引力波官方論文中英對照【機器翻譯】.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從一個黑洞的合并gravitationalwaves觀察LIGO科學合作和處女座的合作在09:50:45 UTC兩探測器的激光干涉引力波2015年9月14日天文臺（LIGO）同時觀察到一個短暫的引力波信號。信號把以上的頻率從35赫茲到250赫茲以1:0 _ 1021峰引力波應變。它與波形的靈感和一對廣義相對論所預言的黑洞合并和由此產(chǎn)生的單一黑洞的響鈴。一個匹配濾波器的信號，觀察信號噪音之比為24和假警報率估計為小于1事件每000 203年，相當于一個意義大于5:1 _。源位于160 + 410的亮度距離180 MPC相應一個紅移z = + 0:03 0:090:04。在源框架，初始黑洞群眾36 + 54m_和29 + 44m_，而最終黑洞質量為6244m_，以3:0 + 0:50:5m_c2輻射引力波。所有不確定因素定義90%可信區(qū)間。這些觀察表明存在的二進制恒星質量黑洞系統(tǒng)。這是第一個直接探測引力波和第一個觀察的二元黑洞合并。PACS編號：04.80.nn，04.25.dg，95.85.sz，D 97.80。介紹-在1916，年后的最后制定廣義相對論的場方程，愛因斯坦艾伯特預測引力波的存在。他發(fā)現(xiàn)線性化的弱場方程有波解決方案：橫向波的空間應變，旅行光的速度，所產(chǎn)生的時間變化的質量四極矩的來源 1，2 。愛因斯坦明白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,這種引力波的振幅將非常明顯??；而且，直到教堂山會議在1957關于物理現(xiàn)實的重大辯論引力波 3 。在1916出版的，史瓦西解場方程 4 ，后來被理解為描述黑洞 5，6 ，并在1963克爾廣義的解決方案旋轉黑洞 7 。從20世紀70年代開始的理論工作導致黑洞似的理解模式 8，10 ，并在20世紀90年代高階牛頓計算 11 之前廣泛的分析相對論雙體動力學研究 12，13 。在過去的十年中，這些分析的進步，與突破在數(shù)值相對論 14，16 ，使精確二元黑洞合并的模擬。而現(xiàn)在已經(jīng)確定了許多黑洞候選通過電磁觀測 17，19 ，黑洞合并以前沒有被觀察到。雙星系統(tǒng)的發(fā)現(xiàn)PSR b1913 + 16哈爾斯和泰勒 20 和隨后的泰勒對其能量損失的觀測韋斯伯格 21 證明引力的存在波。這一發(fā)現(xiàn)，隨著新興天體物理學理解 22 ，導致認識到直接觀察引力波的振幅和相位將使額外的相對論系統(tǒng)的研究和提供新的廣義相對論，特別是在動力強場。探測引力波的實驗開始了在20世紀60年代，韋伯和他的共振質譜檢測器 23 ，其次是一個國際低溫共振網(wǎng)絡探測器 24 。干涉探測器建議在20世紀60年代初 25 和20世紀70年代 26 。一這種探測器的噪聲和性能的研究 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和進一步的概念，以提高他們 28 ，導致建議長基線寬帶激光干涉儀潛在的顯著增加的敏感性 29，32 。在本世紀初，一組初始探測器完成，包括在日本的TAMA300，GEO600在德國，激光干涉引力波天文臺（LIGO）在美國，意大利和處女座。這些探測器的組合進行聯(lián)合觀測從2002到2011，設定上限引力波的來源，同時發(fā)展成為一個全球性的網(wǎng)絡。2015高級LIGO成為第一先進探測器的更靈敏的網(wǎng)絡開始觀察 33，36 。一個世紀后，愛因斯坦的基本預測和史瓦西，我們報告的第一個直接的檢測引力波和二元的直接觀測黑洞系統(tǒng)合并形成一個黑洞。我們的觀察提供了獨特的訪問屬性在強場，高速度的制度和確定非線性廣義相對論的預測高度不安的黑洞動力學。在09:50:45 UTC 2015年9月14日觀測LIGO漢福德，WA，和利文斯頓，La，天文臺檢測到的信號gw150914表現(xiàn)一致圖1。初始檢測是由低延遲搜索一般的引力波瞬變 41 和據(jù)報道，三分鐘內(nèi)的數(shù)據(jù)采集 43 。隨后，匹配濾波器的分析，使用相對論緊湊的二進制波形模型 44，45 恢復gw150914從每個探測器的最重大的事件這里的觀測報告。發(fā)生在10毫秒站點間的傳播時間，事件有一個組合信噪比（信噪比）為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 0.4510.5零零點五一H1的觀察L1觀察H1觀察（移，倒）恒福利文斯頓，華盛頓（H1），路易斯安那（L1）10.5零零點五一應變（21 - 10）數(shù)值相對論重構（小波）重構（模板）數(shù)值相對論重構（小波）重構（模板）0.5零零點五殘留殘留0.35 0.40 0.45 0.30時間（秒）三十二六十四一百二十八二百五十六五百一十二頻率（赫茲）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時間（秒）零二四六八歸一化振幅圖1。通過LIGO漢福德觀測引力波事件gw150914（H1，左柱板）和利文斯頓（L1，右欄面板）探測器。時間是相對于2015年9月14日在09:50:45 UTC。用于可視化，所有時間序列被過濾的35個350赫茲的帶通濾波器，以抑制大的波動以外的探測器的最敏感的頻段，和帶阻濾波器，以消除在圖3譜圖中所見的強譜線。后排，左：H1菌株。頂排，右邊：L1菌株。gw150914先到達了L1和9 + 0:50:4 MS后來在H1；一個視覺比較的數(shù)據(jù)也顯示，在轉移時間通過這個量和反轉（以帳戶的探測器的相對方向）。第二行：引力波應變投影在35至350赫茲波段上的每個探測器。固體線顯示一個參數(shù)一致的系統(tǒng)的數(shù)值相對性波形與那些從gw150914 38 37恢復，證實99.9%基于 15 獨立計算。陰影區(qū)域顯示獨立波形重建的90%個可信區(qū)域。一個（暗灰色）模型的信號，使用二進制黑洞模板波形 39 。其他（淺灰色）不使用物理模型，而計算應變信號為線性正弦-高斯小波的組合 40，41 。這些重建有94%個重疊，如圖39所示。第三行：殘差減去濾波后的數(shù)值相對論波形的濾波檢測器的時間序列。底部行：時頻表示 42 的應變數(shù)據(jù)，示出的信號頻率隨著時間的推移而增加。只有LIGO探測器觀測時gw150914。處女座的探測器正在升級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，雖然沒有檢測到足夠的敏感事件，正在運行，但不是在觀察模式。隨著只有2個探測器的源位置主要是確定相對到達時間和局部區(qū)域約600 deg2（90%可信區(qū)間） 39，46 。對gw150914點的基本特征，它產(chǎn)生由兩個黑洞即聚結，他們軌道inspiral和合并，以及隨后的最后的黑洞振鈴。在0:2的頻率信號的增加和幅度在約8個周期從35到150赫茲的地方振幅達到最大值。最可信的解釋這種演變是兩軌道的靈感二ligo-p150914-v130.35 0.40 0.45 0.30時間（秒）零點三零點四零點五零點六速度（丙）黑洞分離黑洞相對速度零一二三四分離（盧比）10.5零零點五一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應變（21 - 10）靈感合并振鈴數(shù)值相對論重構（模板）圖2。頂：估計引力波振幅從gw150914投射到H1。這顯示了全帶寬的波形，沒有用于圖1的過濾。嵌入圖像顯示黑色的數(shù)值相對論模型孔的視野為黑洞合并。底部：開普勒在史瓦西黑洞的單位有效分離半徑（RS = 2GM = C2）和有效相對速度給定采用后牛頓參數(shù)V = C =（gm_f = 1 = 3，其中C3）用數(shù)值計算的引力波頻率相對和我是總的質量（從表我的價值）。群眾，M1和M2，由于引力波輻射。在較低的頻率，這樣的演變特征由線性調頻質量 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_是所觀察到的頻率和時間衍生工具和克和碳是引力常數(shù)和光的速度。從圖1中的數(shù)據(jù)估計F和f_我們得到一個線性調頻質量間的30m_，暗示總質量M = M1 + M2 _在探測器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幀。這個邊界的史瓦西半徑的總和以綠肥= C2_二進制組件210公里。到達75赫茲（半引力波的一半的軌道頻率頻率）的對象必須是非常接近和非常在這個頻率下繞軌道運行的緊湊型將只“350公里外。一對中子星星，雖然致密，不會有所需的質量，黑洞中子星雙星與推導出線性調頻質量將有一個非常大的總質量，并將因此，合并在低得多的頻率。這片樹葉黑色孔作為唯一已知的對象，結構緊湊，足以達到?jīng)]有接觸的75赫茲的軌道頻率。此外，波形峰后的衰減是一致的隨著阻尼振蕩的黑洞放松到最后靜止的克爾配置。下面，我們提出一個gw150914廣義相對論分析；如圖2所示。使用所得的源參數(shù)計算出的波形。探測引力波天文學利用多個，廣泛分離的探測器來區(qū)分引力波從當?shù)氐膬x器和環(huán)境噪聲，到天空提供源定位，并測量波的極化。LIGO網(wǎng)站每運行一個單一的先進LIGO探測器 33 ，一種改進的邁克爾遜干涉儀（見圖3），測量引力波的應變正交臂長度差。每只手臂由雙反射鏡形成的，作為測試群眾，由LX =，= L = 4公里。有效地傳遞引力波改變臂的長度，使得測量的差異是_l（t）= _lx_ly = h（t），其中h是將引力波應變振幅投射到探測器上。這種差分長度的變化，改變相位差兩光場回到分束器之間，發(fā)送光信號與所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