Discovery of Two Gravitationally Lensed Quasars with Image Separations of 3 Arcseconds from
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INTO THE UNIVERSE WITH STEPHEN HA WKING----TIME TRA VELHello! My name is Stephen Hawking 大家好我是史提芬·霍金Physicist, cosmologist, and something of a dreamer. 物理学家宇宙学家有时是个梦想家Although I cannot move and I have to speak through a computer. 虽然我行动不便说话需要电脑的帮助In my mind, I am free. 但我的思想是自由的Free to explore the universe 自由地探索宇宙And ask the big questions. 探究宇宙问题Such as is time travel possible? 例如:时间旅行是否可行Can we open a portal to the past? 如何开启通往过去之门Or find a shortcut to the future? 或找到前往未来的捷径Can we ultimately use the laws of nature. 最终我们是否可以T o become masters of time itself ? 利用大自然的法则操控时间呢Check it out.来解开这个谜与霍金一起了解宇宙Time travel was once considered scientific heresy. 时间旅行曾经被认为是科学的异端邪说I used to avoid talking about it 我一向都回避这个话题For fear of being labeled a crank. 避免被贴上狂想家的标签But these days, I'm not so cautious. 但这段日子我不再犹豫In fact, I'm more like the people who built Stonehenge. 事实上我更中情于建造巨石柱的人(英国Salisbury 平原上)I'm obsessed by time. 我被时间记录了If I had a time machine.. 如果我有台时间机器I'd visit Marilyn Monroe in her prime. 我可以拜访玛莉莲·梦露在她当红的时期Or drop in on Galileo, as he turned his telescope to the heavens. 拜访伽利略当他把望远镜指向宇宙Perhaps I'd even travel to the end of the universe 可能我还会到宇宙的尽头T o find out how our whole cosmic story ends. 揭开我们宇宙的全貌T o see how this might be possible 要验证我们的想法是否可行We need to look at time as physicists do 我们就要以物理学家的眼光去研究时间As the fourth dimension.也就是四维时空1It's not as hard as it sounds.四维时空并不难理解All physical objects, even me and my chair,所有的物体甚至是我和我的椅子Exist in three dimensions.都是三维的Everything has a width and a height and a length.任何物体都有宽·高·长But there is another kind of length 但还存在另一种维度A length in time. 即时间维度While a human may survive for 80 years,一个正常人可以活80岁These stones will last much longer...这堆石头可以存在更长时间For thousands of years. 可能是数千年And the solar system will last for billions of years.而太阳系则是数十亿年Everything has a length in time, as well as space.所有东西都在时间上有长度空间也一样Traveling in time 在时间中旅行Means traveling through this fourth dimension.意味着要穿梭四维的时空T o see what that means, let's do a bit of normal every day traveling just to get a feel for it.为更好地理解我们以日常旅行为例来直观体会一下思维空间的含义A fast car makes it a bit more fun.高速的车带来更多的乐趣Drive in a straight line, and you're traveling in one dimension.直走意味着穿过其中一维的空间T urn right or left, and you add the second dimension.左转或右转就增加了第二维空间Drive up or down a twisty mountain road, And that adds height.在弯曲的山路中爬上爬下带来高度的变化So that's traveling in all three dimensions.那样就在三维中穿梭了But how on Earth do we travel in time? 但我们怎样穿梭时间呢How do we find a path through the fourth dimension? 怎样才能找到第四维呢Let's indulge in a little science fiction for a moment.先让我们换一个话题来看一个科幻的假想Time-travel movies often feature a vast energy-hungry machine.关于时间旅行的电影通常有体积巨大超耗能的机器The machine creates a path through the fourth dimension机器创造出一条通往第四维的通道A tunnel through time.一条时间的隧道A time traveler, a brave一个时间的旅行者是勇敢者Perhaps foolhardy individual也许也算是准备踏入Prepared for who knows what, 未知空间的愚勇之士Steps into the time tunnel . 义无反顾迈入时间隧道2And emerges who knows when.在未知的时间再现The concept may be far-fetched,构想上可能大不相同And the reality may be very different than this,真实情况可能与此大相径庭But the idea itself is not so crazy.但这种想法本身并不疯狂Physicists have been thinking about tunnels in time, too,物理学家也一直为时间隧道绞尽脑汁But we covered it from a different angle.不过我们要从另一个角度来揭示这个问题We wonder if portals to the past or the future 我们不知道在自然法则允许的范围内Could ever be possible within the laws of nature.是否可能出现通往过去或者未来的大门As it turns out..事实上We think they are. 我们认为有可能What's more we' even given them a name... 甚至给他们命名Wormholes. “虫洞”The truth is the wormholes are all around us...事实上虫洞布满在我们身边Only they're too small to see. 只是它们细小得看不到Wormholes are very tiny. 虫洞非常微型They occur in nooks and crannies in space and time.虫洞存在于时空的每个角落(nooks and crannies)Y ou might find it a tough concept, but stay with me. 你可能难以理解但请继续看下去Nothing is flat or solid.没有东西是平坦的或者实心的If you look closely enough at anything, 如果靠得足够近看任何东西Y ou'll find holes and wrinkles in it. 你会发现小洞和裂痕无处不在It's a basic physical principle, 这是基本的物理法则And it even applies to time. 同样适用于时间T ake this pool table. 像这个桌球台The surface looks flat and smooth, but up close, 表面看起来又平坦又光滑但靠近来看it's actually anything but. 事实并非如此It's full of gaps and holes.满是缝和孔Even something as smooth as a pool ball. 就算是光滑得像台球Has tiny crevices, wrinkles, and voids. 也有细小的裂痕皱褶瑕疵Now, it's easy to show that this is true in the first three dimensions,在三维世界就容易说明这一点But, trust me, it's also true of the fourth dimension, as well.相信我在第四维同样是正确的3There are tiny crevices, wrinkles, and voids. In time. 时间中存在细小的裂痕皱褶瑕疵Down at the smallest of scale,在非常小的尺度Smaller even than molecules, 甚至比分子原子还微小smaller than atoms, we get to a place 我们所得到的called the quantum foam.我们把那一区域叫做量子泡沫(Quantum Foam)This is where wormholes exist.虫洞就存在于此Tiny tunnels, or shortcuts, through space and time穿越时空的微小隧道和捷径Constantly form, disappear, and reform Within this quantum world.在这个量子的世界里面不断地形成——消失——再形成And they actually link T wo separate places and two different times.连接两个独立地点和不同的时间Unfortunately, these real-life time tunnels are just a billion trillion trillionths of a centimeter across...很不幸这种时空的隧道只有10的-33次方厘米的大小(普朗克长度)Way too small for a human to pass through.不足以令人类可以通行But here's where the notion of wormhole time machines . Is leading.不过引出了虫洞型的时间机器的概念Some scientists think it may be possible to capture one and enlarge it many trillions of times有些科学家认为有可能抓住其中一个将之扩大数亿亿亿倍T o make it big enough for a human or even a spaceship to enter.使其足以通过一个人甚至一艘太空船Given enough power and advanced technology, 假设有足够的动力和超前的科技Perhaps a giant wormhole could even be constructed in space.或许可以在宇宙中制造出大虫洞I'm not saying it can be done, but if it could be, 我不保证可行但如果真的面世It would be a truly remarkable device. 它将是一个非常卓越的机器One end could be here near the Earth,一端在地球附近And the other far, far away, near some distant planet.另一端则在遥远的宇宙的深处Theoretically, a wormhole could do even more.理论上虫洞可以有更多的用途If both ends were in the same place .And separated by time instead of distance,如果虫洞的两个开口在相同的地点不同的时间A ship could fly in and come out still near the Earth,飞船可以穿越到地球形成之前的世界But in the distant past.一个遥远的过去Maybe dinosaurs would witness The ship coming in for a landing.或许恐龙们可以目睹飞船的降落Now , I realize that thinking in four dimensions is not easy现在我觉得四维时空的概念很难理解And that wormholes are a tricky concept to wrap your head around.虫洞的概念更加令人摸不着头脑But hang in there.不过再坚持一下I've thought up a simple experiment that could reveal if human time travel through a wormhole is possible now...4我曾构想出一种简单的实验验证人类是否可以通过虫洞穿越时间Or even in the future.甚至在遥远的未来I like simple experiments and champagne.我喜欢简单的实验和香槟So I've combined two of my favorite things T o see if time travel from the future to the past is possible所以我结合两样我喜欢的东西来验证从未来穿越到过去是否可行I'm throwing a party... 我搞了一个派对A welcome reception for future time travelers. 未来的时间旅行者的欢迎酒会But there's a twist. 不过有点小插曲I am not letting anyone know about it until after the party has happened.在派对结束前我不打算让任何人知道这事Here is the invitation, giving the exact coordinates in time and space.这就是那张请柬告知确切的时间和地点I am hoping a piece of it, in one form or another, 我希望其中的一张无论以何种形态will survive for many thousands of years. 能留存至数千年以后Maybe one day someone living in the future will find the information可能在未来的某一天有人可以看到这份请柬And use a wormhole time machine to come back to my party,用虫洞型的时间机器来参加我的派对Proving that time travel will one day be possible.证明时间旅行在未来可以实现My time-traveler guests could be arriving any moment now.我的穿越客人可能随时都会到Five Four Three T wo One 5...4...3...2 (1)What a shame很遗憾I was hoping a future miss universe was going to step through the door.我本希望有位未来的“环球小姐”前来光顾So, why didn't the experiment work? 那么为何这个实验不起效呢I think one of the reasons might be because of a well-known problem with time travel to the past...我想其中一个原因是众所周知穿越过去的问题The problem of paradoxes.即谬论的问题Paradoxes are fun to think about.谬论十分有趣祖父谬论:回到过去,在(外)祖父生你父母之前把他杀了\n因此你不能出生,更不能回到过去杀你的祖父。
中考英语经典科学实验与科学理论深度剖析阅读理解20题1<背景文章>Isaac Newton is one of the most famous scientists in history. He is known for his discovery of the law of universal gravitation. Newton was sitting under an apple tree when an apple fell on his head. This event led him to think about why objects fall to the ground. He began to wonder if there was a force that acted on all objects.Newton spent many years studying and thinking about this problem. He realized that the force that causes apples to fall to the ground is the same force that keeps the moon in orbit around the earth. He called this force gravity.The discovery of the law of universal gravitation had a huge impact on science. It helped explain many phenomena that had previously been mysteries. For example, it explained why planets orbit the sun and why objects fall to the ground.1. Newton was sitting under a(n) ___ tree when he had the idea of gravity.A. orangeB. appleC. pearD. banana答案:B。
Observation of Gravitational Waves from a Binary Black Hole MergerB.P.Abbott et al.*(LIGO Scientific Collaboration and Virgo Collaboration)(Received21January2016;published11February2016)On September14,2015at09:50:45UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal.The signal sweeps upwards in frequency from35to250Hz with a peak gravitational-wave strain of1.0×10−21.It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole.The signal was observed with a matched-filter signal-to-noise ratio of24and a false alarm rate estimated to be less than1event per203000years,equivalent to a significance greaterthan5.1σ.The source lies at a luminosity distance of410þ160−180Mpc corresponding to a redshift z¼0.09þ0.03−0.04.In the source frame,the initial black hole masses are36þ5−4M⊙and29þ4−4M⊙,and the final black hole mass is62þ4−4M⊙,with3.0þ0.5−0.5M⊙c2radiated in gravitational waves.All uncertainties define90%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.DOI:10.1103/PhysRevLett.116.061102I.INTRODUCTIONIn1916,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 the speed of light,generated by time variations of the mass quadrupole moment of the source[1,2].Einstein understood that gravitational-wave amplitudes would be remarkably small;moreover,until the Chapel Hill conference in 1957there was significant debate about the physical reality of gravitational waves[3].Also in1916,Schwarzschild published a solution for the field equations[4]that was later understood to describe a black hole[5,6],and in1963Kerr generalized the solution to rotating black holes[7].Starting in the1970s theoretical work led to the understanding of black hole quasinormal modes[8–10],and in the1990s higher-order post-Newtonian calculations[11]preceded extensive analytical studies of relativistic two-body dynamics[12,13].These advances,together with numerical relativity breakthroughs in the past decade[14–16],have enabled modeling of binary black hole mergers and accurate predictions of their gravitational waveforms.While numerous black hole candidates have now been identified through electromag-netic observations[17–19],black hole mergers have not previously been observed.The discovery of the binary pulsar system PSR B1913þ16 by Hulse and Taylor[20]and subsequent observations of its energy loss by Taylor and Weisberg[21]demonstrated the existence of gravitational waves.This discovery, along with emerging astrophysical 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 waves began with Weber and his resonant mass detectors in the1960s[23], followed by an international network of cryogenic reso-nant detectors[24].Interferometric detectors were first suggested in the early1960s[25]and the1970s[26].A study of the noise and performance of such detectors[27], and further concepts to improve them[28],led to proposals for long-baseline broadband laser interferome-ters with the potential for significantly increased sensi-tivity[29–32].By the early2000s,a set of initial detectors was completed,including TAMA300in Japan,GEO600 in Germany,the Laser Interferometer Gravitational-Wave Observatory(LIGO)in the United States,and Virgo in binations of these detectors made joint obser-vations from2002through2011,setting upper limits on a variety of gravitational-wave sources while evolving into a global network.In2015,Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations[33–36].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 black hole.Our observations provide unique access to the*Full author list given at the end of the article.Published by the American Physical Society under the terms of the Creative Commons Attribution3.0License.Further distri-bution of this work must maintain attribution to the author(s)and the published article’s title,journal citation,and DOI.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.II.OBSERVATIONOn September14,2015at09:50:45UTC,the LIGO Hanford,W A,and Livingston,LA,observatories detected the coincident signal GW150914shown in Fig.1.The initial detection was made by low-latency searches for generic gravitational-wave transients[41]and was reported within three minutes of data acquisition[43].Subsequently, matched-filter analyses that use relativistic models of com-pact binary waveforms[44]recovered GW150914as the most significant event from each detector for the observa-tions reported here.Occurring within the10-msintersite FIG.1.The gravitational-wave event GW150914observed by the LIGO Hanford(H1,left column panels)and Livingston(L1,rightcolumn panels)detectors.Times are shown relative to September14,2015at09:50:45UTC.For visualization,all time series are filtered with a35–350Hz bandpass filter to suppress large fluctuations outside the detectors’most sensitive frequency band,and band-reject filters to remove the strong instrumental spectral lines seen in the Fig.3spectra.Top row,left:H1strain.Top row,right:L1strain.GW150914arrived first at L1and6.9þ0.5−0.4ms later at H1;for a visual comparison,the H1data are also shown,shifted in time by this amount and inverted(to account for the detectors’relative orientations).Second row:Gravitational-wave strain projected onto each detector in the35–350Hz band.Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914[37,38]confirmed to99.9%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 hole template waveforms [39].The other(light gray)does not use an astrophysical model,but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets[40,41].These reconstructions have a94%overlap,as shown in[39].Third row:Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series.Bottom row:A time-frequency representation[42]of the strain data,showing the signal frequency increasing over time.propagation time,the events have a combined signal-to-noise ratio(SNR)of24[45].Only the LIGO detectors were observing at the time of GW150914.The Virgo detector was being upgraded, and GEO600,though not sufficiently sensitive to detect this event,was operating but not in observational mode.With only two detectors the source position is primarily determined by the relative arrival time and localized to an area of approximately600deg2(90% credible region)[39,46].The basic features of GW150914point to it being produced by the coalescence of two black holes—i.e., their orbital inspiral and merger,and subsequent final black hole ringdown.Over0.2s,the signal increases in frequency and amplitude in about8cycles from35to150Hz,where the amplitude reaches a maximum.The most plausible explanation for this evolution is the inspiral of two orbiting masses,m1and m2,due to gravitational-wave emission.At the lower frequencies,such evolution is characterized by the chirp mass[11]M¼ðm1m2Þ3=5121=5¼c3G596π−8=3f−11=3_f3=5;where f and_f are the observed frequency and its time derivative and G and c are the gravitational constant and speed of light.Estimating f and_f from the data in Fig.1, we obtain a chirp mass of M≃30M⊙,implying that the total mass M¼m1þm2is≳70M⊙in the detector frame. This bounds the sum of the Schwarzschild radii of thebinary components to2GM=c2≳210km.To reach an orbital frequency of75Hz(half the gravitational-wave frequency)the objects must have been very close and very compact;equal Newtonian point masses orbiting at this frequency would be only≃350km apart.A pair of neutron stars,while compact,would not have the required mass,while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency.This leaves black holes as the only known objects compact enough to reach an orbital frequency of75Hz without contact.Furthermore,the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration. Below,we present a general-relativistic analysis of GW150914;Fig.2shows the calculated waveform using the resulting source parameters.III.DETECTORSGravitational-wave astronomy exploits multiple,widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise,to provide source sky localization,and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector[33],a modified Michelson interferometer(see Fig.3)that measures gravitational-wave strain as a differ-ence in length of its orthogonal arms.Each arm is formed by two mirrors,acting as test masses,separated by L x¼L y¼L¼4km.A passing gravitational wave effec-tively alters the arm lengths such that the measured difference isΔLðtÞ¼δL x−δL y¼hðtÞL,where h is the gravitational-wave strain amplitude projected onto the detector.This differential length variation alters the phase difference between the two light fields returning to the beam splitter,transmitting an optical signal proportional to the gravitational-wave strain to the output photodetector. To achieve sufficient sensitivity to measure gravitational waves,the detectors include several enhancements to the basic Michelson interferometer.First,each arm contains a resonant optical cavity,formed by its two test mass mirrors, that multiplies the effect of a gravitational wave on the light phase by a factor of300[48].Second,a partially trans-missive power-recycling mirror at the input provides addi-tional resonant buildup of the laser light in the interferometer as a whole[49,50]:20W of laser input is increased to700W incident on the beam splitter,which is further increased to 100kW circulating in each arm cavity.Third,a partially transmissive signal-recycling mirror at the outputoptimizes FIG. 2.Top:Estimated gravitational-wave strain amplitude from GW150914projected onto H1.This shows the full bandwidth of the waveforms,without the filtering used for Fig.1. The inset images show numerical relativity models of the black hole horizons as the black holes coalesce.Bottom:The Keplerian effective black hole separation in units of Schwarzschild radii (R S¼2GM=c2)and the effective relative velocity given by the post-Newtonian parameter v=c¼ðGMπf=c3Þ1=3,where f is the gravitational-wave frequency calculated with numerical relativity and M is the total mass(value from Table I).the gravitational-wave signal extraction by broadening the bandwidth of the arm cavities [51,52].The interferometer is illuminated with a 1064-nm wavelength Nd:Y AG laser,stabilized in amplitude,frequency,and beam geometry [53,54].The gravitational-wave signal is extracted at the output port using a homodyne readout [55].These interferometry techniques are designed to maxi-mize the conversion of strain to optical signal,thereby minimizing the impact of photon shot noise (the principal noise at high frequencies).High strain sensitivity also requires that the test masses have low displacement noise,which is achieved by isolating them from seismic noise (low frequencies)and designing them to have low thermal noise (intermediate frequencies).Each test mass is suspended as the final stage of a quadruple-pendulum system [56],supported by an active seismic isolation platform [57].These systems collectively provide more than 10orders of magnitude of isolation from ground motion for frequen-cies above 10Hz.Thermal noise is minimized by using low-mechanical-loss materials in the test masses and their suspensions:the test masses are 40-kg fused silica substrates with low-loss dielectric optical coatings [58,59],and are suspended with fused silica fibers from the stage above [60].To minimize additional noise sources,all components other than the laser source are mounted on vibration isolation stages in ultrahigh vacuum.To reduce optical phase fluctuations caused by Rayleigh scattering,the pressure in the 1.2-m diameter tubes containing the arm-cavity beams is maintained below 1μPa.Servo controls are used to hold the arm cavities on resonance [61]and maintain proper alignment of the optical components [62].The detector output is calibrated in strain by measuring its response to test mass motion induced by photon pressure from a modulated calibration laser beam [63].The calibration is established to an uncertainty (1σ)of less than 10%in amplitude and 10degrees in phase,and is continuously monitored with calibration laser excitations at selected frequencies.Two alternative methods are used to validate the absolute calibration,one referenced to the main laser wavelength and the other to a radio-frequencyoscillator(a)FIG.3.Simplified diagram of an Advanced LIGO detector (not to scale).A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave;these length changes are reversed during the other half-cycle.The output photodetector records these differential cavity length variations.While a detector ’s directional response is maximal for this case,it is still significant for most other angles of incidence or polarizations (gravitational waves propagate freely through the Earth).Inset (a):Location and orientation of the LIGO detectors at Hanford,WA (H1)and Livingston,LA (L1).Inset (b):The instrument noise for each detector near the time of the signal detection;this is an amplitude spectral density,expressed in terms of equivalent gravitational-wave strain amplitude.The sensitivity is limited by photon shot noise at frequencies above 150Hz,and by a superposition of other noise sources at lower frequencies [47].Narrow-band features include calibration lines (33–38,330,and 1080Hz),vibrational modes of suspension fibers (500Hz and harmonics),and 60Hz electric power grid harmonics.[64].Additionally,the detector response to gravitational waves is tested by injecting simulated waveforms with the calibration laser.To monitor environmental disturbances and their influ-ence on the detectors,each observatory site is equipped with an array of sensors:seismometers,accelerometers, microphones,magnetometers,radio receivers,weather sensors,ac-power line monitors,and a cosmic-ray detector [65].Another∼105channels record the interferometer’s operating point and the state of the control systems.Data collection is synchronized to Global Positioning System (GPS)time to better than10μs[66].Timing accuracy is verified with an atomic clock and a secondary GPS receiver at each observatory site.In their most sensitive band,100–300Hz,the current LIGO detectors are3to5times more sensitive to strain than initial LIGO[67];at lower frequencies,the improvement is even greater,with more than ten times better sensitivity below60Hz.Because the detectors respond proportionally to gravitational-wave amplitude,at low redshift the volume of space to which they are sensitive increases as the cube of strain sensitivity.For binary black holes with masses similar to GW150914,the space-time volume surveyed by the observations reported here surpasses previous obser-vations by an order of magnitude[68].IV.DETECTOR VALIDATIONBoth detectors were in steady state operation for several hours around GW150914.All performance measures,in particular their average sensitivity and transient noise behavior,were typical of the full analysis period[69,70]. Exhaustive investigations of instrumental and environ-mental disturbances were performed,giving no evidence to suggest that GW150914could be an instrumental artifact [69].The detectors’susceptibility to environmental disturb-ances was quantified by measuring their response to spe-cially generated magnetic,radio-frequency,acoustic,and vibration excitations.These tests indicated that any external disturbance large enough to have caused the observed signal would have been clearly recorded by the array of environ-mental sensors.None of the environmental sensors recorded any disturbances that evolved in time and frequency like GW150914,and all environmental fluctuations during the second that contained GW150914were too small to account for more than6%of its strain amplitude.Special care was taken to search for long-range correlated disturbances that might produce nearly simultaneous signals at the two sites. No significant disturbances were found.The detector strain data exhibit non-Gaussian noise transients that arise from a variety of instrumental mecha-nisms.Many have distinct signatures,visible in auxiliary data channels that are not sensitive to gravitational waves; such instrumental transients are removed from our analyses [69].Any instrumental transients that remain in the data are accounted for in the estimated detector backgrounds described below.There is no evidence for instrumental transients that are temporally correlated between the two detectors.V.SEARCHESWe present the analysis of16days of coincident observations between the two LIGO detectors from September12to October20,2015.This is a subset of the data from Advanced LIGO’s first observational period that ended on January12,2016.GW150914is confidently detected by two different types of searches.One aims to recover signals from the coalescence of compact objects,using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals,with minimal assumptions about waveforms.These searches use independent methods,and their response to detector noise consists of different,uncorrelated,events. However,strong signals from binary black hole mergers are expected to be detected by both searches.Each search identifies candidate events that are detected at both observatories consistent with the intersite propa-gation time.Events are assigned a detection-statistic value that ranks their likelihood of being a gravitational-wave signal.The significance of a candidate event is determined by the search background—the rate at which detector noise produces events with a detection-statistic value equal to or higher than the candidate event.Estimating this back-ground is challenging for two reasons:the detector noise is nonstationary and non-Gaussian,so its properties must be empirically determined;and it is not possible to shield the detector from gravitational waves to directly measure a signal-free background.The specific procedure used to estimate the background is slightly different for the two searches,but both use a time-shift technique:the time stamps of one detector’s data are artificially shifted by an offset that is large compared to the intersite propagation time,and a new set of events is produced based on this time-shifted data set.For instrumental noise that is uncor-related between detectors this is an effective way to estimate the background.In this process a gravitational-wave signal in one detector may coincide with time-shifted noise transients in the other detector,thereby contributing to the background estimate.This leads to an overestimate of the noise background and therefore to a more conservative assessment of the significance of candidate events.The characteristics of non-Gaussian noise vary between different time-frequency regions.This means that the search backgrounds are not uniform across the space of signals being searched.To maximize sensitivity and provide a better estimate of event significance,the searches sort both their background estimates and their event candidates into differ-ent classes according to their time-frequency morphology. The significance of a candidate event is measured against the background of its class.To account for having searchedmultiple classes,this significance is decreased by a trials factor equal to the number of classes [71].A.Generic transient searchDesigned to operate without a specific waveform model,this search identifies coincident excess power in time-frequency representations of the detector strain data [43,72],for signal frequencies up to 1kHz and durations up to a few seconds.The search reconstructs signal waveforms consistent with a common gravitational-wave signal in both detectors using a multidetector maximum likelihood method.Each event is ranked according to the detection statistic ηc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2E c =ð1þE n =E c Þp ,where E c is the dimensionless coherent signal energy obtained by cross-correlating the two reconstructed waveforms,and E n is the dimensionless residual noise energy after the reconstructed signal is subtracted from the data.The statistic ηc thus quantifies the SNR of the event and the consistency of the data between the two detectors.Based on their time-frequency morphology,the events 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 ηc ¼20.0,GW150914is the strongest event of the entire search.Consistent with its coalescence signal signature,it is found in the search class C3of events with increasing time-frequency evolution.Measured on a background equivalent to over 67400years of data and including a trials factor of 3to account for the search classes,its false alarm rate is lower than 1in 22500years.This corresponds to a probability <2×10−6of observing one or more noise events as strong as GW150914during the analysis time,equivalent to 4.6σ.The left panel of Fig.4shows the C3class results and background.The selection criteria that define the search class C3reduce the background by introducing a constraint on the signal morphology.In order to illustrate the significance of GW150914against 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 without this constraint.Specifically,we use only two search classes:the C1class and the union of C2and C3classes (C 2þC 3).In this two-class search the GW150914event is found in the C 2þC 3class.The left panel of Fig.4shows the C 2þC 3class results and background.In the background of this class there are four events with ηc ≥32.1,yielding a false alarm rate for GW150914of 1in 8400years.This corresponds to a false alarm probability of 5×10−6equivalent to 4.4σ.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 mean number of background events (black lines)in the search class where GW150914was found as a function of the search detection statistic and with a bin width of 0.2.The scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background.The significance of GW150914is greater than 5.1σand 4.6σfor the binary coalescence and the generic transient searches,respectively.Left:Along with the primary 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 (C 2þC 3).The classes C2and C3are defined in the text.Right:The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914in 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 consistency requirements used in that search.)The purple curve is the background excluding those coincidences,which is used to assess the significance of the second strongest event.For robustness and validation,we also use other generic transient search algorithms[41].A different search[73]and a parameter estimation follow-up[74]detected GW150914 with consistent significance and signal parameters.B.Binary coalescence searchThis search targets gravitational-wave emission from binary systems with individual masses from1to99M⊙, total mass less than100M⊙,and dimensionless spins up to 0.99[44].To model systems with total mass larger than 4M⊙,we use the effective-one-body formalism[75],whichcombines results from the post-Newtonian approach [11,76]with results from black hole perturbation theory and numerical relativity.The waveform model[77,78] assumes that the spins of the merging objects are alignedwith the orbital angular momentum,but the resultingtemplates can,nonetheless,effectively recover systemswith misaligned spins in the parameter region ofGW150914[44].Approximately250000template wave-forms are used to cover this parameter space.The search calculates the matched-filter signal-to-noiseratioρðtÞfor each template in each detector and identifiesmaxima ofρðtÞwith respect to the time of arrival of the signal[79–81].For each maximum we calculate a chi-squared statisticχ2r to test whether the data in several differentfrequency bands are consistent with the matching template [82].Values ofχ2r near unity indicate that the signal is consistent with a coalescence.Ifχ2r is greater than unity,ρðtÞis reweighted asˆρ¼ρ=f½1þðχ2rÞ3 =2g1=6[83,84].The final step enforces coincidence between detectors by selectingevent pairs that occur within a15-ms window and come fromthe same template.The15-ms window is determined by the10-ms intersite propagation time plus5ms for uncertainty inarrival time of weak signals.We rank coincident events basedon the quadrature sumˆρc of theˆρfrom both detectors[45]. To produce background data for this search the SNR maxima of one detector are time shifted and a new set of coincident events is computed.Repeating this procedure ∼107times produces a noise background analysis time equivalent to608000years.To account for the search background noise varying acrossthe target signal space,candidate and background events aredivided into three search classes based on template length.The right panel of Fig.4shows the background for thesearch class of GW150914.The GW150914detection-statistic value ofˆρc¼23.6is larger than any background event,so only an upper bound can be placed on its false alarm rate.Across the three search classes this bound is1in 203000years.This translates to a false alarm probability <2×10−7,corresponding to5.1σ.A second,independent matched-filter analysis that uses adifferent method for estimating the significance of itsevents[85,86],also detected GW150914with identicalsignal parameters and consistent significance.When an event is confidently identified as a real gravitational-wave signal,as for GW150914,the back-ground used to determine the significance of other events is reestimated without the contribution of this event.This is the 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 of1per2.3years and corresponding Poissonian false alarm probability of0.02. Waveform analysis of this event indicates that if it is astrophysical in origin it is also a binary black hole merger[44].VI.SOURCE DISCUSSIONThe 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[77,78,87,88],some of which include spin precession,and for each model perform a coherent Bayesian analysis to derive posterior distributions of the source parameters[89].The initial and final masses, final spin,distance,and redshift of the source are shown in Table I.The spin of the primary black hole is constrained to be<0.7(90%credible interval)indicating it is not maximally spinning,while the spin of the secondary is only weakly constrained.These source parameters are discussed in detail in[39].The parameter uncertainties include statistical errors and systematic errors from averaging the results of different waveform models.Using the fits to numerical simulations of binary black hole mergers in[92,93],we provide estimates of the mass and spin of the final black hole,the total energy radiated in gravitational waves,and the peak gravitational-wave luminosity[39].The estimated total energy radiated in gravitational waves is3.0þ0.5−0.5M⊙c2.The system reached apeak gravitational-wave luminosity of3.6þ0.5−0.4×1056erg=s,equivalent to200þ30−20M⊙c2=s.Several analyses have been performed to determine whether or not GW150914is consistent with a binary TABLE I.Source parameters for GW150914.We report median values with90%credible intervals that include statistical errors,and systematic errors from averaging the results of different waveform models.Masses are given in the source frame;to convert to the detector frame multiply by(1þz) [90].The source redshift assumes standard cosmology[91]. Primary black hole mass36þ5−4M⊙Secondary black hole mass29þ4−4M⊙Final black hole mass62þ4−4M⊙Final black hole spin0.67þ0.05−0.07 Luminosity distance410þ160−180MpcSource redshift z0.09þ0.03−0.04。
Certainly! Here’s an essay exploring the conjectures about extraterrestrial civilizations, delving into the scientific, philosophical, and speculative aspects of the topic. Extraterrestrial Civilizations: The Great Beyond and Our Place in the CosmosThe universe, vast and ancient, stretches its arms across 93 billion light-years of observable space, containing billions of galaxies, each with billions of stars. Within this cosmic tapestry, the question of whether we are alone has captivated human minds for centuries. This essay explores the conjectures surrounding extraterrestrial civilizations, from the scientific theories to the speculative musings that fuel our imaginations.The Drake Equation: A Mathematical Framework for SpeculationAt the heart of the search for extraterrestrial intelligence (SETI) lies the Drake equation, formulated by astronomer Frank Drake in 1961. This mathematical framework attempts to estimate the number of active, communicative civilizations in the Milky Way galaxy. Variables include the rate of star formation, the fraction of stars with planetary systems, the number of planets capable of supporting life, the fraction of those planets where life actually emerges, the fraction of those life-bearing planets that develop intelligent life, the fraction of those that develop a civilization with technology, and the length of time such civilizations release detectable signals into space. While many of these variables remain unknown, the Drake equation serves as a tool for structured speculation and highlights the immense challenge in estimating the likelihood of extraterrestrial life.The Fermi Paradox: Where Are They?The Fermi paradox, named after physicist Enrico Fermi, poses a compelling question: Given the vastness of the universe and the high probability of habitable worlds, why have we not encountered any evidence of extraterrestrial civilizations? This paradox has led to numerous hypotheses. Perhaps civilizations tend to destroy themselves before achieving interstellar communication. Or, advanced civilizations might exist but choose to avoid contact with less developed species, adhering to a cosmic form of the “prime directive” seen in science fiction. Alternatively, the distances between stars could simply be too great for practical interstellar travel or communication, making detection exceedingly difficult.The Search for TechnosignaturesIn the quest for extraterrestrial intelligence, scientists have focused on detecting technosignatures—signs of technology that might indicate the presence of a civilization elsewhere in the universe. These include radio signals, laser pulses, or the dimming of stars due to megastructures like Dyson spheres. SETI projects, such as the Allen Telescope Array and Breakthrough Listen, scan the skies for anomalous signals that could be attributed to alien technology. While no definitive technosignatures have been found to date, the search continues, driven by advances in technology and a growing understanding of the cosmos.Astrobiology: Life Beyond EarthAstrobiology, the study of the origin, evolution, distribution, and future of life in the universe, offers insights into the conditions necessary for life. Research in astrobiology has revealed that life can thrive in extreme environments on Earth, suggesting that the conditions for life might be more widespread in the universe than previously thought. The discovery of exoplanets in the habitable zones of their stars, where liquid water can exist, increases the probability of finding environments suitable for life.Continued exploration of our solar system, particularly of Mars and the icy moons of Jupiter and Saturn, holds promise for uncovering signs of past or present microbial life. The Philosophical ImplicationsThe possibility of extraterrestrial civilizations raises profound philosophical questions about humanity’s place in the universe. Encountering another intelligence would force us to reevaluate our understanding of consciousness, culture, and ethics. It could lead to a new era of global unity as humanity comes together to face the challenges and opportunities of interstellar diplomacy. Conversely, it might also highlight our vulnerabilities and prompt introspection on our stewardship of the planet and our responsibilities as members of the cosmic community.Concluding ThoughtsWhile the existence of extraterrestrial civilizations remains a conjecture, the pursuit of answers has expanded our understanding of the universe and our place within it. The search for life beyond Earth is not just a scientific endeavor; it is a philosophical journey that challenges us to consider our origins, our destiny, and our role in the vast cosmic drama unfolding around us. Whether we find ourselves alone or part of a galactic community, the quest for knowledge about the universe and our place in it is one of humanity’s most enduring and inspiring pursuits.This essay explores various aspects of the conjectures surrounding extraterrestrial civilizations, from the scientific frameworks used to estimate their likelihood to the philosophical implications of their existence. If you have specific areas of interest within this broad topic, feel free to ask for further elaboration! If you have any further questions or need additional details on specific topics related to extraterrestrial life or astrobiology, please let me know!。
U n i t5A F e w K i n d W o r d f o r S u p e r s t i t i o n 引言中文译文本文“为迷信辩解一二”最初发表在1978年11月20日的《新闻周刊》上。
为了分析迷信这个复杂的话题,戴维斯将其作了分类,然后详细探讨了为何有人会相信法术和机缘。
尽管人们对他划分的四类迷信现象并不陌生,但是很少有人花费心思进行界定。
戴维斯理性地分析了许多人认为是个非理性的话题,对人性提出了一些非常有趣的看法。
1. 在我们当代有关“非理性复兴”的严肃讨论中,迷信并未对理性和科学形成严重挑战。
超心理学、不明飞行物、神奇治疗、超脱禅定法以及所有瞬间彻悟方式都遭人谴责,但是人们对迷信却只有一声哀叹。
难道这是因为我们当中许多人依然受制于它吗?虽然我们不公开承认。
2. 很少有人承认自己迷信,因为那意味着幼稚或愚昧。
但我生活在一个很大的大学里,发现在那些无疑是头脑理性、满腹经纶的学者中间,迷信仍以四种方式大行其道,香火旺盛。
3. 你不知道迷信有四种存在的方式吗?神学家使我们确信它们确实存在。
他们称第一种方式为镇邪压魔,如切忌在梯子下面行走等。
我看到一位知识渊博的人类学教授不小心弄撒了盐后,撮了点盐撒向自己的左肩膀后方。
当我问起他缘故时,他眼睛一眨,回答说那是“用来击中恶魔的眼睛。
”我没有继续问他有关恶魔的迷信,但我留意到在我问他之前,他脸上没有笑容。
4. 第二种是占卜,即求神问卦。
我认识的另一位渊博的教授对抛硬币解决问题(这是对命运之神谦卑的请求方式)嗤之以鼻,但有一回他却认真地告诉我,他通过拜读《易经》解决了一件本校的事务。
为什么不呢?这块大陆上有成千上万的人求助于《易经》,而他们普遍的知识水平很高,似乎不至于盲从迷信。
几乎如此,但并非完全如此。
令理性主义者难堪的,《易经》往往会给出绝佳的忠告。
5. 第三种是盲目崇拜,大学里面这种情况司空见惯,举不胜举。
你如果在大教室里当过监考,就会知道在课桌上放护符、幸运币等其他祈运物件的考生有多少。
斯蒂芬·霍金《时间简史》导言(中英文互译)斯蒂芬·威廉·霍金(Stephen William Hawking,1942—2018),英国著名物理学家,剑桥大学数学及理论物理学系教授,主要研究领域是宇宙论和黑洞,证明了广义相对论的奇性定理和黑洞面积定理,提出了黑洞蒸发理论和无边界的霍金宇宙模型。
1963年,霍金就被确诊患上肌肉萎缩性侧索硬化症(卢伽雷氏症),全身瘫痪,不能言语,手部只有三根手指可以活动。
代表作包括《时间简史》《果壳中的宇宙》《大设计》等。
Introduction to "A Brief History of Time"《时间简史》导言We go about our daily lives understanding almost nothing of the world. We give little thought to the machinery that generates the sunlight that makes life possible, to the gravity that glues us to an Earth that would otherwise send us spinning off into space, or to the atoms of which we are made and on whose stability we fundamentally depend. Except for children (who don't know enough not to ask the important questions), few of us spend much time wondering why nature is the way it is; where the cosmos came from, or whether it was always here; if time will one day flow backward and effects precede causes; or whether there are ultimate limits to what humans can know. There are even children, and I have met some of them, who want to know what a black hole looks like; what is the smallest piece of matter; why we remember the past and not the future;how it is, if there was chaos early, that there is, apparently, order today; and why there is a universe.我们在几乎对世界毫无了解的情形下进行日常生活。
课时提能练(十四)Ⅰ.阅读理解(2019·长沙测评)Scientists found gravitational waves as they watched the effects of two black holes running into each other and forming a much bigger one,a century after Albert Einstein predicted that such an event would send ripples(波纹) through space-time.Scientists“heard”the wave with the help of laser beams(激光束) sent through two pipes which form an angle of 90° between each other and are nearly 2,000 miles apart in the US.That equipment let them glimpse the nature of black holes.Together they made up the Laser Interferometer Gravitational-Wave Observatory(LIGO).Gravitational waves were first observed in September 2015 and the second detection(发现) occurred three months later.The third detection,which the astronomers calledGW170104,was made on January 4,2017.The astronomers believed their latestfinding“provides clues about the directions in which the black holes are spinning”.“Black holes are beautifully simple.You just need two numbers to describe them completely:mass,how much they bend space-time,and a spin,how much space-time moves about them,”said Dr. Christopher Berry of the University of Birmingham,one of the researchers in the project.“But it takes lots of hard work to measure these from our data.We now have wonderful mass measurements,and are starting to uncover details about the spins of these black holes,which could give evidence for how they formed.”The researchers said their discovery added further evidence to support Einstein's general theory of relativity and confirmed the existence of previously unknown black holes.More than 1,000 scientists from the LIGO Scientific Collaboration were involved in the project along with an additional 280 researchers from the European-based Virgo Collaboration.Scientists hope gravitational waves will offer a completely different view of the universe,allowing them to study events that might be hidden from traditional telescopes.“We have further confirmation of the existence of stellar(恒星的)-mass black holes that are larger than 20 solar masses.We didn't know they existed before LIGO detected them,”MIT researcher David Shoemaker said.【语篇解读】本文是一篇科普说明文。
标题:Exploring the Mysterious Universe - A Journey for the Curious MindIn the vast and infinite expanse of the universe, there lies a world of wonders and mysteries that have fascinated humans for generations. From the twinkling stars above us to the distant galaxies beyond imagination, the universe is a never-ending source of curiosity and exploration. Join me as we embark on a journey through this mysterious universe, discovering its secrets and wondering about its vastness. The universe is vast and beyond comprehension. It is estimated that there are over 200 billion galaxies in the universe, and each galaxy contains billions of stars. Just imagine the magnitude of it! It's like a vast ocean of stars, with our planet Earth being just a tiny speck inthis vast cosmos.One of the most fascinating aspects of the universe is the phenomenon of black holes. These mysterious objects have a strong gravitational pull that is so powerful that nothing, even light, can escape from them. Scientists are still trying to understand the properties and behavior ofblack holes, but what they have discovered so far is truly mind-boggling.Another remarkable feature of the universe is the beauty and diversity of galaxies. Galaxies like the Milky Way are vast collections of stars, dust, and gas that form patterns and shapes that are truly breathtaking. The swirling arms of galaxies and the bright centers filled with stars create a stunning visual display that is a testament to the beauty and complexity of the universe.But the universe is not just about beauty and mystery. It is also a place of discovery and learning. Astronomers and scientists use telescopes and advanced technology to observe and study the universe, trying to understand its origin, evolution, and future. Their findings have not only changed our understanding of the universe but have also led to new discoveries and advancements in science and technology.As we explore the universe, we also discover the potential for life beyond Earth. The existence of planets and solar systems similar to our own raises the question of whether there is other life in the universe. This questionhas fascinated humans for centuries, and the search for extraterrestrial life continues to be a major focus of space exploration.In conclusion, the universe is a vast and mysterious place that continues to inspire and fascinate humans. It is a never-ending source of discovery and learning, and as we continue to explore it, we discover more about ourselves and our place in the universe. So, let's keep our minds open to the wonders of the universe and continue to ask questions, explore, and discover.**宇宙探索的神秘之旅——好奇心的征途**在宇宙这片广阔无垠、深邃神秘的领域中,存在着无数令人着迷的奇迹。
1:cnn:The Higgs boson, or the "God particle," which was discovered last year, garnered two physicists the Nobel Prize in physics on Tuesday.Nearly 50 years ago, Francois Englert of Belgium and Peter Higgs of the United Kingdom had the foresight to predict that the particle existed.Now, the octogenarian pair share the Nobel Prize in physics in recognitionof a theoretical brilliance that was vindicated by the particle's discovery last year.The Royal Swedish Academy of Sciences awarded the prize to them.Higgs and Englert's theories behind the elusive Higgs boson explained what gives matter its mass.The universe is filled with Higgs bosons. As atoms and parts of atoms zoom around, they interact with and attract Higgs bosons, which cluster around them in varying numbers.Certain particles will attract larger clusters of Higgs bosons, and the more of them a particle attracts, the greater its mass will be.The explanation helped complete scientists' understanding of the nature of all matter."The awarded theory is a central part of the Standard Model of particle physics that describes how the world is constructed," the Royal Swedish Academy said in a post on Twitter.As is tradition, the academy phoned the scientists during the announcement to inform them of their win. They were unable to reach Higgs, for whom the particle is named.The conversation with Englert was short and sweet. "I feel very well, of course," he said, when he heard the news. "Now, I'm very happy.。
a rXiv:as tr o-ph/411250v215Dec24Discovery of Two Gravitationally Lensed Quasars with Image Separations of 3Arcseconds from the Sloan Digital Sky Survey Masamune Oguri,1,2Naohisa Inada,3Joseph F.Hennawi,1,4,5Gordon T.Richards,1David E.Johnston,1Joshua A.Frieman,6,7Bartosz Pindor,8Michael A.Strauss,1Robert J.Brunner,9Robert H.Becker,10,11Francisco J.Castander,12Michael D.Gregg,10,11Patrick B.Hall,13Hans-Walter Rix,14Donald P.Schneider,15Neta A.Bahcall,1Jonathan Brinkmann,16and Donald G.York 6,17ABSTRACT We report the discovery of two doubly-imaged quasars,SDSS J100128.61+502756.9and SDSS J120629.65+433217.6,at redshifts of 1.838and 1.789and with image sep-arations of 2.′′86and 2.′′90,respectively.The objects were selected as lens candidates from the Sloan Digital Sky Survey (SDSS).Based on the identical nature of the spectra of the two quasars in each pair and the identification of the lens galaxies,we concludethat the objects are gravitational lenses.The lenses are complicated;in both systemsthere are several galaxies in thefields very close to the quasars,in addition to the lensgalaxies themselves.The lens modeling implies that these nearby galaxies contributesignificantly to the lens potentials.On larger scales,we have detected an enhancementin the galaxy density near SDSS J100128.61+502756.9.The number of lenses withimage separation of∼3′′in the SDSS already exceeds the prediction of simple theoreti-cal models based on the standard Lambda-dominated cosmology and observed velocityfunction of galaxies.Subject headings:cosmology:observation—cosmology:theory—gravitational lens-ing—quasars:individual(SDSS J100128.61+502756.9)—quasars:individual(SDSSJ120629.65+433217.6)1.IntroductionIn strong gravitational lensing of quasars,the separations between multiple images,θ,is the most important observable linking observations to theory.Since the image separation is determined by the potential depth of the lens,the image separation distribution of lensed quasars offers a direct probe of the hierarchical structure of the universe.For instance,normal galaxies can produce strongly lensed quasars with image separations of∼1′′,while lenses with image separation>10′′can only be caused by clusters of galaxies.About70of∼1′′lenses are known to date1,and there is one example of a lensed quasar system in which the lens potential is dominated by that of dark matter(Inada et al.2003b;Oguri et al.2004a).Among gravitationally lensed quasars,those with intermediate image separations(3′′ θ 7′′)are of great interest because they represent a link between small-and large-separation lenses.In the standard modeling procedure used to predict the distribution of image separations,assuming isothermal profiles and an a priori velocity function of galaxies,lenses with image separations 3′′are very rare,because even the largest early type galaxies do not have Einstein radii this large. Thus the probability for∼7′′lensing is almost negligible.However,while Q0957+561(θ=6.′′26; Walsh,Carswell,&Weymann1979)is primarily lensed by a galaxy,the image separation is boosted by the cluster in which the lensing galaxy resides.This example implies that the environment of the lens galaxy may significantly affect the distribution of image separations in the3′′−7′′range (Keeton,Christlein,&Zabludoff2000;Martel,Premadi,&Matzner2002).In addition,a secondary mass along the line of sight could affect strong lensing(Wambsganss,Bode,&Ostriker2005),and this also may enhance the lensing probabilities in this image separation range.Finally,there is a predicted contribution in this range from clusters;simple theoretical models that include transitionof the property of lenses at∼1013M⊙(e.g.,Oguri2002)predict that large-separation lenses due to clusters begin to dominate the total lensing probability.Therefore,the overall lensing probability distribution forθ 3′′is predicted to depend on the interplay of these two effects;the environmental effects and the emergence of cluster lenses.However,the overall lensing probability atθ 3′′is quite small,thus a large number of quasars is needed to investigate the lensing probability distribution. Indeed,even the current largest homogeneous sample of lensed quasars(Myers et al.2003;Browne et al.2003)contains only one lens in this image separation range.In this paper,we present the discovery of two∼3′′gravitationally lensed quasars,SDSS J100128.61+502756.9(hereafter SDSS J1001+5027)and SDSS SDSS J120629.65+433217.6(here-after SDSS J1206+4332).These gravitational lenses were identified from an ongoing lens search using the data of the Sloan Digital Sky Survey(SDSS;York et al.2000;Stoughton et al.2002; Abazajian et al.2003,2004,2005).Currently the SDSS contains more than50,000spectroscopically classified quasars;thus the SDSS provides the opportunity to construct the largest homogeneous lens catalog in existence.Indeed,13new gravitationally lensed quasars have been found by using the SDSS(e.g.,Inada et al.2003a).In this paper,we describe photometric and spectroscopic observations of two new lens candidates and show that they are gravitational lenses.We model the lens systems and discuss the environments of the lens galaxies.We also compare the image separation distributions of lensed quasars in the SDSS(though still very preliminary because of the limited statistics)with a simple theoretical model.This paper is organized as follows.In§2,we briefly describe our method of searching for lens candidates from the SDSS data.Section3presents the results of both photometric and spectroscopic follow-up observations,and§4shows the result of lens modeling.Section5is devoted to a discussion of the environments of the lens galaxies.We also discuss the lensing probability distribution,which is shown in§6.We summarize our results in§7.2.Selecting Candidates from the SDSS dataAll gravitational lenses presented in this paper were selected as lens candidates from the SDSS, which is a survey to image104deg2of the sky.The SDSS also conducts spectroscopy of galaxies and quasars that are selected from the imaging data(Eisenstein et al.2001;Strauss et al.2002;Richards et al.2002;Blanton et al.2003).A dedicated2.5-meter telescope at Apache Point Observatory (APO)is equipped with a multi-CCD camera(Gunn et al.1998)withfive optical broad bands centered at3551,4686,6166,7480,and8932˚A(Fukugita et al.1996;Stoughton et al.2002).The imaging data are automatically reduced by the photometric pipeline(Lupton et al.2001).The astrometric positions are accurate to about0.′′1for sources brighter than r=20.5(Pier et al. 2003),and the photometric errors are typically less than0.03magnitude(Hogg et al.2001;Smith et al.2002;Ivezi´c et al.2004).The spectra cover3800–9200˚A at a resolution of1800–2100.We use spectroscopically classified quasars with z>0.6to search for gravitational lens candi-dates.SDSS J1001+5027and SDSS J1206+4332are identified as lens candidates by our standard candidate selection algorithm(N.Inada et al.,in preparation).This algorithm is based on the idea that the image of a quasar pair with a small separation appears to be more extended than that of single quasar,and characterizes the extent by the following SDSS image parameters:devL(the likelihood by an exponential disk),and star2IRAF is distributed by the National Optical Astronomy Observatories,which are operated by the Association of Universities for Research in Astronomy,Inc.,under cooperative agreement with the National Science Foundation.UH88images were calibrated by the standard star PG1528+062(Landolt1992).Astrometry and photometry of the UH88images are summarized in Table2.3.1.SDSS J1001+5027Spectra and images of this object are shown in Figures2and3,respectively.In Figure2, both components show C IV,C III],and Mg II emission lines redshifted by z=1.838.It is worth noting that theflux ratios(B/A)of the emission lines,particularly the C IV emission lines,are larger than that of the continuum;the equivalent widths of C IV emission lines are56˚A and76˚A for A and B,respectively.Such difference can be caused by the difference of the emission regions of continuum and broad emission lines combined with microlensing by stars.Wefind two extended objects near the quasar images(see Figure3;the image separation is2.′′86).When subtracting a quasar component,we used a nearby star as a point-spread function(PSF)template.The objects, denoted by G1and G2,have colors consistent with those of early-type galaxies at0.2 z 0.5 (Fukugita,Shimasaku,&Ichikawa1995).Since galaxy G1is nearly colinear with the two quasar components,it is likely that G1is the main contributor to the lens potential.However,galaxy G2 is also quite close to the lens system,and could affect the lens potential significantly.We note that component B could be reddened by the lens galaxy G1.3.2.SDSS J1206+4332The spectra of the two components shown in Figure4show Si IV,C IV,C III],and Mg II emission lines at the same wavelengths,which supports the idea that this is a gravitationally lensed quasar at z=1.789.However,theflux ratios(B/A)of the emission lines are slightly smaller than that of the continuum;the equivalent widths of C IV emission lines are69˚A and53˚A for A and B,respectively.The images in Figure5clearly reveal the lensing galaxy G1as well as two quasar components separated by2.′′90,further supporting the lensing hypothesis.We also found other galaxies G2and G3near component B.These galaxies,particularly G2,may contribute to the lens potential to some extent.Indeed,both G1and G2are quite red(see Table2)and are consistent with being high-redshift(z 0.7)early-type galaxies(Fukugita et al.1995),while G3 is blue and thus may be a chance superposition of a local galaxy.There is strong Mg II absorption (equivalent width>2˚A)at∼4900˚A in the spectrum of component B.The redshift of the absorber is z=0.748,consistent with the color of G1.Therefore the absorber may be associated with the lensing galaxy G1.4.Lens ModelingAlthough the lens systems appear quite complex,we willfirst attempt to model the lens systems with simple models.Specifically,we try models that describe G1by a Singular Isothermal Ellipsoid(SIE),or Singular Isothermal Sphere(SIS)plus external shear.Even these simple models, however,have eight parameters(the galaxy position x g and y g,the Einstein ring radius R E,the ellipticity e or shearγ,the position angleθe orθγ,the source position x s and y s,and theflux of the quasar f)that is equal to the number of observational constraints from the UH88imaging data (the image positions,the galaxy position,andfluxes of the images;see Table2).Thus there are no degrees of freedom and in usual cases we will be able tofind models that perfectly reproduce the observables.Tofit the models,we use standard lens modeling techniques as implemented in the lensmodel software(Keeton2001).SDSS J1001+5027is wellfitted by both the SIS plus shear and SIE models.The resulting fitting parameters are shown in Table3.The ellipticity e=0.25in the SIE model is similar to that of the light,though the position angleθe=10.9(measured East of North)is quite different from that of the light(∼−60◦)measured from the UH88image.In general the position angles of the light and lens models are aligned(Keeton,Kochanek,&Falco1998);therefore this result suggests that the externalfield,rather than the galaxy G1,is responsible for the quadrupole moment of the lens potential.The position angles in the models are rather close to the direction to G2.Since in general the position angle of external shear gives an idea of the direction to a main perturber,it seems that G2significantly affects the lens models.We also predict the time delay as∆t∼45h−1day(A leads B),assuming a lens redshift of z=0.3.Fitting SDSS J1206+4332by either SIS plus shear or SIE failed;the models yielded large chi-squaresχ2>2with no degrees of freedom,and the models required unnaturally large e orγ. We also tried a SIE plus shear model,but the resultingfit was similarly poor.This implies that the lens system is too complicated to be described by such simple models.Thus we add G2,which is modeled by a SIS,as well as galaxy G1modeled by SIE,in order to make the model more realistic. We derive best-fit models by changing the value of the Einstein radius of G2,R E(G2).Wefind that this“SIE+G2”modelfits the data well when R E(G2) 1′′,although the maximum value is slightly smaller than that inferred from the Faber-Jackson relation(R E(G2)/R E(G1)=0.92from the R-bandflux ratio,assuming G1and G2are at the same redshift).As a specific example,we show the bestfit parameters for R E(G2)=1′′in Table3.The position angle of galaxy G1in the model(θe=−89.3)is in good agreement with that observed.The time delay is derived to be∆t=92.6h−1day(A leads B),assuming the strong Mg II absorption system at z=0.748is associated with the lens galaxy.Even if we decrease the value of R E(G2)up to0.′′1,the time delay is affected only moderately;the time delay is predicted to be104.4h−1day when R E(G2)=0.′′1.In summary,lens modeling has revealed that neither system is simple.In particular,the secondary galaxies may play an important role in both lenses.5.Lens Galaxy EnvironmentsLens galaxies of lensed quasars,particularly in systems with relatively large image separations ( 3′′),commonly lie in groups or clusters(Keeton et al.2000;Faure et al.2004).Such“compound”lens systems include Q0957+561(Walsh et al.1979),PG1115+080(Weymann et al.1980),MG 2016+112(Lawrence et al.1984),RX J0911+0551(Bade et al.1997),MG0751+2716(Tonry &Kochanek1999),SDSS J0903+5028(Johnston et al.2003),CLASS B1608+656(Fassnacht et al.2004),B2108+213(McKean et al.2005),and HE0435-1223(Morgan et al.2005).If dense environments of the lens galaxies are common,then they could affect strong lens studies in several ways(Keeton&Zabludoff2004).On the theoretical side,estimation of environmental effects remains controversial:While Keeton et al.(2000)and Holder&Schechter(2003)argued that the large fraction of lens systems should lie in dense environments and thus the environmental effects are significant,Dalal&Watson(2005)estimated using a halo occupation distribution that the typical values for the external convergence and shear are quite small.Although we have already seen in§3and§4that SDSS J1001+5027and SDSS J1206+4332have additional galaxies that likely affect the lens potential,it is important to check the largerfield for hints of groups or clusters.Figure6shows thefields around the lens systems obtained at UH88.Wefind many galaxies around SDSS J1001+5027,indicating that there may be a group or cluster along the line of sight. For SDSS J1206+4332,we cannot see any noticeable enhancement of the number of galaxies around the lens system,though there are several faint galaxies near the lens system.To explore the environments further,we derived the number densities of galaxies around each lens system using the UH88images.We perform object identifications using the Source Extractor algorithm(SExtractor;Bertin&Arnouts1996).We define galaxies as objects with SExtractor parameter CLASSThus the lens galaxy may lie in a group or a cluster that is located to the north-west of the lens; spectroscopic identifications of these galaxies as well as the lens galaxy should be undertaken.6.Is the number of3”lenses consistent with theory?Thus far,13gravitationally lensed quasars have been discovered using the SDSS.In addition, we have recovered several previously known lensed quasar systems.Table4summarizes the current status of our lens search in the SDSS.Note that limitations of follow-up time have forced us to focus on the SDSS spectroscopic sample of quasars3.Thus the list does not contain lenses that do not have SDSS spectra(e.g.,APM08279+5255;see Pindor et al.2003).The Table does not contain SDSS J1402+6321(Bolton et al.2005)either,since the redshift(z=0.48)is below our criterion for the quasar sample(see discussion below).Among gravitational lenses in the Table, SDSS J1004+4112and Q0957+561were selected by searching around each quasar for stellar objects that have similar colors as the quasar itself(Oguri et al.2004a;Hennawi2004),and the rest were successfully selected by our standard candidate selection algorithm(see§2)though the first identifications of some of the candidates were made by different algorithms.An exception is SDSS J0903+5028(Johnston et al.2003)which was targeted as a luminous red galaxy(Eisenstein et al.2001)because of the bright lens galaxy;however,we include this system in the statistical analysis below,since the quasar would have been targeted as a high-redshift quasar if it had not been obscured by the foreground lens galaxy(Richards et al.2002).The Table shows that we have discovered a relatively large number of∼3′′lenses.We note that our current lens sample shown in Table4is quite incomplete4,and that future follow-up observations would increase the number of lenses even in the current quasar sample.Therefore we now calculate the expected lensing probability in the SDSS quasar sample and compare it with the number of∼3′′lenses in the sample.In particular,we neglect the contribution of lens galaxy environments,as has normally been done,to see whether the assumption is still valid or not.In computing the lensing probability, we assume a spatiallyflat universe(ΩM+ΩΛ=1).We compute the lensing probability distribution along the lines described by Turner,Ostriker, &Gott(1984).The lens galaxies are modeled by SISρ(r)=σ2/(2πGr2),whereσis the velocity dispersion of the lens galaxy.We adopt the velocity function of early-type galaxies determined from∼30,000SDSS galaxies at0.01<z<0.3(Sheth et al.2003;Bernardi et al.2005;Mitchell et al.2005),and neglect the redshift evolution(i.e.,we assume that the velocity function is constant in comoving units).The use of the velocity function of early-type galaxies is sufficient for ourcalculation because atθ 3′′lensing by early-type galaxies is dominant(Turner et al.1984). We need also to incorporate the selection function of the SDSS lens search;which we do in a preliminary way by making the following assumptions.First,we use the magnification factor of the brighter image,µbright=(θE/θS)+1,whereθE is the Einstein radius andθS is the position of the source relative to the lens galaxy,to compute the magnification bias,because atθ 3′′two lensed components are well separated in the SDSS data.Although we may have an alternative choice of using the magnification factor of the fainter image,we adoptµbright to calculate the upper limit of the lensing probability;thus the actual lensing rate atθ 3′′might be smaller than our calculation5.Next,for the limiting bright-to-faintflux ratio we assume f max=10;this is justified because all lenses in Table4satisfy this condition.Lensing probabilities calculated with this selection function represent an upper limit at relatively large image separationθ∼3′′.To calculate the expected number of lensed quasars in the current SDSS quasar sample,we need the luminosity function of quasars as well as the redshift and magnitude distributions of the quasar sample.We adopt a sample of∼47,000quasars at0.6<z<4.0.The sample is constructed in the same way as in Oguri et al.(2004a).We did not search for lensed quasars at z<0.6as low-redshift quasars are intrinsically extended,and we do not use high-redshift quasar(z>4.0) sample because it contains a significant fraction of objects whose spectra were misidentified by the SDSS spectroscopic pipeline(c.f.,discussion in Schneider et al.2003).The redshift distribution is similar to that shown in Oguri et al.(2004a).For the luminosity function of quasars,we use what is called LF1in Oguri et al.(2004a),which has a faint end slope of1.64and a bright end slope of 3.43(z<3)or2.58(z>3).The result is shown in Figure9.As seen,the number of∼3′′lenses already exceeds the theoretical expectations,when we adopt the standard value of the cosmological constant,ΩΛ∼0.7. The situation is similar if we increaseΩΛto0.8.In terms of the constraint on the cosmological constant,the excess in the bin centered atθ=3′′is described asΩΛ>0.90(68%confidence limit)assuming a Poisson distribution,which is highly inconsistent with recent measurements of the cosmological constantΩΛ∼0.70with errors of less than10%(e.g.,Tegmark et al.2004).We emphasis that our current lens sample is quite incomplete;indeed,currently we have several∼3′′quasar pairs with the same redshifts which could also be gravitational lenses(Hennawi2004),which need deep imaging tofind the putative lens galaxies.Thus observations of these quasar pairs as well as lens candidates should be conducted,which might make the discrepancy even larger.Such an excess may indicate that our simple treatment of lensing statistics is inaccurate and that we need to include other effects.7.SummaryWe report the discovery of two gravitationally lensed quasars,SDSS J1001+5027and SDSS J1206+4332.The systems were identified as new lens candidates in the SDSS,and confirmed as lenses by spectroscopic and imaging observations at the ARC3.5m and the UH88telescope.SDSS J1001+5027is a lensed quasar at z=1.838,and consists of two lensed images separated by2.′′86. SDSS J1206+4332is a lensed quasar at z=1.789,and consists of two lensed images separated by 2.′′90.In each system we have identified the galaxy responsible for the lensing.We have found that the lens systems are complicated.The imaging data clearly show other galaxies that are very close to the main lens galaxies.The lens modeling has shown that these galaxies affect the lens potentials significantly.We have examined the widefield images,which show an enhancement of the galaxy number density within60′′of SDSS J1001+5027.Spectroscopic follow-up observations are needed to see if the group/cluster(z∼0.2)is actually associated with the lens galaxy.Although the SDSS lens survey is ongoing,we have made a preliminary comparison of the-oretical lensing probability distributions with the observed distribution.We have found that the number of lenses withθ∼3′′already exceeds the theoretical expectations.We still have many lens candidates withθ 3′′that remain to be observed(Hennawi2004);if some of them turn out to be true gravitational lenses,the conflict will become even stronger.This excess may be caused by external convergence and shearfields which we have not taken into account in our cal-culation.Basically,external shear broadens the distribution of image separations for a given mass of a lens object(e.g.,Huterer,Keeton,&Ma2005).This broadening is enough to enhance the lensing probability atθ 3′′because the lensing probability at the image separation region is a strong function of image separations.More significant enhancement may be achieved by external convergence,since it increases both image separation and lensing probability.Indeed,amongfive intermediate-separation lenses in Table4,two lens systems(RX J0911+0551and Q0957+561)lie in clusters,and two other lens systems(SDSS J0903+5028and SDSS J1001+5027)also appear to lie in dense environments.In addition,the two lens systems reported in this paper are complex in the sense that galaxies very close to the main lens galaxies affect the lens potentials.Other possible systematic effects include triaxiality of lenses(Oguri&Keeton2004)and massive substructures (Cohn&Kochanek2004).In either case,lens statistics at this image separation should be done with caution;simple models that consider only isolated single lens objects can be misleading.We thank Paul Schechter for useful comments,and anonymous referee for many suggestions. M.O.and N.I.are supported by JSPS through JSPS Research Fellowship for Young Scientists. 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