW150914 arrived first at L1 and 6:9+0:50:4 ms later at H1; for a visual comparison the H1 data are also shown, shifted intime by this amount and inverted (to account for the detectors relative orientations). Second row: Gravitational-wave strain projectedonto each detector in the 35350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistentwith those recovered from GW150914 37, 38 confirmed to 99.9% by an independent calculation based on 15. Shaded areas show90% credible regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black holetemplate waveforms 39. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linearcombination of sine-Gaussian wavelets 40, 41. These reconstructions have a 94% overlap, as shown in 39. Third row: Residualsafter subtracting the filtered numerical relativity waveform from the filtered detector time series. Bottom row: A time-frequencyrepresentation 42 of the strain data, showing the signal frequency increasing over time.Only the LIGO detectors were observing at the time ofGW150914. The Virgo detector was being upgraded, and时间（秒）零二四六八归一化振幅图1。通过LIGO汉福德观测引力波事件gw150914（H1，左柱板）和利文斯顿（L1，右栏面板）探测器。时间是相对于2015年9月14日在09:50:45 UTC。用于可视化，所有时间序列被过滤的35个350赫兹的带通滤波器，以抑制大的波动以外的探测器的最敏感的频段，和带阻滤波器，以消除在图3谱图中所见的强谱线。后排，左：H1菌株。顶排，右边：L1菌株。gw150914先到达了L1和9 + 0:50:4 MS后来在H1；一个视觉比较的数据也显示，在转移时间通过这个量和反转（以帐户的探测器的相对方向）。第二行：引力波应变投影在35至350赫兹波段上的每个探测器。固体线显示一个参数一致的系统的数值相对性波形与那些从gw150914 38 37恢复，证实99.9%基于 15 独立计算。阴影区域显示独立波形重建的90%个可信区域。一个（暗灰色）模型的信号，使用二进制黑洞模板波形 39 。其他（浅灰色）不使用物理模型，而计算应变信号为线性正弦-高斯小波的组合 40，41 。这些重建有94%个重叠，如图39所示。第三行：残差减去滤波后的数值相对论波形的滤波检测器的时间序列。底部行：时频表示 42 的应变数据，示出的信号频率随着时间的推移而增加。只有LIGO探测器观测时gw150914。处女座的探测器正在升级GEO600, though not sensitive enough to have detected thisevent, was operating but not in observational mode. Withonly two detectors the source position is primarily determinedby the relative arrival time and localized to an areaof approximately 600 deg2 (90% credible region) 39, 46.The basic features of GW150914 point to it being producedby the coalescence of two black holesi.e., theirorbital inspiral and merger, and subsequent final black holeringdown. Over 0:2 s, the signal increases in frequencyand amplitude in about 8 cycles from 35 to 150 Hz wherethe amplitude reaches a maximum. The most plausible explanationfor this evolution is the inspiral of two orbiting2LIGO-P150914-v130.30 0.35 0.40 0.45Time (s)0.6Velocity (c)Black hole separationBlack hole relative velocity01234Separation (RS)-1.0-0.50.00.51.0GEO600，虽然没有检测到足够的敏感事件，正在运行，但不是在观察模式。随着只有2个探测器的源位置主要是确定相对到达时间和局部区域约600 deg2（90%可信区间） 39，46 。对gw150914点的基本特征，它产生由两个黑洞即聚结，他们轨道inspiral和合并，以及随后的最后的黑洞振铃。在0:2的频率信号的增加和幅度在约8个周期从35到150赫兹的地方振幅达到最大值。最可信的解释这种演变是两轨道的灵感二ligo-p150914-v130.35 0.40 0.45 0.30时间（秒）零点三零点四零点五零点六速度（丙）黑洞分离黑洞相对速度零一二三四分离（卢比）10.5零零点五一Strain (10 21)Inspiral Merger RingdownNumerical relativityReconstructed (template)FIG. 2. Top: Estimated gravitational-wave strain amplitudefrom GW150914 projected onto H1. This shows the full bandwidthof the waveforms, without the filtering used for Fig. 1.The inset images show numerical-relativity models of the blackhole horizons as the black holes coalesce. Bottom: The Keplerianeffective black hole separation in units of Schwarzschildradii (RS = 2GM=c2) and the effective relative velocity givenby the post-Newtonian parameter v=c = (GM_f=c3)1=3, wheref is the gravitational-wave frequency calculated with numericalrelativity and M is the total mass (value from Table I).masses, m1 and m2, due to gravitational-wave emission.At the lower frequencies, such evolution is characterizedby the chirp mass 47M=(m1m2)3=5(m1 + m2)1=5 =c3G_596_8=3f11=3f_3=5;where f and f_ are the observed frequency and its timederivative and G and c are the gravitational constant andspeed of light. Estimating f and f_ from the data in Fig. 1we obtain a chirp mass ofM 30M_, implying that thetotal mass M = m1 + m2 is _70M_ in the detector应变（21 - 10）灵感合并振铃数值相对论重构（模板）图2。顶：估计引力波振幅从gw150914投射到H1。这显示了全带宽的波形，没有用于图1的过滤。嵌入图像显示黑色的数值相对论模型孔的视野为黑洞合并。底部：开普勒在史瓦西黑洞的单位有效分离半径（RS = 2GM = C2）和有效相对速度给定采用后牛顿参数V = C =（gm_f = 1 = 3，其中C3）用数值计算的引力波频率相对和我是总的质量（从表我的价值）。群众，M1和M2，由于引力波辐射。在较低的频率，这样的演变特征由线性调频质量 47 米=（m2）3 = 5（M1 + M2）1 = 5 =C3G_五九十六_8 = 11 = 3f_ 3F_3 = 5；其中F和f_是所观察到的频率和时间衍生工具和克和碳是引力常数和光的速度。从图1中的数据估计F和f_我们得到一个线性调频质量间的30m_，暗示总质量M = M1 + M2 _在探测器70m_frame. This bounds the sum of the Schwarzschild radii ofthe binary components to 2GM=c2 _210 km. To reachan orbital frequency of 75 Hz (half the gravitational-wavefrequency) the objects must have been very close and verycompact; equal Newtonian point masses orbiting at this frequencywould be only 350 km apart. A pair of neutronstars, while compact, would not have the required mass,while a black hole-neutron star binary with the deducedchirp mass would have a very large total mass, and wouldthus merge at much lower frequency. This leaves blackholes as the only known objects compact enough to reachan orbital frequency of 75 Hz without contact. Furthermore,the decay of the waveform after it peaks is consistentwith the damped oscillations of a black hole relaxingto a final stationary Kerr configuration. Below, we presenta general-relativistic analysis of GW150914; Fig. 2 showsthe calculated waveform using the resulting source parameters.DetectorsGravitational-wave astronomy exploits multiple,widely separated detectors to distinguish gravitationalwaves from local instrumental and environmental noise, toprovide source sky localization, and to measure wave polarizations.The LIGO sites each operate a single AdvancedLIGO detector 33, a modified Michelson interferometer(see Fig. 3) that measures gravitational-wave strain as adifference in length of its orthogonal arms. Each arm isformed by two mirrors, acting as test masses, separated byLx = Ly = L = 4 km. A passing gravitational wave effectivelyalters the arm lengths such that the measured differenceis _L(t) = _Lx _Ly = h(t)L, where h is thegravitational-wave strain amplitude projected onto the detector.This differential length variation alters the phase differencebetween the two light fields returning to the beamsplitter,transmitting an optical signal proportional to the帧。这个边界的史瓦西半径的总和以绿肥= C2_二进制组件210公里。到达75赫兹（半引力波的一半的轨道频率频率）的对象必须是非常接近和非常在这个频率下绕轨道运行的紧凑型将只“350公里外。一对中子星星，虽然致密，不会有所需的质量，黑洞中子星双星与推导出线性调频质量将有一个非常大的总质量，并将因此，合并在低得多的频率。这片树叶黑色孔作为唯一已知的对象，结构紧凑，足以达到没有接触的75赫兹的轨道频率。此外，波形峰后的衰减是一致的随着阻尼振荡的黑洞放松到最后静止的克尔配置。下面，我们提出一个gw150914广义相对论分析；如图2所示。使用所得的源参数计算出的波形。探测引力波天文学利用多个，广泛分离的探测器来区分引力波从当地的仪器和环境噪声，到天空提供源定位，并测量波的极化。LIGO网站每运行一个单一的先进LIGO探测器 33 ，一种改进的迈克尔逊干涉仪（见图3），测量引力波的应变正交臂长度差。每只手臂由双反射镜形成的，作为测试群众，由LX =，= L = 4公里。有效地传递引力波改变臂的长度，使得测量的差异是_l（t）= _lx_ly = h（t），其中h是将引力波应变振幅投射到探测器上。这种差分长度的变化，改变相位差两光场回到分束器之间，发送光信号与所gravitational-wave strain to the output photodetector.To achieve sufficient sensitivity to measure gravitationalwaves the detectors include several enhancements to thebasic Michelson interferometer. First, each arm containsa resonant optical cavity, formed by its two test mass mirrors,that multiplies the effect of a gravitational wave onthe light phase by a factor of 300 49. Second, a partiallytransmissive power-recycling mirror at the input providesadditional resonant buildup of the laser light in the interferometeras a whole 50, 51: 20Wof laser input is increasedto 700W incident on the beamsplitter, which is further increasedto 100kW circulating in each arm cavity. Third,a partially transmissive signal-recycling mirror at the outputoptimizes the gravitational-wave signal extraction bybroadening the bandwidth of the arm cavities 52, 53.The interferometer is illuminated with a 1064-nm wavelengthNd:YAG laser, stabilized in amplitude, frequency,and beam geometry 54, 55. The gravitational-wave signalis extracted at the output port using homodyne readout56.These interferometry techniques are designed to maximizethe conversion of strain to optical signal, thereby minimizingthe impact of photon shot noise (the principal noiseat high frequencies). High strain sensitivity also requiresthat the test masses have low displacement noise, whichis achieved by isolating them from seismic noise (low frequencies)and designing them to have low thermal noise(mid frequencies). Each test mass is suspended as the finalstage of a quadruple pendulum system 57, supported byan active seismic isolation platform 58. These systemscollectively provide more than 10 orders of magnitude ofisolation from ground motion for freq