On the viability of neutron star black hole binaries as central engines of gamma-ray bursts

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创造一篇神话作文英语

In the realm of ancient legends, there lies a tale that has been passed down through the ages, a story that speaks of the dawn of creation and the birth of our world. This is not just a myth, but a narrative that holds the essence of our existence, a testament to the power of imagination and the boundless creativity of the human spirit.Once upon a time, in the vast expanse of the cosmos, there existed a realm beyond our comprehension, a place where time and space were but mere concepts. This was the home of the celestial beings, the gods and goddesses who held dominion over the elements and the forces of nature. They were the architects of creation, the weavers of destiny, and the keepers of the cosmic balance.In the beginning, there was only chaos, a swirling maelstrom of energy and potential. The gods gazed upon this formless void and saw the potential for greatness. They convened in the celestial council, discussing the blueprint of creation, the design of the universe, and the destiny of the beings that would inhabit it.The first among the gods, the mighty Zeus, raised his hand and commanded the winds to gather. The air swirled and coalesced, forming the firmament above. His sister, the gentle Gaia, reached into the depths of the earth and brought forth the land, the mountains, and the seas. The oceans roared to life, and the continents took shape, a testament to Gaias nurturing touch.As the world took form, the gods bestowed upon it the gift of life. Thegoddess of wisdom, Athena, breathed knowledge into the minds of the first humans, endowing them with the ability to reason, to create, and to dream. The god of the sun, Apollo, brought light and warmth, illuminating the world and driving away the shadows of ignorance.But creation was not without its challenges. The god of the sea, Poseidon, was a force to be reckoned with. His mighty trident stirred the waters, causing great storms and tempests that threatened to undo the work of the gods. It was then that the goddess of love, Aphrodite, stepped forward. With her charm and grace, she calmed the raging seas and brought harmony to the world.The gods continued to shape the world, each contributing their unique gifts and talents. Demeter, the goddess of the harvest, brought forth the fruits of the earth, nourishing the land and its people. Ares, the god of war, instilled in humanity the spirit of competition and the courage to stand against adversity.As the world flourished, the gods looked upon their creation with pride and joy. They had given life to a world filled with wonder and beauty, a place where the forces of nature danced in harmony, and where humanity could thrive and prosper.But with creation came responsibility. The gods knew that they must guide and protect their creation, ensuring that the balance of the cosmos was maintained. They descended to the mortal realm, taking on the roles of mentors and guardians, teaching humanity the ways of the world and theimportance of living in harmony with nature.This myth, this tale of creation, is more than just a story. It is a reflection of our own journey, a reminder of our connection to the world around us and the power that lies within us to shape our own destiny. It is a testament to the enduring spirit of humanity, a celebration of the creativity and imagination that have allowed us to build civilizations, explore the stars, and dream of a better future.As we look to the heavens and ponder our place in the universe, let us remember the lessons of the gods. Let us embrace the power of creation, the beauty of life, and the potential that lies within each and every one of us. For in the end, we are all creators, we are all dreamers, and we are all part of the grand tapestry of existence.。

Stellar Remnants White Dwarfs, Neutron Stars & Black Holes

Sirius & Sirius B a White Dwarf Star
White Dwarfs
• composed mainly of Carbon & Oxygen • formed from stars that are no more than 8 Solar masses • White Dwarfs can be no more than 1.4 Solar masses and have diameters about the size of the Earth (1/100 the diameter of the Sun). • If a White Dwarf is in a binary system and close enough to its companion A White Dwarf pulling material star it may draw material off off of another star in a binary system this star. This material can then build up on the surface of the White Dwarf. 2
– once matter or light crosses the event horizon it can never return – tidal forces are extreme at the event horizon
11
Two dimensional representation of the Event Horizon
Neutron Stars
• Except for a thin crust of iron atoms a neutron star is composed entirely of neutrons. • The gravitational forces inside a neutron star are too strong for atoms to exist. • Instead electrons get crushed into the protons in the atomic nucleus forming neutrons. • Neutron stars have very intense magnetic fields and very rapid rotatdius: The Radius of the Event Horizon

两性互动下的解构与重构——论爱丽丝·沃克《紫颜色》中的黑人男性气概

91隋红升、陈吉：两性互动下的解构与重构两性互动下的解构与重构*——论爱丽丝沃克《紫颜色》中的黑人男性气概隋红升　陈　吉内容提要：笔者通过对爱丽丝沃克的《紫颜色》中两性互动关系的分析，阐述传统黑人男性气概在女性反抗以及主体意识觉醒过程中逐步被解构以及新型男性气概在相互理解与尊重的两性互动中得以建构的过程，由此管窥两性互动对黑人男性气概建构的重要意义。

关键词：《紫颜色》　男性气概　解构与重构　两性互动作者简介：隋红升，浙江大学外国语言文化与国际交流学院，主要研究美国文学、性别诗学。

陈吉，浙江大学外国语言文化与国际交流学院，主要研究美国文学。

Title:Destruction and Reconstruction under Gender Interactions:On the Black Masculinity in Alice Walker's The Color Purple Abstract:By exploring the gender interactions among the main characters in Alice Walker's The Color Purple,the paper is to analyze the procedures of destruction of the traditional masculinity with the black women's protest and the awakening of their subjectivity and the construction of new masculinity in gender interaction characterized by mutual understanding and respect, thus probing the profound signi cance of gender interaction to the construction of black masculinity.Key wor ds:The Color Pur ple　masculinity　destruction and construction　gender interactionsAuthor s:Sui Hongsheng,is from the School of International Studies,Zhejiang University,specializing in American literature and gender studies.Chen Ji,is from the School of International Studies,Zhejiang University,specializing in American literature.就美国黑人作家爱丽丝沃克的代表作《紫颜色》的研究现状而言，已有的研究主要侧重于该作中黑人女性的成长及其主体意识的觉醒，比如唐红梅女士认为该作凸显了“黑人女性的自我不断拓展”（唐红梅211）。

托付词汇打印版(带翻译)

sensitivity hypersensitive photosensitive sensory sentimental sentimentalize
acumen adapt adaptable adaptation
converge conversation conversational converse
novel novelty novice nowadays now and then noxious nuclear nuclei nucleus null
accessible accessibility accessory
construct construction consult
frightening
accuracy accuse accusation accustomed achieve achievement acid
continuum contour funding fundamental contract fungi furious furnish contraction contractor contradict furnishing furniture furry further
notorious notoriously nourish
consternation constituent
freight
nourishing nourishment
freighter constitution constitute constitutional constrain constraint constrict constricted freshly freshness friction frenetic fanatical frenzy fresco

有关哥伦比亚大学的英语阅读理解

有关哥伦比亚大学的英语阅读理解Scientists have long understood that supermassive black holes weighing millions or billions of suns can tear apart stars that come too close.The black hotels gravity pulls harder on the nearest part of the star，an imbalance that pulls the star apart over a period of minutes or hours，once it gets close enough.Scientists say this Uneven pulling is not the only hazard facing the star.The strain of these unbalanced forces can also trigger a nuclear explosion powerful enough to destroy the star from within.Matthieu Brassart and Jean-Pierre Luminet of the Observatoire de Paris in Meudon，France1,carried out computer simulations of the final moments of such an unfortunate star’s life，as it veered towards a supermassive black hole.When the star gets close enough，the uneven forces flatten it into a pancake shape.Some previous studies had suggested this flattening would increase the density and temperature inside the star enough to trigger intense nuclear reactions that would tear it apart.But other studies had suggested that the picture would becomplicated by shock waves generated during the flattening process and that no nuclear explosion should occur.The new simulations investigated the effects of shock waves in detail，and found that even when their effects are included，the conditions favor a nuclear explosion.“There will be an explosion of the star —it will be completely destroyed,” Brassart says. Although the explosion obliterates the star，it saves some of the star’s matter from being devoured by the black hole.The explosion is powerful enough to hurl much of the star’s matter out of the black hole’s reach，he says.The devouring of stars by black holes may already have been observed，although at a much later stage.It is thought that several months after the event that rips the star apart，its matter starts swirling into the hole itself.It heats up as it does so，releasing ultraviolet light and X-rays.If stars disrupted near black holes really do explode，then they could in principle allow these events to be detected at a much earlier stage，says Jules Hatpern of Columbia University in New York，US2.“It may make it possible to see the disruption of that starimmediately if it gets hot enough,” he says.Brassart agrees.“Perhaps it can be observed in the X-rays and gamma rays，but it’s something that needs to be more studied,” he says.Supernova researcher Chris Fryer of the Los Alamos National Laboratory in Los Alamos，New Mexico，US3，says the deaths of these stars are difficult to simulate，and he is not sure whether the researchers have proven their case that they explode in the process.注释：1. the Observatoire de Paris in Meudon，France：位于法国默顿的巴黎天文台。

英语黑漆漆与猎户星观后感

英语黑漆漆与猎户星观后感英文回答：In the realm of cosmic wonders, two celestial entities emerge from the celestial tapestry, each holding a profound allure and enigmatic presence: the pitch-black void known as the Black Hole and the resplendent constellation of Orion. Both have captivated the imaginations of stargazers, scientists, philosophers, and countless others throughout history. Their contrasting nature—one an abyss of infinite darkness, the other a shimmering beacon of light—makes for a fascinating exploration of the duality of the universe.The Black Hole, a formidable gravitational behemoth, defies the very laws of physics as we know them. Its gravitational pull is so immense that nothing, not even light, can escape its clutches. At its heart lies a singularity, an infinitely dense point where space-time is warped beyond recognition. The event horizon, the boundary beyond which nothing can return, marks the threshold ofthis cosmic abyss.Orion, in stark contrast, is a constellation ablaze with celestial brilliance. Its most prominent feature is the three stars that form Orion's Belt, a celestial landmark that has guided sailors and stargazers for centuries. Rigel, the brightest star in the constellation, illuminates the sky with its bluish-white radiance. Betelgeuse, a red supergiant, pulsates with an irregular rhythm, casting an ethereal crimson glow upon its surroundings.The mythology surrounding the Black Hole and Orion is as diverse as their celestial appearances. In ancient Egyptian lore, Orion was associated with the god Osiris, the ruler of the underworld. The Black Hole, on the other hand, has been interpreted as a symbol of chaos and destruction, a cosmic entity that represents the ultimate fate of all matter.In modern science, the Black Hole has become a subject of intense research, with astronomers seeking to unravelthe mysteries of its gravity, time dilation, and potential for generating powerful cosmic jets. Orion, too, hasyielded valuable insights into the formation and evolutionof stars, providing astronomers with a laboratory to study stellar processes up close.中文回答：在浩瀚的宇宙奇观中，两个天体从天幕中脱颖而出，它们都具有深远的魅力和神秘的存在，黑洞这个漆黑的虚空和猎户座这个辉煌的星座。

Accomodating Solar and Atmospheric Neutrino Deficits, Hot Dark Matter, and a Double Beta De

UCSB–HEP–94-03 UMD-PP-94-90 February,1994 Accommodating solar and atmospheric neutrino deﬁcits, hot dark matter, and a double beta decay signal
arXiv:hep-ph/9402231v2 9 Feb 1994
−6 2 2 −3 a)Small − angle MSW, ∆m2 ei ∼ 6 × 10 eV , sin 2θei ∼ 7 × 10 ,
2
−6 2 2 b)Large − angle MSW, ∆m2 ei ∼ 9 × 10 eV , sin 2θei ∼ 0.6, −10 eV2 , sin2 2θ ∼ 0.9. c)Vacuum oscillation, ∆m2 ei ei ∼ 10
(1)
Of these, (a) is favored over (b) by the ﬁts to the solar neutrino data [9], and both (b) and (c) are disfavored by information from the neutrino burst from supernova 1987A [11]. B. Atmospheric Neutrino Deﬁcit The second set of experiments indicating non-zero neutrino masses and mixings has to do with atmospheric νµ ’s and νe ’s arising from the decays of π ’s and K ’s and the subsequent decays of secondary muons produced in the ﬁnal states of the π and K decays. In the underground experiments the νµ and ν ¯µ produce muons and the νe and ν ¯e lead to e± . Observations of µ± and e± indicate a far lower value for νµ and ν ¯µ than suggested by na¨ ıve counting arguments which imply that N (νµ + ν ¯µ ) = 2N (νe + ν ¯e ). More precisely, the ratio of µ events to e-events can be normalized to the ratio of calculated ﬂuxes to reduce ﬂux uncertainties, giving [3] R(µ/e) = 0.60 ± 0.07 ± 0.05 (Kamiokande), = 0.54 ± 0.05 ± 0.12 (IMB), = 0.69 ± 0.19 ± 0.09 (Soudan II). Combining these results with observations of upward going muons by Kamiokande [3], IMB [3], and Baksan [12] and the negative Fr´ ejus [13] and NUSEX [14] results leads to the conclusion [15] that neutrino oscillations can give an explanation of these results, provided

The mysteries of the universe Dark matter

The mysteries of the universe DarkmatterDark matter is one of the most enigmatic and perplexing concepts in the field of astrophysics and cosmology. It is a substance that makes up a significantportion of the universe, yet it remains largely elusive and mysterious to scientists. The existence of dark matter was first proposed in the 1930s by Swiss astronomer Fritz Zwicky, who observed that the visible matter in the Coma galaxy cluster could not account for the gravitational forces that were holding thecluster together. This led him to hypothesize the presence of unseen "dark" matter that was responsible for the gravitational effects. Since then, numerous observations and experiments have provided compelling evidence for the existenceof dark matter, but its true nature continues to elude researchers. One of the most compelling lines of evidence for dark matter comes from the study of the rotation curves of galaxies. When astronomers measure the velocities of stars and gas in a galaxy as a function of their distance from the galactic center, theyfind that the velocities do not decrease as expected with increasing distance. Instead, the velocities remain constant or even increase, indicating the presence of additional unseen mass that is providing the gravitational pull to keep thestars and gas in their orbits. This discrepancy between the observed motion of galactic objects and the visible matter in galaxies has led scientists to conclude that there must be a significant amount of dark matter present in galaxies, outweighing the visible matter by a factor of about six to one. Another piece of evidence for dark matter comes from the study of the large-scale structure of the universe. Observations of the cosmic microwave background radiation, the afterglow of the Big Bang, have revealed subtle patterns in the distribution of matter onthe largest scales. These patterns can be explained by the presence of dark matter, which exerts gravitational forces to shape the distribution of galaxies and galaxy clusters in the universe. Additionally, the gravitational lensing of distant galaxies by intervening mass concentrations, such as galaxy clusters, provides further evidence for the presence of dark matter. The bending of light from these distant galaxies can only be explained by the gravitational influence of unseenmass, which is consistent with the properties of dark matter. Despite the overwhelming evidence for the existence of dark matter, its true nature remains a profound mystery. Dark matter does not emit, absorb, or reflect light, making it invisible to telescopes and other instruments that rely on electromagnetic radiation for detection. This has made it incredibly challenging for scientists to directly observe and study dark matter, leading to a wide range of theoretical and experimental efforts to uncover its properties. One of the leading candidates for the identity of dark matter is a type of particle that interacts only weakly with ordinary matter and electromagnetic forces, known as a weakly interacting massive particle (WIMP). WIMPs are a theoretical class of particles that arise in extensions of the standard model of particle physics, and they are thought to have been produced in the early universe in sufficient quantities to account for the observed abundance of dark matter today. Numerous experiments around the world are dedicated to detecting WIMPs through their rare interactions with ordinary matter, such as through the recoil of atomic nuclei in underground detectors or the production of secondary particles in particle accelerators. Another potential explanation for dark matter is the existence of primordial black holes, which are hypothesized to have formed in the early universe from the gravitational collapse of overdense regions. These black holes would not emit significant amounts oflight or other radiation, making them difficult to detect directly. However, their gravitational influence on surrounding matter could betray their presence, and ongoing observational campaigns are searching for the signatures of primordial black holes in the universe. In addition to these particle-based and astrophysical explanations, some scientists have proposed modifications to the laws of gravity as an alternative to dark matter. These modified gravity theories seek to explain the observed gravitational effects in galaxies and galaxy clusters without invoking the presence of additional unseen mass. While these theories have had some success in reproducing certain observational data, they have yet to provide a comprehensive and consistent explanation for the full range of evidence for dark matter. The search for dark matter continues to be a vibrant and active area of research in astrophysics and particle physics. New generations of experiments are pushing the boundaries of sensitivity and precision in the huntfor dark matter particles, while astronomers are mapping the distribution ofmatter in the universe with ever-increasing detail. The discovery of dark matter would represent a profound breakthrough in our understanding of the fundamental constituents of the universe and the forces that govern its evolution. It would also have far-reaching implications for our understanding of the cosmos, from the formation of galaxies and galaxy clusters to the ultimate fate of the universe itself. The quest to unravel the mysteries of dark matter is not just ascientific endeavor, but also a deeply human one. It speaks to our innatecuriosity about the nature of the universe and our place within it. Therealization that the majority of the matter in the universe is invisible and fundamentally different from the matter we interact with on a daily basis is both humbling and awe-inspiring. It challenges our preconceived notions of the cosmos and forces us to confront the limits of our current understanding. The search for dark matter is a testament to the human spirit of exploration and discovery, as we strive to push the boundaries of knowledge and unlock the secrets of the universe. In conclusion, dark matter remains one of the most captivating and tantalizing mysteries in modern science. Its existence is supported by a wealth of observational evidence, yet its true nature continues to elude us. Whether it is composed of exotic particles, primordial black holes, or a modification of thelaws of gravity, the discovery of dark matter would revolutionize our understanding of the cosmos and our place within it. The ongoing quest to uncover the secrets of dark matter is a testament to the enduring human spirit ofcuriosity and exploration, as we continue to push the boundaries of knowledge and strive to unlock the mysteries of the universe.。

黑洞的准正模式(quasinormal modes)

Quasi-Normal Modes of Stars and Black HolesKostas D.KokkotasDepartment of Physics,Aristotle University of Thessaloniki,Thessaloniki54006,Greece.kokkotas@astro.auth.grhttp://www.astro.auth.gr/˜kokkotasandBernd G.SchmidtMax Planck Institute for Gravitational Physics,Albert Einstein Institute,D-14476Golm,Germany.bernd@aei-potsdam.mpg.dePublished16September1999/Articles/Volume2/1999-2kokkotasLiving Reviews in RelativityPublished by the Max Planck Institute for Gravitational PhysicsAlbert Einstein Institute,GermanyAbstractPerturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades.They are of partic-ular importance today,because of their relevance to gravitational waveastronomy.In this review we present the theory of quasi-normal modes ofcompact objects from both the mathematical and astrophysical points ofview.The discussion includes perturbations of black holes(Schwarzschild,Reissner-Nordstr¨o m,Kerr and Kerr-Newman)and relativistic stars(non-rotating and slowly-rotating).The properties of the various families ofquasi-normal modes are described,and numerical techniques for calculat-ing quasi-normal modes reviewed.The successes,as well as the limits,of perturbation theory are presented,and its role in the emerging era ofnumerical relativity and supercomputers is discussed.c 1999Max-Planck-Gesellschaft and the authors.Further information on copyright is given at /Info/Copyright/.For permission to reproduce the article please contact livrev@aei-potsdam.mpg.de.Article AmendmentsOn author request a Living Reviews article can be amended to include errata and small additions to ensure that the most accurate and up-to-date infor-mation possible is provided.For detailed documentation of amendments, please go to the article’s online version at/Articles/Volume2/1999-2kokkotas/. Owing to the fact that a Living Reviews article can evolve over time,we recommend to cite the article as follows:Kokkotas,K.D.,and Schmidt,B.G.,“Quasi-Normal Modes of Stars and Black Holes”,Living Rev.Relativity,2,(1999),2.[Online Article]:cited on<date>, /Articles/Volume2/1999-2kokkotas/. The date in’cited on<date>’then uniquely identiﬁes the version of the article you are referring to.3Quasi-Normal Modes of Stars and Black HolesContents1Introduction4 2Normal Modes–Quasi-Normal Modes–Resonances7 3Quasi-Normal Modes of Black Holes123.1Schwarzschild Black Holes (12)3.2Kerr Black Holes (17)3.3Stability and Completeness of Quasi-Normal Modes (20)4Quasi-Normal Modes of Relativistic Stars234.1Stellar Pulsations:The Theoretical Minimum (23)4.2Mode Analysis (26)4.2.1Families of Fluid Modes (26)4.2.2Families of Spacetime or w-Modes (30)4.3Stability (31)5Excitation and Detection of QNMs325.1Studies of Black Hole QNM Excitation (33)5.2Studies of Stellar QNM Excitation (34)5.3Detection of the QNM Ringing (37)5.4Parameter Estimation (39)6Numerical Techniques426.1Black Holes (42)6.1.1Evolving the Time Dependent Wave Equation (42)6.1.2Integration of the Time Independent Wave Equation (43)6.1.3WKB Methods (44)6.1.4The Method of Continued Fractions (44)6.2Relativistic Stars (45)7Where Are We Going?487.1Synergism Between Perturbation Theory and Numerical Relativity487.2Second Order Perturbations (48)7.3Mode Calculations (49)7.4The Detectors (49)8Acknowledgments50 9Appendix:Schr¨o dinger Equation Versus Wave Equation51Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt41IntroductionHelioseismology and asteroseismology are well known terms in classical astro-physics.From the beginning of the century the variability of Cepheids has been used for the accurate measurement of cosmic distances,while the variability of a number of stellar objects(RR Lyrae,Mira)has been associated with stel-lar oscillations.Observations of solar oscillations(with thousands of nonradial modes)have also revealed a wealth of information about the internal structure of the Sun[204].Practically every stellar object oscillates radially or nonradi-ally,and although there is great diﬃculty in observing such oscillations there are already results for various types of stars(O,B,...).All these types of pulsations of normal main sequence stars can be studied via Newtonian theory and they are of no importance for the forthcoming era of gravitational wave astronomy.The gravitational waves emitted by these stars are extremely weak and have very low frequencies(cf.for a discussion of the sun[70],and an im-portant new measurement of the sun’s quadrupole moment and its application in the measurement of the anomalous precession of Mercury’s perihelion[163]). This is not the case when we consider very compact stellar objects i.e.neutron stars and black holes.Their oscillations,produced mainly during the formation phase,can be strong enough to be detected by the gravitational wave detectors (LIGO,VIRGO,GEO600,SPHERE)which are under construction.In the framework of general relativity(GR)quasi-normal modes(QNM) arise,as perturbations(electromagnetic or gravitational)of stellar or black hole spacetimes.Due to the emission of gravitational waves there are no normal mode oscillations but instead the frequencies become“quasi-normal”(complex), with the real part representing the actual frequency of the oscillation and the imaginary part representing the damping.In this review we shall discuss the oscillations of neutron stars and black holes.The natural way to study these oscillations is by considering the linearized Einstein equations.Nevertheless,there has been recent work on nonlinear black hole perturbations[101,102,103,104,100]while,as yet nothing is known for nonlinear stellar oscillations in general relativity.The study of black hole perturbations was initiated by the pioneering work of Regge and Wheeler[173]in the late50s and was continued by Zerilli[212]. The perturbations of relativistic stars in GR wereﬁrst studied in the late60s by Kip Thorne and his collaborators[202,198,199,200].The initial aim of Regge and Wheeler was to study the stability of a black hole to small perturbations and they did not try to connect these perturbations to astrophysics.In con-trast,for the case of relativistic stars,Thorne’s aim was to extend the known properties of Newtonian oscillation theory to general relativity,and to estimate the frequencies and the energy radiated as gravitational waves.QNMs wereﬁrst pointed out by Vishveshwara[207]in calculations of the scattering of gravitational waves by a Schwarzschild black hole,while Press[164] coined the term quasi-normal frequencies.QNM oscillations have been found in perturbation calculations of particles falling into Schwarzschild[73]and Kerr black holes[76,80]and in the collapse of a star to form a black hole[66,67,68]. Living Reviews in Relativity(1999-2)5Quasi-Normal Modes of Stars and Black Holes Numerical investigations of the fully nonlinear equations of general relativity have provided results which agree with the results of perturbation calculations;in particular numerical studies of the head-on collision of two black holes [30,29](cf.Figure 1)and gravitational collapse to a Kerr hole [191].Recently,Price,Pullin and collaborators [170,31,101,28]have pushed forward the agreement between full nonlinear numerical results and results from perturbation theory for the collision of two black holes.This proves the power of the perturbation approach even in highly nonlinear problems while at the same time indicating its limits.In the concluding remarks of their pioneering paper on nonradial oscillations of neutron stars Thorne and Campollataro [202]described it as “just a modest introduction to a story which promises to be long,complicated and fascinating ”.The story has undoubtedly proved to be intriguing,and many authors have contributed to our present understanding of the pulsations of both black holes and neutron stars.Thirty years after these prophetic words by Thorne and Campollataro hundreds of papers have been written in an attempt to understand the stability,the characteristic frequencies and the mechanisms of excitation of these oscillations.Their relevance to the emission of gravitational waves was always the basic underlying reason of each study.An account of all this work will be attempted in the next sections hoping that the interested reader will ﬁnd this review useful both as a guide to the literature and as an inspiration for future work on the open problems of the ﬁeld.020406080100Time (M ADM )-0.3-0.2-0.10.00.10.20.3(l =2) Z e r i l l i F u n c t i o n Numerical solutionQNM fit Figure 1:QNM ringing after the head-on collision of two unequal mass black holes [29].The continuous line corresponds to the full nonlinear numerical calculation while the dotted line is a ﬁt to the fundamental and ﬁrst overtone QNM.In the next section we attempt to give a mathematical deﬁnition of QNMs.Living Reviews in Relativity (1999-2)K.D.Kokkotas and B.G.Schmidt6 The third and fourth section will be devoted to the study of the black hole and stellar QNMs.In theﬁfth section we discuss the excitation and observation of QNMs andﬁnally in the sixth section we will mention the more signiﬁcant numerical techniques used in the study of QNMs.Living Reviews in Relativity(1999-2)7Quasi-Normal Modes of Stars and Black Holes 2Normal Modes–Quasi-Normal Modes–Res-onancesBefore discussing quasi-normal modes it is useful to remember what normal modes are!Compact classical linear oscillating systems such asﬁnite strings,mem-branes,or cavitiesﬁlled with electromagnetic radiation have preferred time harmonic states of motion(ωis real):χn(t,x)=e iωn tχn(x),n=1,2,3...,(1) if dissipation is neglected.(We assumeχto be some complex valuedﬁeld.) There is generally an inﬁnite collection of such periodic solutions,and the“gen-eral solution”can be expressed as a superposition,χ(t,x)=∞n=1a n e iωn tχn(x),(2)of such normal modes.The simplest example is a string of length L which isﬁxed at its ends.All such systems can be described by systems of partial diﬀerential equations of the type(χmay be a vector)∂χ∂t=Aχ,(3)where A is a linear operator acting only on the spatial variables.Because of theﬁniteness of the system the time evolution is only determined if some boundary conditions are prescribed.The search for solutions periodic in time leads to a boundary value problem in the spatial variables.In simple cases it is of the Sturm-Liouville type.The treatment of such boundary value problems for diﬀerential equations played an important role in the development of Hilbert space techniques.A Hilbert space is chosen such that the diﬀerential operator becomes sym-metric.Due to the boundary conditions dictated by the physical problem,A becomes a self-adjoint operator on the appropriate Hilbert space and has a pure point spectrum.The eigenfunctions and eigenvalues determine the periodic solutions(1).The deﬁnition of self-adjointness is rather subtle from a physicist’s point of view since fairly complicated“domain issues”play an essential role.(See[43] where a mathematical exposition for physicists is given.)The wave equation modeling theﬁnite string has solutions of various degrees of diﬀerentiability. To describe all“realistic situations”,clearly C∞functions should be suﬃcient. Sometimes it may,however,also be convenient to consider more general solu-tions.From the mathematical point of view the collection of all smooth functions is not a natural setting to study the wave equation because sequences of solutionsLiving Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt8 exist which converge to non-smooth solutions.To establish such powerful state-ments like(2)one has to study the equation on certain subsets of the Hilbert space of square integrable functions.For“nice”equations it usually happens that the eigenfunctions are in fact analytic.They can then be used to gen-erate,for example,all smooth solutions by a pointwise converging series(2). The key point is that we need some mathematical sophistication to obtain the “completeness property”of the eigenfunctions.This picture of“normal modes”changes when we consider“open systems”which can lose energy to inﬁnity.The simplest case are waves on an inﬁnite string.The general solution of this problem isχ(t,x)=A(t−x)+B(t+x)(4) with“arbitrary”functions A and B.Which solutions should we study?Since we have all solutions,this is not a serious question.In more general cases, however,in which the general solution is not known,we have to select a certain class of solutions which we consider as relevant for the physical problem.Let us consider for the following discussion,as an example,a wave equation with a potential on the real line,∂2∂t2χ+ −∂2∂x2+V(x)χ=0.(5)Cauchy dataχ(0,x),∂tχ(0,x)which have two derivatives determine a unique twice diﬀerentiable solution.No boundary condition is needed at inﬁnity to determine the time evolution of the data!This can be established by fairly simple PDE theory[116].There exist solutions for which the support of theﬁelds are spatially compact, or–the other extreme–solutions with inﬁnite total energy for which theﬁelds grow at spatial inﬁnity in a quite arbitrary way!From the point of view of physics smooth solutions with spatially compact support should be the relevant class–who cares what happens near inﬁnity! Again it turns out that mathematically it is more convenient to study all solu-tions ofﬁnite total energy.Then the relevant operator is again self-adjoint,but now its spectrum is purely“continuous”.There are no eigenfunctions which are square integrable.Only“improper eigenfunctions”like plane waves exist.This expresses the fact that weﬁnd a solution of the form(1)for any realωand by forming appropriate superpositions one can construct solutions which are “almost eigenfunctions”.(In the case V(x)≡0these are wave packets formed from plane waves.)These solutions are the analogs of normal modes for inﬁnite systems.Let us now turn to the discussion of“quasi-normal modes”which are concep-tually diﬀerent to normal modes.To deﬁne quasi-normal modes let us consider the wave equation(5)for potentials with V≥0which vanish for|x|>x0.Then in this case all solutions determined by data of compact support are bounded: |χ(t,x)|<C.We can use Laplace transformation techniques to represent such Living Reviews in Relativity(1999-2)9Quasi-Normal Modes of Stars and Black Holes solutions.The Laplace transformˆχ(s,x)(s>0real)of a solutionχ(t,x)isˆχ(s,x)= ∞0e−stχ(t,x)dt,(6) and satisﬁes the ordinary diﬀerential equations2ˆχ−ˆχ +Vˆχ=+sχ(0,x)+∂tχ(0,x),(7) wheres2ˆχ−ˆχ +Vˆχ=0(8) is the homogeneous equation.The boundedness ofχimplies thatˆχis analytic for positive,real s,and has an analytic continuation onto the complex half plane Re(s)>0.Which solutionˆχof this inhomogeneous equation gives the unique solution in spacetime determined by the data?There is no arbitrariness;only one of the Green functions for the inhomogeneous equation is correct!All Green functions can be constructed by the following well known method. Choose any two linearly independent solutions of the homogeneous equation f−(s,x)and f+(s,x),and deﬁneG(s,x,x )=1W(s)f−(s,x )f+(s,x)(x <x),f−(s,x)f+(s,x )(x >x),(9)where W(s)is the Wronskian of f−and f+.If we denote the inhomogeneity of(7)by j,a solution of(7)isˆχ(s,x)= ∞−∞G(s,x,x )j(s,x )dx .(10) We still have to select a unique pair of solutions f−,f+.Here the information that the solution in spacetime is bounded can be used.The deﬁnition of the Laplace transform implies thatˆχis bounded as a function of x.Because the potential V vanishes for|x|>x0,the solutions of the homogeneous equation(8) for|x|>x0aref=e±sx.(11) The following pair of solutionsf+=e−sx for x>x0,f−=e+sx for x<−x0,(12) which is linearly independent for Re(s)>0,gives the unique Green function which deﬁnes a bounded solution for j of compact support.Note that for Re(s)>0the solution f+is exponentially decaying for large x and f−is expo-nentially decaying for small x.For small x however,f+will be a linear com-bination a(s)e−sx+b(s)e sx which will in general grow exponentially.Similar behavior is found for f−.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt 10Quasi-Normal mode frequencies s n can be deﬁned as those complex numbers for whichf +(s n ,x )=c (s n )f −(s n ,x ),(13)that is the two functions become linearly dependent,the Wronskian vanishes and the Green function is singular!The corresponding solutions f +(s n ,x )are called quasi eigenfunctions.Are there such numbers s n ?From the boundedness of the solution in space-time we know that the unique Green function must exist for Re (s )>0.Hence f +,f −are linearly independent for those values of s .However,as solutions f +,f −of the homogeneous equation (8)they have a unique continuation to the complex s plane.In [35]it is shown that for positive potentials with compact support there is always a countable number of zeros of the Wronskian with Re (s )<0.What is the mathematical and physical signiﬁcance of the quasi-normal fre-quencies s n and the corresponding quasi-normal functions f +?First of all we should note that because of Re (s )<0the function f +grows exponentially for small and large x !The corresponding spacetime solution e s n t f +(s n ,x )is therefore not a physically relevant solution,unlike the normal modes.If one studies the inverse Laplace transformation and expresses χas a com-plex line integral (a >0),χ(t,x )=12πi +∞−∞e (a +is )t ˆχ(a +is,x )ds,(14)one can deform the path of the complex integration and show that the late time behavior of solutions can be approximated in ﬁnite parts of the space by a ﬁnite sum of the form χ(t,x )∼N n =1a n e (αn +iβn )t f +(s n ,x ).(15)Here we assume that Re (s n +1)<Re (s n )<0,s n =αn +iβn .The approxi-mation ∼means that if we choose x 0,x 1, and t 0then there exists a constant C (t 0,x 0,x 1, )such that χ(t,x )−N n =1a n e (αn +iβn )t f +(s n ,x ) ≤Ce (−|αN +1|+ )t (16)holds for t >t 0,x 0<x <x 1, >0with C (t 0,x 0,x 1, )independent of t .The constants a n depend only on the data [35]!This implies in particular that all solutions deﬁned by data of compact support decay exponentially in time on spatially bounded regions.The generic leading order decay is determined by the quasi-normal mode frequency with the largest real part s 1,i.e.slowest damping.On ﬁnite intervals and for late times the solution is approximated by a ﬁnite sum of quasi eigenfunctions (15).It is presently unclear whether one can strengthen (16)to a statement like (2),a pointwise expansion of the late time solution in terms of quasi-normal Living Reviews in Relativity (1999-2)11Quasi-Normal Modes of Stars and Black Holes modes.For one particular potential(P¨o schl-Teller)this has been shown by Beyer[42].Let us now consider the case where the potential is positive for all x,but decays near inﬁnity as happens for example for the wave equation on the static Schwarzschild spacetime.Data of compact support determine again solutions which are bounded[117].Hence we can proceed as before.Theﬁrst new point concerns the deﬁnitions of f±.It can be shown that the homogeneous equation(8)has for each real positive s a unique solution f+(s,x)such that lim x→∞(e sx f+(s,x))=1holds and correspondingly for f−.These functions are uniquely determined,deﬁne the correct Green function and have analytic continuations onto the complex half plane Re(s)>0.It is however quite complicated to get a good representation of these func-tions.If the point at inﬁnity is not a regular singular point,we do not even get converging series expansions for f±.(This is particularly serious for values of s with negative real part because we expect exponential growth in x).The next new feature is that the analyticity properties of f±in the complex s plane depend on the decay of the potential.To obtain information about analytic continuation,even use of analyticity properties of the potential in x is made!Branch cuts may occur.Nevertheless in a lot of cases an inﬁnite number of quasi-normal mode frequencies exists.The fact that the potential never vanishes may,however,destroy the expo-nential decay in time of the solutions and therefore the essential properties of the quasi-normal modes.This probably happens if the potential decays slower than exponentially.There is,however,the following way out:Suppose you want to study a solution determined by data of compact support from t=0to some largeﬁnite time t=T.Up to this time the solution is–because of domain of dependence properties–completely independent of the potential for suﬃciently large x.Hence we may see an exponential decay of the form(15)in a time range t1<t<T.This is the behavior seen in numerical calculations.The situation is similar in the case ofα-decay in quantum mechanics.A comparison of quasi-normal modes of wave equations and resonances in quantum theory can be found in the appendix,see section9.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt123Quasi-Normal Modes of Black HolesOne of the most interesting aspects of gravitational wave detection will be the connection with the existence of black holes[201].Although there are presently several indirect ways of identifying black holes in the universe,gravitational waves emitted by an oscillating black hole will carry a uniqueﬁngerprint which would lead to the direct identiﬁcation of their existence.As we mentioned earlier,gravitational radiation from black hole oscillations exhibits certain characteristic frequencies which are independent of the pro-cesses giving rise to these oscillations.These“quasi-normal”frequencies are directly connected to the parameters of the black hole(mass,charge and angu-lar momentum)and for stellar mass black holes are expected to be inside the bandwidth of the constructed gravitational wave detectors.The perturbations of a Schwarzschild black hole reduce to a simple wave equation which has been studied extensively.The wave equation for the case of a Reissner-Nordstr¨o m black hole is more or less similar to the Schwarzschild case,but for Kerr one has to solve a system of coupled wave equations(one for the radial part and one for the angular part).For this reason the Kerr case has been studied less thoroughly.Finally,in the case of Kerr-Newman black holes we face the problem that the perturbations cannot be separated in their angular and radial parts and thus apart from special cases[124]the problem has not been studied at all.3.1Schwarzschild Black HolesThe study of perturbations of Schwarzschild black holes assumes a small per-turbation hµνon a static spherically symmetric background metricds2=g0µνdxµdxν=−e v(r)dt2+eλ(r)dr2+r2 dθ2+sin2θdφ2 ,(17) with the perturbed metric having the formgµν=g0µν+hµν,(18) which leads to a variation of the Einstein equations i.e.δGµν=4πδTµν.(19) By assuming a decomposition into tensor spherical harmonics for each hµνof the formχ(t,r,θ,φ)= mχ m(r,t)r Y m(θ,φ),(20)the perturbation problem is reduced to a single wave equation,for the func-tionχ m(r,t)(which is a combination of the various components of hµν).It should be pointed out that equation(20)is an expansion for scalar quantities only.From the10independent components of the hµνonly h tt,h tr,and h rr transform as scalars under rotations.The h tθ,h tφ,h rθ,and h rφtransform asLiving Reviews in Relativity(1999-2)13Quasi-Normal Modes of Stars and Black Holes components of two-vectors under rotations and can be expanded in a series of vector spherical harmonics while the components hθθ,hθφ,and hφφtransform as components of a2×2tensor and can be expanded in a series of tensor spher-ical harmonics(see[202,212,152]for details).There are two classes of vector spherical harmonics(polar and axial)which are build out of combinations of the Levi-Civita volume form and the gradient operator acting on the scalar spherical harmonics.The diﬀerence between the two families is their parity. Under the parity operatorπa spherical harmonic with index transforms as (−1) ,the polar class of perturbations transform under parity in the same way, as(−1) ,and the axial perturbations as(−1) +11.Finally,since we are dealing with spherically symmetric spacetimes the solution will be independent of m, thus this subscript can be omitted.The radial component of a perturbation outside the event horizon satisﬁes the following wave equation,∂2∂t χ + −∂2∂r∗+V (r)χ =0,(21)where r∗is the“tortoise”radial coordinate deﬁned byr∗=r+2M log(r/2M−1),(22) and M is the mass of the black hole.For“axial”perturbationsV (r)= 1−2M r ( +1)r+2σMr(23)is the eﬀective potential or(as it is known in the literature)Regge-Wheeler potential[173],which is a single potential barrier with a peak around r=3M, which is the location of the unstable photon orbit.The form(23)is true even if we consider scalar or electromagnetic testﬁelds as perturbations.The parameter σtakes the values1for scalar perturbations,0for electromagnetic perturbations, and−3for gravitational perturbations and can be expressed asσ=1−s2,where s=0,1,2is the spin of the perturbingﬁeld.For“polar”perturbations the eﬀective potential was derived by Zerilli[212]and has the form V (r)= 1−2M r 2n2(n+1)r3+6n2Mr2+18nM2r+18M3r3(nr+3M)2,(24)1In the literature the polar perturbations are also called even-parity because they are characterized by their behavior under parity operations as discussed earlier,and in the same way the axial perturbations are called odd-parity.We will stick to the polar/axial terminology since there is a confusion with the deﬁnition of the parity operation,the reason is that to most people,the words“even”and“odd”imply that a mode transforms underπas(−1)2n or(−1)2n+1respectively(for n some integer).However only the polar modes with even have even parity and only axial modes with even have odd parity.If is odd,then polar modes have odd parity and axial modes have even parity.Another terminology is to call the polar perturbations spheroidal and the axial ones toroidal.This deﬁnition is coming from the study of stellar pulsations in Newtonian theory and represents the type ofﬂuid motions that each type of perturbation induces.Since we are dealing both with stars and black holes we will stick to the polar/axial terminology.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt14where2n=( −1)( +2).(25) Chandrasekhar[54]has shown that one can transform the equation(21)for “axial”modes to the corresponding one for“polar”modes via a transforma-tion involving diﬀerential operations.It can also be shown that both forms are connected to the Bardeen-Press[38]perturbation equation derived via the Newman-Penrose formalism.The potential V (r∗)decays exponentially near the horizon,r∗→−∞,and as r−2∗for r∗→+∞.From the form of equation(21)it is evident that the study of black hole perturbations will follow the footsteps of the theory outlined in section2.Kay and Wald[117]have shown that solutions with data of compact sup-port are bounded.Hence we know that the time independent Green function G(s,r∗,r ∗)is analytic for Re(s)>0.The essential diﬃculty is now to obtain the solutions f±(cf.equation(10))of the equations2ˆχ−ˆχ +Vˆχ=0,(26) (prime denotes diﬀerentiation with respect to r∗)which satisfy for real,positives:f+∼e−sr∗for r∗→∞,f−∼e+r∗x for r∗→−∞.(27) To determine the quasi-normal modes we need the analytic continuations of these functions.As the horizon(r∗→∞)is a regular singular point of(26),a representation of f−(r∗,s)as a converging series exists.For M=12it reads:f−(r,s)=(r−1)s∞n=0a n(s)(r−1)n.(28)The series converges for all complex s and|r−1|<1[162].(The analytic extension of f−is investigated in[115].)The result is that f−has an extension to the complex s plane with poles only at negative real integers.The representation of f+is more complicated:Because inﬁnity is a singular point no power series expansion like(28)exists.A representation coming from the iteration of the deﬁning integral equation is given by Jensen and Candelas[115],see also[159]. It turns out that the continuation of f+has a branch cut Re(s)≤0due to the decay r−2for large r[115].The most extensive mathematical investigation of quasi-normal modes of the Schwarzschild solution is contained in the paper by Bachelot and Motet-Bachelot[35].Here the existence of an inﬁnite number of quasi-normal modes is demonstrated.Truncating the potential(23)to make it of compact support leads to the estimate(16).The decay of solutions in time is not exponential because of the weak decay of the potential for large r.At late times,the quasi-normal oscillations are swamped by the radiative tail[166,167].This tail radiation is of interest in its Living Reviews in Relativity(1999-2)。

黑暗闪光人物介绍英文作文

黑暗闪光人物介绍英文作文Title: Introduction to the Enigmatic Antihero。

In the realm of literature and popular culture, there exists a compelling archetype that captivates audienceswith its complexity and ambiguity – the enigmatic antihero. These characters, often shrouded in darkness yet possessing a magnetic allure, challenge conventional notions ofmorality and virtue. In this essay, we will explore the intricacies of the enigmatic antihero, examining their characteristics, motivations, and enduring appeal.At the heart of the enigmatic antihero lies a profound sense of contradiction. Unlike traditional heroes who embody noble ideals and unwavering righteousness, the antihero navigates a moral landscape fraught with shades of gray. They may possess admirable qualities such as intelligence, charisma, or even a sense of justice, yet these virtues are often overshadowed by their morally ambiguous actions. This inherent duality lends depth andcomplexity to their character, inviting audiences to ponder the nature of right and wrong.One defining trait of the enigmatic antihero is their troubled past or traumatic experiences that have shaped their worldview. Whether it be a tragic loss, a profound betrayal, or a sense of disillusionment with society, these characters are often driven by inner demons that fuel their actions. Their motivations may range from seeking revenge and redemption to simply surviving in a hostile world. This sense of internal conflict adds layers of psychological depth to the antihero, making them both relatable and compelling.Moreover, the enigmatic antihero is often portrayed as an outsider or loner, estranged from mainstream society. This alienation may stem from their refusal to conform to societal norms or their inability to connect with others on a meaningful level. Despite their reluctance to form bonds, antiheroes often find themselves drawn to individuals who challenge their beliefs or provide a glimpse of redemption. These complex relationships serve to humanize the antihero,showcasing their capacity for vulnerability and growth.Perhaps what truly distinguishes the enigmatic antihero is their ambiguous moral code. Unlike traditional heroes who adhere to a strict sense of right and wrong, antiheroes operate in a moral gray area where the ends may justify the means. They are capable of committing morally questionable acts in pursuit of their goals, yet they may also display moments of compassion or selflessness. This moral ambiguity forces audiences to confront their own preconceptions and wrestle with the complexities of the human condition.The enduring appeal of the enigmatic antihero lies in their ability to mirror the contradictions and complexities of real life. In a world that is often defined by uncertainty and moral ambiguity, these characters offer a sense of catharsis and introspection. They remind us that heroism is not always defined by grand gestures or noble deeds, but by the choices we make in the face of adversity.In conclusion, the enigmatic antihero stands as a testament to the enduring power of storytelling to explorethe depths of human nature. Through their complexity, contradiction, and moral ambiguity, these characters challenge us to question our assumptions and confront the complexities of the human experience. In a world that is rarely black and white, the enigmatic antihero shines as a beacon of gray, reminding us that the true measure of heroism lies in our ability to navigate the shadows.。

2021届高考英语二轮复习语法填空-阅读理解题源02-中子星有多大？-含答案

备考2021高考语法填空02中子星有多大？第一部分练习Neutron-star collisions teach us about the nature of the densest matter in 1、________ Universe. The properties of this matter can 2、________ (understand) in part by measuring the radii of neutron stars. Until recently, observers inferred 3、________ typical neutron-star radii ranged from 10–14 km with large uncertainties. The present work determines the neutron-star radius4、________ (depend) and more accurately. The improved constraints will have implications for the interpretation of future 5、________ (observe) of neutron stars and will help scientists 6、________ (well) understand the universe.Neutron stars are the remnants of supernova explosions 7、________ have extreme properties. In particular, the cores of neutron stars are made8、________ of extremely dense nuclear matter. 9、________ two neutron stars collide, they give off gravitational waves, electromagnetic radiation, cosmic rays, and neutrinos, so-called multi-messenger signals. Scientists observed one of these binary neutron-star collisions with several multi-messenger signals 10、________ August 2017.参考答案：1、the2、be understood3、that4、independently5、observations6、better7、and8、up9、When10、in备考2021高考科技类时政新闻阅读题源02How large are neutron stars?中子星有多大？Part 1 第一部分导读：一个跨学科的研究小组已经确定了中子星半径的新的、更窄的限制。

Neutron Stars, Pulsars and Supernova Remnants concluding remarks

a r X i v :a s t r o -p h /0208563v 1 30 A u g 2002Proceedings of the 270.WE-Heraeus Seminar on:“Neutron Stars,Pulsars and Supernova Remnants”Physikzentrum Bad Honnef,Germany,Jan.21-25,2002,eds.W.Becker,H.Lesch &J.Tr¨u mper,MPE Report 278,pp.300-302Neutron Stars,Pulsars and Supernova Remnants:concluding remarksF.Pacini 1,21Arcetri Astrophysical Observatory,L.go E.Fermi,5,I-50125Firenze,Italy2Dept.of Astronomy and Space Science,University of Florence,L.go E.Fermi,2,I-50125Firenze,Italy1.IntroductionMore than 30years have elapsed since the discovery of pul-sars (Hewish et al.1968)and the realization that they are connected with rotating magnetized neutron stars (Gold 1968;Pacini 1967,1968).It became soon clear that these objects are responsible for the production of the relativis-tic wind observed in some Supernovae remnants such as the Crab Nebula.For many years,the study of pulsars has been car-ried out mostly in the radio band.However,many recent results have come from observations at much higher fre-quencies (optical,X-rays,gamma rays).These observa-tions have been decisive in order to establish a realistic demography and have brought a better understanding of the relationship between neutron stars and SN remnants.The Proceedings of this Conference cover many aspects of this relationship (see also previous Conference Proceed-ings such as Bandiera et al.1998;Slane and Gaensler,2002).Because of this reason,my summary will not re-view all the very interesting results which have been pre-sented here and I shall address brieﬂy just a few issues.The choice of these issues is largely personal:other col-leagues may have made a diﬀerent selection.2.Demography of Neutron Stars:the role of the magnetic ﬁeld For a long time it has been believed that only Crab-like remnants (plerions)contain a neutron star and that the typical ﬁeld strength of neutron stars is 1012Gauss.The basis of this belief was the lack of pulsars associated with shell-type remnants or other manifestations of a relativis-tic wind.The justiﬁcation given is that some SN explo-sions may blow apart the entire star.Alternatively,the central object may become a black hole.However,the number of shell remnants greatly exceeds that of pleri-ons:it becomes then diﬃcult to invoke the formation of black holes,an event much more rare than the formation of neutron stars.The suggestion that shell remnants such as Cas A could be associated with neutron stars which have rapidly lost their initial rotational energy because of an ultra-strong magnetic ﬁeld B ∼1014−1015Gauss (Cavaliere &Pacini,1970)did receive little attention.The observa-tional situation has now changed:a compact thermal X-ray source has been discovered close to the center of Cas A (Tananbaum,1999)and it could be the predicted ob-ject.Similar sources have been found in association with other remnants and are likely to be neutron stars.We have also heard during this Conference that some shell-type remnants (including Cas A)show evidence for a weak non-thermal X-ray emission superimposed on the thermal one:this may indicate the presence of a residual relativis-tic wind produced in the center.Another important result has been the discovery of neutron stars with ultra-strong magnetic ﬁelds,up to 1014−1015G.In this case the total magnetic energy could be larger than the rotational en-ergy (”magnetars”).This possibility had been suggested long time ago (Woltjer,1968).It should be noticed,how-ever,that the slowing down rate determines the strength of the ﬁeld at the speed of light cylinder and that the usually quoted surface ﬁelds assume a dipolar geometry corresponding to a braking index n =3.Unfortunately the value of n has been measured only in a few cases and it ranges between 1.4−2.8(Lyne et al.,1996).The present evidence indicates that neutron stars man-ifest themselves in diﬀerent ways:–Classical radio pulsars (with or without emission at higher frequencies)where the rotation is the energy source.–Compact X-ray sources where the energy is supplied by accretion (products of the evolution in binary sys-tems).–Compact X-ray sources due to the residual thermal emission from a hot surface.–Anomalous X-ray pulsars (AXP)with long periods and ultra strong ﬁelds (up to 1015Gauss).The power emit-ted by AXPs exceeds the energy loss inferred from the slowing down rate.It is possible that AXPs are asso-ciated with magnetized white dwarfs,rotating close to the shortest possible period (5−10s)or,alternatively,they could be neutron stars whose magnetic energy is dissipated by ﬂares.–Soft gamma-ray repeaters.2 F.Pacini:Neutron Stars,Pulsars and Supernova Remnants:concluding remarks In addition it is possible that some of the unidentiﬁedgamma ray sources are related to neutron stars.Thepresent picture solves some previous inconsistencies.Forinstance,the estimate for the rate of core-collapse Super-novae(roughly one every30-50years)was about a factorof two larger than the birth-rate of radio pulsars,suggest-ing already that a large fraction of neutron stars does not appear as radio pulsars.The observational evidence supports the notion of a large spread in the magnetic strength of neutron stars and the hypothesis that this spread is an important factor in determining the morphology of Supernova remnants.A very strongﬁeld would lead to the release of the bulk of the rotational energy during a short initial period(say, days up to a few years):at later times the remnant would appear as a shell-type.A more moderateﬁeld(say1012 Gauss or so)would entail a long lasting energy loss and produce a plerion.3.Where are the pulses emitted?Despite the great wealth of data available,there is no gen-eral consensus about the radiation mechanism for pulsars. The location of the region where the pulses are emitted is also controversial:it could be located close to the stellar surface or,alternatively,in the proximity of the speed of light cylinder.The radio emission is certainly due to a coherent pro-cess because of the very high brightness temperatures(T b up to and above1030K have been observed).A possible model invokes the motion of bunches of charges sliding along the curvedﬁeld lines with a relativistic Lorentz fac-torγsuch that the critical frequencyνc∼c2π:Ψ∼10−2;B⊥∼104G;γ∼102−103.The model leads to the expectation of a very fast de-crease of the synchrotron intensity with period because of the combination of two factors:a)the reduced particles ﬂux when the period increases;b)the reduced eﬃciency of synchrotron losses(which scale∝B2∝R−6L∝P−6)at the speed of light cylinder(Pacini,1971;Pacini&Salvati 1983,1987).The predictionﬁts the observed secular de-crease of the optical emission from the Crab Nebula and the magnitude of the Vela pulsar.A recent re-examination of all available optical data conﬁrms that this model can account for the luminosity of the known optical pulsars (Shearer and Golden,2001).If so,the optical radiation supports strongly the notion that the emitting region is located close to the speed of light cylinder.4.A speculation:can the thermal radiation fromyoung neutron stars quench the relativisticwind?Myﬁnal remarks concern the possible eﬀect of the ther-mal radiation coming from the neutron star surface upon the acceleration of particles.This problem has been inves-tigated for the near magnetosphere(Supper&Truemper, 2000)and it has been found that the Inverse Compton Scattering(ICS)against the thermal photons is impor-tant only in marginal cases.However,if we assume that the acceleration of the relativistic wind and the radiation of pulses occur close to the speed of light cylinder,the sit-uation becomes diﬀerent and the ICS can dominate over synchrotron losses for a variety of parameters.The basic reason is that the importance of ICS at the speed of light distance R L scales like the energy density of the thermal photons uγ∝R−2L∝P−2;on the other hand, the synchrotron losses are proportional to the magnetic energy density in the same region u B∝R−6L∝P−6.Numerically,oneﬁnds that ICS losses dominate over synchrotron losses ifT6>0.4B1/2121012G; P s is the pulsar period in seconds).The corresponding upper limit for the energy of the electrons,assuming that the acceleration takes place for a length of order of the speed of light distance and that the gains are equal to the losses is given by:E max≃1.2×103T6−4P s GeV.F.Pacini:Neutron Stars,Pulsars and Supernova Remnants:concluding remarks3Provided that the particles are accelerated and radi-ate in proximity of the speed of light cylinder distance,weconclude that the thermal photons can limit the acceler-ation of particles,especially in the case of young and hotneutron stars.It becomes tempting to speculate that thismay postpone the beginning of the pulsar activity untilthe temperature of the star is suﬃciently low.The mainmanifestation of neutron stars in this phase would be aﬂux of high energy photons in the gamma-ray band,dueto the interaction of the quenched wind with the thermalphotons from the stellar surface.This model and its ob-servational consequences are currently under investigation(Amato,Blasi,Pacini,work in progress).ReferencesAloisio,R.,&Blasi,P.2002,Astrop.Phys.,Bandiera,R.,et al.1998,Proc.Workshop”The Relationshipbetween Neutron Stars and Supernova Remnants”,Mem.Societ Astronomica Italiana,vol.69,n.4Cavaliere,A.,&Pacini,F.1970,ApJ,159,170Gold,T.1968,Nature,217,731Hewish A.,et al.1968,Nature217,709Lyne,G.,et al.1996,Nature,381,497Pacini,F.1967,Nature,216,567Pacini,F.1968,Nature,219,145Pacini,F.1971,ApJ,163,L17Pacini,F.,&Salvati,M.1983,ApJ,274,369Pacini F.,&Salvati,M.1987,ApJ.,321,447Shearer,A.,and Golden,A.2001,ApJ,547,967Slane,P.,Gaensler,B.2002,Proc.Workshop”Neutron Starsin Supernova Remnants”ASP Conference Proceedings(inpress)Supper,R.,&Trumper,J.2000,A&A,357,301Tananbaum,B,et al.1999,IAU Circular7246Thompson,C.,Duncan,R.C.1996,ApJ,473,322Woltjer,L.1968,ApJ,152,179。

了不起的盖茨比第七章英语单词知乎

了不起的盖茨比第七章英语单词知乎全文共3篇示例，供读者参考篇1The Vocabulary of Chapter 7 in The Great Gatsby: A Student's In-Depth AnalysisWhat's up, fellow literature lovers and word nerds? Today, we're diving deep into the rich and symbolic vocabulary found in Chapter 7 of F. Scott Fitzgerald's masterpiece, The Great Gatsby. As a student who adores dissecting literary works, I'm thrilled to share my insights and personal interpretations of the language used in this pivotal chapter.First things first, let's set the stage. Chapter 7 is the climax of the novel, where tensions reach a boiling point, and the illusions surrounding Gatsby's persona and his pursuit of Daisy begin to unravel. The atmosphere is thick with dramatic irony, and Fitzgerald masterfully employs evocative diction to convey the underlying emotions and thematic elements.One word that immediately caught my attention is "inexplicable." Fitzgerald describes the "inexplicable certified confusion" surrounding Gatsby's background and wealth. Thisword not only highlights the mystery and ambiguity surrounding Gatsby but also foreshadows the eventual revelation of his shady past and the disillusionment that follows.Moving on, we encounter the phrase "fantastic conceits." This phrase perfectly encapsulates the grandiose delusions and unrealistic expectations that have driven the characters' actions throughout the novel. It's a poignant reminder of the theme of disillusionment and the harsh reality that often shatters our idealized dreams.Another standout word is "appalling." Used to describe Gatsby's reaction to Tom's revelations about his past, it conveys the profound sense of shock and dismay that overwhelms him as his carefully crafted persona crumbles. The intensity of this word mirrors the devastating impact of the truth on Gatsby's psyche.Let's not forget the word "colossal." Fitzgerald employs this adjective to depict the sheer magnitude of Gatsby's illusions and the scale of his dreams. It's a testament to the grandiose nature of his aspirations, which ultimately prove to be his undoing.Shifting gears, the phrase "grotesque, circumstantial" caught my eye. Fitzgerald uses it to describe the evidence Tom presents against Gatsby, hinting at the sordid and unsavory details of his past. This phrase adds a sense of ugliness and distortion to therevelations, further emphasizing the stark contrast between Gatsby's idealized persona and the harsh realities of his life.One word that struck me as particularly powerful is "holocaust." Fitzgerald employs this term to describe the intense emotional turmoil and devastation that Gatsby experiences as his dreams are shattered. The word's connotations of complete destruction and sacrifice resonate deeply with the theme of disillusionment and the sacrifices Gatsby made in pursuit of his dreams.Finally, let's explore the phrase "obscurity borne once more in line of sight." This poetic line refers to the resurfacing of Gatsby's obscure past, which had been carefully concealed until this point. It's a haunting reminder that no matter how hard we try to reinvent ourselves, our pasts have a way of catching up with us, and the truth ultimately prevails.In conclusion, the vocabulary employed by Fitzgerald in Chapter 7 of The Great Gatsby is a masterclass in literary craftsmanship. Each word and phrase is meticulously chosen to convey deeper meanings, symbolism, and thematic elements. From the sense of mystery and ambiguity to the harsh realities of disillusionment, the diction in this chapter is a powerful tool thatenhances the emotional impact of the narrative and leaves a lasting impression on the reader.So, there you have it, my fellow word enthusiasts – a deep dive into the vocabulary of Chapter 7 of The Great Gatsby. I hope this analysis has piqued your interest and inspired you to delve deeper into the rich tapestry of language woven by Fitzgerald in this literary masterpiece.篇2Vocabulary Gems from Chapter 7 of The Great GatsbyHey fellow bookworms! As an avid reader and lover of literature, I always look forward to diving deep into the linguistic riches found in classic novels. Today, I want to share some of the juiciest vocabulary morsels from Chapter 7 of F. Scott Fitzgerald's masterpiece, The Great Gatsby.Let's kick things off with a word that perfectly encapsulates the lavish lifestyle portrayed in the novel: "sumptuous." When Gatsby's house is described as "a solemn, haunting house, broodingly immense among its fringed and sumptuous gardens," the word "sumptuous" conjures up images of extravagant opulence and luxurious splendor. It's a word that screams "over-the-top" and "no expense spared."Speaking of lavish parties, the word "revelers" caught my eye. It refers to the raucous, carefree merrymakers who attended Gatsby's legendary bashes. Can't you just picture a horde of revelers, decked out in their finest threads, dancing the night away with reckless abandon?Now, let's delve into a word that carries a more ominous undertone: "sinister." When Nick describes Gatsby's smile as having "a quality of eternal reassurance in that conclusive smile, the vigorous promise that the rock of the world was founded securely on a fairy's wing," the word "sinister" is used to describe the smile's "sinister resilience." This word choice hints at something darker lurking beneath the surface, foreshadowing the tragic events to come.Moving on, we have the delightfully whimsical word "oblivious." When the narrative states that Gatsby was "oblivious of the sunshine," it paints a vivid picture of someone so lost in their own thoughts and preoccupations that they fail to notice the world around them. It's a relatable feeling we've all experienced at one point or another.Next up is a word that evokes a sense of mystique and intrigue: "inscrutable." When Nick observes Gatsby's "inscrutable vision," it suggests a depth and complexity to Gatsby's characterthat defies easy comprehension. It's a tantalizing hint at the layers of mystery surrounding this enigmatic figure.Let's not forget the deliciously descriptive word "grotesque." When Nick describes the "grotesque, fascinating brightness" of Gatsby's wealth and possessions, it simultaneously conveys a sense of awe and repulsion. It's a word that perfectly captures the allure and excess of the Gatsby lifestyle while hinting at its inherent ugliness.Moving on, we have the evocative word "haunt." When Nick mentions Gatsby's "haunting loneliness," it conjures up images of a specter-like figure, forever trapped in a state of melancholic solitude. It's a word that adds a haunting, ethereal quality to Gatsby's character.Finally, let's explore the word "permeate." When Nick describes the "permeating scent" of Gatsby's house, it creates a vivid sensory experience, as if the reader can smell the rich, lingering aromas wafting through the air. It's a word that adds depth and texture to the descriptive passages.Well, there you have it, fellow word nerds! A tantalizing glimpse into the rich vocabulary that permeates Chapter 7 of The Great Gatsby. Whether you're a seasoned literary connoisseur or a budding bibliophile, these words are sure to add somelinguistic sparkle to your reading experience. Happy reading, and may the words dance off the page and into your heart!篇3The Dazzling Vocabulary of Gatsby's ReunionChapter 7 of The Great Gatsby is a pivotal moment in the novel, where the long-awaited reunion between Gatsby and Daisy finally occurs. As a student of literature, I was struck by the masterful way Fitzgerald uses language to convey the intense emotions and tensions at play during this climactic scene. The vocabulary he employs is rich, evocative, and at times, dazzlingly complex, adding layers of depth and nuance to the narrative. Let's delve into some of the most captivating words and phrases from this chapter.One word that immediately caught my attention was "colossal," used to describe Gatsby's dreams and aspirations. This adjective conjures up images of something vast, monumental, and awe-inspiring, perfectly capturing the grandiose nature of Gatsby's pursuit of Daisy. The word's etymological roots in Greek further emphasize its magnitude, lending a sense of timelessness and universality to Gatsby's desires.Another striking word is "feign," which Fitzgerald employs when describing Gatsby's attempts to appear casual and nonchalant in Daisy's presence. The term "feign" suggests a deliberate act of deception or pretense, hinting at the complex web of emotions and facades that Gatsby has woven around himself. This word choice skillfully underscores the deep vulnerability and insecurity that lie beneath Gatsby's carefully constructed persona.Fitzgerald's use of the word "ineffable" is particularly noteworthy, as he applies it to describe the quality of Gatsby's smile when he finally reunites with Daisy. "Ineffable" suggests something that is too profound or too sublime to be adequately expressed in words, perfectly capturing the depth of Gatsby's emotional state in that moment. This word choice elevates the scene to a level of almost spiritual transcendence, reflecting the intensity of Gatsby's long-held dreams and desires.The phrase "furnace of vitriol" is another evocative turn of phrase that caught my eye. Fitzgerald uses this vivid metaphor to describe Tom Buchanan's simmering anger and hostility towards Gatsby. The word "vitriol" conjures up images of a highly corrosive and toxic substance, while "furnace" implies an intense and uncontrollable heat, together painting a powerful picture ofTom's barely contained rage. This metaphor foreshadows the explosive confrontation that ultimately erupts between the two men, heightening the sense of tension and impending conflict.Fitzgerald's use of the word "appalling" is particularly interesting, as it carries a dual meaning. On one level, it suggests something that is shocking or horrifying, reflecting the profound emotional turmoil and disillusionment that Gatsby experiences as his dreams begin to unravel. However, the word "appalling" can also mean "causing dismay or disappointment," which aptly describes the sense of disenchantment that Gatsby must feel as he realizes the true nature of Daisy's character and the insurmountable challenges standing in the way of their reunion.The phrase "grotesque and fantastic conceits" is another standout example of Fitzgerald's rich vocabulary. "Conceits" refers to fanciful or imaginative notions, while "grotesque" and "fantastic" suggest something that is both distorted and whimsical. This phrase is used to describe the extravagant and over-the-top decorations adorning Gatsby's mansion, reflecting the grandiose and almost absurd lengths to which he has gone in his pursuit of wealth and status – all in an effort to win over Daisy. This vivid description not only paints a striking visualpicture but also serves as a metaphor for the distorted and fantastical nature of Gatsby's dreams and aspirations.Throughout Chapter 7, Fitzgerald employs a multitude of evocative and richly descriptive words and phrases, such as "riotous," "curtains of azaleas," "vanished trees," and "ecstatic caress." These word choices not only create a vivid and immersive reading experience but also serve to reinforce the overarching themes of the novel, such as the futility of pursuing the past, the corrupting influence of wealth and materialism, and the disillusionment that often accompanies the pursuit of idealized dreams.As a student of literature, I am in awe of Fitzgerald's masterful command of language and his ability to weave together words in a way that not only tells a compelling story but also resonates on a deeper, emotional level. The vocabulary he employs in Chapter 7, with its rich tapestry of evocative and nuanced terms, is a testament to his literary genius and his profound understanding of the human condition.In conclusion, the dazzling vocabulary and artful use of language in Chapter 7 of The Great Gatsby are a true hallmark of Fitzgerald's literary prowess. From the grandiose "colossal" to the sublime "ineffable," and the vivid "furnace of vitriol," eachword is carefully chosen and expertly woven into the narrative, adding depth, nuance, and emotional resonance to this pivotal moment in the novel. As a student, exploring and unpacking the meanings and connotations of these words has not only enriched my understanding of the text but has also deepened my appreciation for the power of language and the craft of great literary works.。

理解黑洞需要一定的想象力和科学知识英语

理解黑洞需要一定的想象力和科学知识英语Understanding Black Holes Requires a Certain Degree of Imagination and Scientific KnowledgeThe vastness of the universe is a constant source of fascination and wonder for human beings. As we gaze up at the night sky, our eyes are drawn to the twinkling stars, the enigmatic planets, and the mysterious celestial bodies that lie beyond our immediate reach. Among these cosmic enigmas, perhaps none have captured the public's imagination more than the phenomenon known as the black hole.Black holes are regions of space-time where the gravitational pull is so immense that nothing, not even light, can escape their grasp. These cosmic behemoths are the result of the collapse of massive stars at the end of their life cycle. When a star runs out of fuel, its core can no longer support the outward pressure that counteracts the inward pull of gravity, causing it to implode and form a singularity – a point in space-time where the laws of physics as we know them break down.Understanding the true nature of black holes requires a certaindegree of imagination and scientific knowledge. On the surface, the concept of a region of space-time where nothing can escape may seem straightforward, but the deeper one delves into the intricacies of black hole physics, the more complex and mind-bending the subject becomes.One of the key aspects of black holes that challenges our intuitive understanding is the concept of the event horizon. The event horizon is the point of no return – the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. Visualizing this invisible barrier and comprehending its significance is a task that requires a significant amount of abstract reasoning.Imagine a person standing on the edge of a cliff, gazing out at the vast expanse of the ocean. As they look down, they can see the waves crashing against the rocks below, but they know that if they were to step over the edge, they would be unable to return. The event horizon of a black hole is analogous to this – it is the point at which the gravitational forces become so overwhelming that even the fastest-moving particles in the universe, photons of light, cannot escape.But the event horizon is just the tip of the iceberg when it comes to the complexities of black hole physics. As one delves deeper into the subject, the challenges to our understanding only grow moreprofound.Consider, for example, the concept of time dilation. According to Einstein's theory of general relativity, the passage of time is affected by the presence of strong gravitational fields. As an object approaches the event horizon of a black hole, the rate at which time passes for that object becomes increasingly slowed down relative to an observer outside the black hole. This means that from the perspective of an external observer, the object appears to be frozen in time, gradually becoming fainter and fainter as it crosses the event horizon.Visualizing this phenomenon requires a significant amount of imagination and a deep understanding of the principles of relativity. It challenges our everyday experience of time and forces us to consider the universe from a radically different perspective – one where the familiar laws of physics no longer apply in the same way.Another aspect of black holes that pushes the limits of our imagination is the nature of the singularity itself. At the center of a black hole, where all the matter and energy of the collapsed star is concentrated, the laws of physics as we know them break down completely. This point of infinite density and infinite curvature of space-time is known as the singularity, and it represents the ultimate limit of our current scientific understanding.Trying to comprehend the singularity, a region where the very fabric of space-time is torn apart, is a task that requires a leap of imagination that few can truly make. It forces us to confront the limitations of our own understanding and to grapple with the fundamental mysteries of the universe.Despite these challenges, the study of black holes has been a cornerstone of modern astrophysics and has led to numerous groundbreaking discoveries. Through the use of sophisticated telescopes and advanced mathematical models, scientists have been able to observe the behavior of black holes in unprecedented detail, shedding light on the most extreme and enigmatic phenomena in the cosmos.From the detection of gravitational waves, the ripples in the fabric of space-time caused by the collision of black holes, to the stunning images of the supermassive black hole at the center of the Milky Way, the study of black holes has pushed the boundaries of our scientific knowledge and our understanding of the universe.But perhaps the greatest contribution of the study of black holes is the way it has challenged our fundamental assumptions about the nature of reality. By confronting us with the limits of our own understanding, black holes have forced us to reckon with thepossibility that there are aspects of the universe that may forever remain beyond our grasp.In this sense, the study of black holes is not just a scientific endeavor, but a philosophical one as well. It reminds us that the universe is a vast and mysterious place, and that our knowledge, no matter how extensive, is always a work in progress. It challenges us to remain humble in the face of the unknown and to continue to explore the limits of our understanding with curiosity, wonder, and a willingness to adapt our perspectives as new evidence emerges.Ultimately, the study of black holes is a testament to the power of the human mind to grapple with the most complex and enigmatic phenomena in the universe. It requires a unique blend of imagination, scientific knowledge, and a willingness to embrace the unknown – qualities that have defined the pursuit of scientific discovery since the dawn of human civilization.。

The Properties of Neutron Stars

The Properties of Neutron Stars IntroductionNeutron stars are the remnants of supernova explosions, they are some of the most extreme objects in the universe. They are incredibly dense, with a mass comparable to the sun, but a size comparable to a city. In this article, we will explore the properties of neutron stars.FormationNeutron stars are formed when a massive star runs out of fuel and undergoes a supernova explosion. During the supernova, the core of the star collapses, creating an incredibly dense object known as a neutron star. The collapsed core is composed mainly of neutrons, which are tightly packed together due to the intense gravitational forces.SizeNeutron stars are incredibly small compared to normal stars, with a typical radius of around 10 km. This makes them incredibly dense, with a mass several times that of our sun, compressed into a volume the size of a city.DensityThe density of a neutron star is incredible, with an average density of around 10^17 kg/m^3. This is around 1 billion times denser than the density of water. Due to their extreme density, neutron stars have a strong gravitational field, which can distort nearby spacetime.Magnetic FieldsNeutron stars are known for their incredibly strong magnetic fields, which can be trillions of times stronger than the Earth's magnetic field. These magnetic fields can create intense radiation, including X-rays and gamma rays, which can be detected by telescopes.RotationNeutron stars can rotate incredibly quickly, with some rotating hundreds of times per second. This rapid rotation is due to their small size and high density, which allows them to conserve their angular momentum as they collapse.Neutrino EmissionNeutron stars are also known for emitting neutrinos, which are subatomic particles that can pass through matter almost unimpeded. These neutrinos are created during the supernova explosion that forms the neutron star, and can carry away up to 99% of the energy produced.ConclusionNeutron stars are some of the most extreme objects in the universe, with incredible properties that make them fascinating to study. Their small size and incredible density make them a unique laboratory for studying the laws of physics under extreme conditions. As we continue to explore and study these objects, we will learn more about the mysteries of the universe.。

克卜勒英文版

克卜勒英文版Kepler is a brilliant scientist who significantly contributed to the field of astronomy. 克卜勒是一位杰出的科学家，为天文学领域作出了重要贡献。

His work on planetary motion revolutionized our understanding of the solar system. 他关于行星运动的研究彻底改变了我们对太阳系的认识。

Kepler’s three laws of planetary motion are fundamental principles that continue to be studied and applied in modern astrophysics. 克卜勒的三大行星运动定律是现代天体物理学中一直被研究和应用的基本原理。

One of the most remarkable aspects of Kepler’s work is his meticulous observations and mathematical calculations. 克卜勒工作最引人注目的一个方面是他细致的观察和数学计算。

He spent years studying the movements of planets and meticulously recorded his findings. 他花费多年时间研究行星的运动，并详细记录下他的发现。

Kepler's dedication to his research and his attention to detail set him apart as a scientist of great integrity and perseverance. 克卜勒对研究的投入和对细节的关注使他成为一位极具诚信和毅力的科学家。

On the mass of the neutron star in V395 Car2S 0921-630

a r X i v :0707.2067v 2 [a s t r o -p h ] 24 S e p 2007TO APPEAR IN THEA STROPHYSICAL J OURNAL L ETTERSPreprint typeset using L A T E X style emulateapj v.10/09/06ON THE MASS OF THE NEUTRON STAR IN V395CAR/2S 0921–630D.S TEEGHS 1,2ANDP.G.J ONKER 2,3,4to appear in the Astrophysical Journal LettersABSTRACTWe report high-resolution optical spectroscopy of the low-mass X-ray binary V395Car/2S 0921–630ob-tained with the MIKE echelle spectrograph on the Magellan-Clay telescope.Our spectra are obtained near inferior conjunction of the mass donor star and we exploit the absorption lines originating from the back-side of the K-type object to accurately derive its rotational ing K0-K1III templates,we ﬁnd v sin i =32.9±0.8km s −1.We show that the choice of template star and the assumed limb darkening coefﬁcient has little impact on the derived rotational velocity.This value is a signiﬁcant revision downwards compared to previously published values.We derive new system parameter constraints in the light of our much lower rotational velocity.We ﬁnd M 1=1.44±0.10M ⊙,M 2=0.35±0.03M ⊙,and q =0.24±0.02where the errors have been estimated through a Monte-Carlo simulation.A possible remaining systematic effect is the fact that we may be over-estimating the orbital velocity of the mass donor due to irradiation effects.However,any correction for this effect will only reduce the compact object mass further,down to a minimum mass of M 1=1.05±0.08M ⊙.There is thus strong evidence that the compact object in this binary is a neutron star of rather typical mass and that the previously reported mass values of 2-4M ⊙were too high due to an over-estimate of the rotational broadening.Subject headings:stars:individual (V395Car/2S 0921–630)—accretion:accretion discs —stars:binaries —stars:neutron —X-rays:binaries1.INTRODUCTIONLow–mass X–ray binaries (LMXBs)are binary systems in which a neutron star or a black hole accretes matter from a low–mass companion star.These systems provide a labora-tory to test the behavior of matter under physical conditions that are unattainable on Earth.One of the ultimate goals of the study of neutron stars is to determine the equation of state (EoS)that describes the relation between pressure and density of matter under the extreme conditions encountered in neutron stars (Lattimer &Prakash 2001,2004).As a result of the cur-rent paucity of observational constraints there are many the-ories of the EoS of matter at neutron–star densities.Through the measurement of the masses and radii of neutron stars these theories can be tested.For a speciﬁc EoS,one can derive a ﬁrm upper limit on the mass of the neutron star,above which the object is not stable and would collapse into a black hole.Neutron stars with masses well above 1.4M ⊙cannot exist for so–called soft EoSs.Therefore,measuring a high mass for even one neutron star would imply the ﬁrm rejection of many proposed EoSs (see discussion by van Paradijs &McClintock 1995).V395Car/2S 0921–630is a promising accreting binary sys-tem for accurate system parameter work.It shows regular eclipses in the X-rays (Mason et al.1987)as well as dips in the optical lightcurve (Chevalier &Ilovaisky 1981).These reveal a 9.02d orbital period and imply a high orbital incli-nation.The unknown orbital inclination is often a signiﬁ-cant handicap when trying to determine binary parameters,but in V395Car the sin i factor is well constrained.In theElectronic address:D.T.H.Steeghs@1Department of Physics,University of Warwick,Coventry,CV49BU,UK 2Harvard-Smithsonian Center for Astrophysics,60Garden Street,Cam-bridge,MA 02138,Massachusetts,U.S.A.3SRON,Netherlands Institute for Space Research,Sorbonnelaan 2,3584CA,Utrecht,NL4Astronomical Institute,Utrecht University,P.O.Box 80000,3508TA,Utrecht,NLoptical,the K-type donor star absorption line spectrum is vis-ible (Branduardi-Raymont et al.1983)which allows us to de-termine its rotational velocity,v sin i (Shahbaz et al.1999),as well as the radial velocity amplitude K 2(Shahbaz et al.2004;Jonker et al.2005).These previous studies suggested the presence of a rather massive compact object with a mass between ∼2-4M ⊙.In the case of V395Car the main source of error in the mass of the compact object is the large error on the rotational velocity (Jonker et al.2005)which was derived from relatively low resolution data (Shahbaz et al.1999).Here,we present Magellan Inamori Kyocera Echelle (MIKE)data of the V ∼16magnitude counterpart of V395Car/2S 0921–630to determine the rotational velocity of the companion star accurately.We show in this Letter that we ﬁnd a signiﬁcantly lower value for the rotational broadening than previously determined,and explore the effects on the in-ferred neutron star mass.2.OBSERV ATIONS &REDUCTIONWe observed V395Car/2S 0921–630with the MIKE echelle spectrograph mounted on the Magellan Clay tele-scope at Las Campanas Observatory.Four exposures of 30mins each were obtained on Jan.25,2005(MJD 53395)between 7:05-9:15UTC.We employed the spectrograph in its dual-beam mode using a 1"wide slit and a dichroic.The 2048x4096pixel CCD detectors were binned on-chip in 2x2mode.This delivers a wavelength coverage of 3430-5140Åon the blue MIT detector with a spectral dispersion of 0.04Å/pixel,while the red SITe detector covered 5220-9400Åat 0.10Å/pixel.The spectrophotometric standard HR 4468was observed immediately after the target exposures.Observing conditions were good with clear skies and 0.5"see-ing which resulted in a seeing limited resolution of ∼0.08Åin the blue and 0.17Åin the red.Exposures of 5bright template stars of spectral type K were obtained with the same setup a few nights earlier on Jan.212005.2Steeghs&JonkerTABLE1R OTATIONAL BROADENING AS A FUNCTION OF TEMPLATEStar Spectral v sin i(km s−1)aID type0.50.75MS mean30.5±0.831.5±0.9Giant mean31.7±0.732.9±0.8The neutron star in V395Car/2S 0921–63032530354045501.9822.02χν2vsini (km/s)F IG . 2.—a)An example showing the dependence of the achieved χ2νstatistic for an optimally subtracted template star as a function of the applied rotational broadening v sin i .Symbols show the actual values returned from our ﬁts,while the solid line is a cubic ﬁt that is used to determine the best v sin i for each run.b)Histogram of the derived rotational broadening val-ues calculated from 500trial runs of subtracting the K1III star HD 121416.The values are well characterised by a Gaussian distribution as shown by the model Gaussian and provides the ﬁnal v sin i and its error for a given template,31.3±0.7km s −1in this case.v sin i value and its 1σerror for each template star.We provide the results for our 5template stars in Table 1for two values of the limb darkening coefﬁcient.For K-giants,one expects a typical limb darkening coefﬁcient of 0.75in the continuum (Claret et al.1995),but we also list the equivalent values for an assumed limb darkening coefﬁcient of 0.50in order to de-termine its effect on the derived v sin i values.4.IMPLICATIONSThanks to the high spectral resolution and good S/N of our Magellan data,we were able to extract accurate v sin i values with <1km s −1errors.The value was also stable against choice of template,although the required v sin i for the giant templates is on average slightly higher than that for the main-sequence templates (Table 1).This likely reﬂects the fact that the absorption lines found in the unbroadened main sequence templates have higher pressure atmospheres and thus are in-trinsically broader and require a slightly smaller amount of additional rotational broadening.This difference is <2σas is the difference between individual templates.It can also be seen that the effect of limb darkening is relatively modest,shifting the v sin i values systematically down by 1km s −1if we lower the coefﬁcient down to 0.5.This trend continues if we push the line limb darkening further down and in the ex-treme lowers v sin i by 3km s −1(see also Shahbaz &Watson2007).Since we expect the Roche-lobe ﬁlling donor star in its 9day orbit around the neutron star to be closer to a giant rather than a main sequence dwarf,we use v sin i =32.9±0.8km s −1in the remainder of this Letter.This is the mean value derived for our three giant templates while using a limb dark-ening of 0.75,as is appropriate for the R-band continuum in early K-giants.We remark that the bias introduced by this choice is very modest since all individual values are within 2σof this and we will see below that the uncertainty on the derived neutron star mass is no longer dominated by the un-certainty in v sin i ,but instead by the radial velocity amplitude K 2.Very similar results were recently obtained by Shahbaz &Watson (2007)using VLT echelle spectroscopy.As mentioned above,these recent v sin i values are a factor of ∼2lower than the previously reported value of Shahbaz et al.(1999).Shahbaz &Watson (2007)conclude that the dom-inant absorption blend near 6495Åmay have biased the 1999v sin i determination which used data with relatively low sig-nal to noise as well as low spectral resolution.In our case,the high spectral resolution ensured that neither the instrumental proﬁle of the spectrograph nor variable slit illumination ef-fects had an impact on the analysis since the rotational broad-ening exceeded our resolution by a large amount.We also used templates that were obtained with the same instrument and had sufﬁcient signal to noise to detect and resolve a large number of absorption lines.This permitted the determination of reliable values for v sin i with a better than 1km s −1statis-tical precision.4.1.The masses of the stellar componentsArmed with an improved determination of v sin i ,we can now derive new constraints on the mass of the compact object and its K-type donor.The measured radial velocity semi–amplitude K 2and the rotational velocity give the mass ra-tio,q =M 2/M 1,of the system via v sin i3(Wade &Horne 1988).We can then solve for the masses of the stellar components using the mass functions which deliver M sin 3i .Deriving actual masses requires knowledge of the bi-nary inclination,i ,which for V395Car is thought to be close to 80degrees (Mason et al.1987).Values for K 2have been reported in Jonker et al.(2005)which found K 2=99.1±3.1km s −1while Shahbaz et al.(2004)quote K 2=92.9±3.8km s −1.This observed amplitude may be subject to a so-called K-correction due to the fact that the inner face of the companion star can be heated by X–ray emission coming from near the compact object.The center of light measured via the spectral absorption features is then offset from the true center of mass causing an overestimate of K 2.The magnitude of this effect depends on the irradiation geometry (e.g.Muñoz-Darias et al.2005)as well as the intensity of the incoming radiation.Shah-baz et al.(2004)argue that this correction is not signiﬁcant in the case of their K 2,but Jonker et al.(2005)provide some evidence that X-ray heating does seem to be play a role in V395Car.In the most extreme case of no absorption line contribution from the heated front face of the Roche lobe,the K-correction can be as large as ∆K <4/3π×v sin i =14km s −1.In order to determine the uncertainties on the component masses given the observables K 2,v sin i and i ,we ran a Monte-Carlo simulation.The X-ray eclipse discussed in Mason et al.(1987)gives us a good handle on the inclination.At face value,K 2=99.1km s −1and v sin i =32.9km s −1gives a mass ra-tio of q =ing Table 2in Mason et al.(1987)suggests4Steeghs &JonkerF IG . 3.—The four panels plot the distribution of system parameters for 5000randomly selected combinations of K 2and v sin i .Clockwise starting at the upper left corner,we show the mass of the companion star,the mass ratio q ,the radial velocity amplitude K 2and v sin i plotted against the neutron star mass.The thick dashed curves show in which direction these probability clouds move when an irradiation correction to K 2is applied with the solid circles indicating the system parameter solutions at the two extremes of no correction and maximum K-correction.that for this mass ratio,ﬁts to the X-ray eclipse lightcurve imply an inclination angle of ∼83degrees.Although some-what model dependent,the inclination simply enters as sin 3i ,which is only a correction at the 2%level for these high ing i =83◦,we select random values for K 2and v sin i by picking values from a normal distribution cor-responding to the mean and 1σerror of the observed values.The system parameters are then calculated for each random set of parameters,and the process is repeated 5000times.Figure 3shows the corresponding probability clouds for var-ious parameters.In order to illustrate the effect of the un-known K 2correction due to X-ray heating,we plot the cloudsfor zero K-correction (K 2=99.1±3.1km s −1)and then show with dashed curves the steady trajectory the probability clouds would take as a function of the K-correction up to the maxi-mally allowed correction.We ﬁnd that at the canonical values for K 2and v sin i ,the neutron star mass is M 1=1.44±0.10M ⊙,M 2=0.35±0.03M ⊙and q =0.24±0.02.The uncertainties reﬂect the 1σ/68%error values obtained by propagating the 1σerror values on the input parameters through our Monte-Carlo simulation.Our revised v sin i value has thus brought the neutron star mass down to a value remarkably close to the canonical neutron star mass.From the curves in Figure 3,we see that the neutron star mass would go down fur-ther if any K-correction is applied with a minimum mass of M 1=1.05±0.08M ⊙at the maximal K-correction.The mass for the donor star is also much lower than previously reported.The evolutionary timescale for such a low mass star is rather long and it is clear that single star evolution is not able to produce a 0.35M ⊙object that is able to ﬁll its Roche-lobe in a 9day orbit.This is not an uncommon ﬁnding in LMXBs and might be due to a phase of unstable and non-conservative mass transfer that caused a signiﬁcant amount of mass to be lost from the donor.We conclude that we have derived a revised estimate for the rotational broadening of the K-type mass donor star in the neutron star binary V395Car.From this we derive new con-straints on the mass of the neutron star which is most likely very close to the canonical neutron star mass of 1.4M ⊙.V395Car is thus yet another case where a potentially massive neu-tron star appears to be brought back into line with the bulk of the known neutron stars.We would like to thank Jeff McClintock and Eric Mama-jec for acquiring the MIKE data at Magellan.The Magellan telescopes are operated at Las Campanas Observatory by the Magellan consortium consisting of the Carnegie Institution of Washington,Harvard University,MIT,the University of Michigan and the University of Arizona.The use of the spec-tral analysis software package MOLLY written by Tom Marsh is acknowledged.DS acknowledges a STFC Advanced Fel-lowship as well as support through the NASA Guest Observer program.REFERENCESBranduardi-Raymont,G.,Corbet,R.H.D.,Mason,K.O.,Parmar,A.N.,Murdin,P.G.,&White,N.E.1983,MNRAS,205,403Chevalier,C.,&Ilovaisky,S.A.1981,A&A,94,L3Claret,A.,Diaz-Cordoves,J.,&Gimenez,A.1995,A&AS,114,247Jonker,P.G.,Steeghs,D.,Nelemans,G.,&van der Klis,M.2005,MNRAS,356,621Lattimer,J.M.,&Prakash,M.2001,ApJ,550,426—.2004,Science,304,536Mason,K.O.,Branduardi-Raymont,G.,Córdova,F.A.,&Corbet,R.H.D.1987,MNRAS,226,423Muñoz-Darias,T.,Casares,J.,&Martínez-Pais,I.G.2005,ApJ,635,502Shahbaz,T.,&Watson,C.A.2007,A&A,in pressShahbaz,T.,Casares,J.,Watson,C.A.,Charles,P.A.,Hynes,R.I.,Shih,S.C.,&Steeghs,D.2004,ApJ,616,L123Shahbaz,T.,Kuulkers,E.,Charles,P.A.,van der Hooft,F.,Casares,J.,&van Paradijs,J.1999,A&A,344,101van Paradijs,J.,&McClintock,J. E.1995(p.58in X-ray Binaries,eds.W.H.G.Lewin,J.van Paradijs,and E.P.J.van den Heuvel,Cambridge:Cambridge Univ.Press)Wade,R.A.,&Horne,K.1988,ApJ,324,411。

古尔德、多声部和多相大脑

古尔德、多声部和多相大脑一乐迷都知道巴赫专家、加拿大钢琴家格伦·古尔德（Glenn Gould，1932-1982），但他后来跨界搞的纪录片大多无关音乐，所以粉丝如我也并不关心，即便知道古尔德自己很看重。

自从读了帕西克的《多相大脑：脑半球的音乐》（Polyphonic Minds：Music of the Hemispheres），才想起來这一块。

我在加拿大居住久了，越发理解古尔德和加拿大的联系，也读了一些加拿大北方的书。

缘分所至，我开始了解古尔德录制的广播剧《孤独三部曲》。

令人吃惊的是，古尔德据传不是患有“阿斯伯格综合征”吗？按说对他人的反应毫不关心，可是他对人的故事怎么这么感兴趣？而且是那种细腻深挚的关心和细品。

这是一部跟音乐无关的“作曲”。

第一部《北方的概念》中，唯一的音乐是西贝柳斯的第五交响曲，作为巴洛克音乐中常见的通奏低音来用。

第二、第三部索性更极端，人物介绍和叙事都没有，只有众多声音进进出出地倾诉。

古尔德绝非随机选取这些声音，而是相当刻意，从第一部开始，他跟录音师常常工作到凌晨，细修每个字甚至每个音节，连火车声都用来形成结构。

三部曲的形成历经十年，每部都是在几百小时录音的材料基础上编辑出来的，完全是古尔德式高度控制的产物。

在这一点上，更大胆的约翰·凯奇的《收音机音乐》就不同，毫无排布，任由人声随机发生。

加拿大的北方，一般特指几个原住民区：育空、西北和一九九九年才成立的努纳武特。

这些地区寒冷广袤，人口极少。

它们本身因为承载殖民历史，有说不完的故事。

当年的殖民者，虽然跟当地的原住民没有美利坚土地上那么暴力的冲突，但矛盾和破碎的历史叙事无处不在，至今也并没简化多少，更没有一个能讲清楚的未来，本身就是让叙述者对付不了的“对位”。

古尔德在多伦多长大，原本跟稀薄的北方相去甚远，这些地方他为了录音才去的。

不过他有北方情结、孤独情结，也有多声部情结，跑去录制纽芬兰岛、因纽特人、温尼佩格等省的门诺会，把录音做成多声音进行的广播节目。

Neutron Star School

Neutron Star SchoolNeutron stars are fascinating celestial objects that have captivated the attention of scientists and astronomers for decades. These incredibly dense remnants of massive stars hold many secrets waiting to be unraveled. In recent years, scientists have proposed an intriguing concept known as the "Neutron Star School." This innovative idea aims to explore the possibility of using neutron stars as natural classrooms in the vastness of space.Neutron stars are formed when massive stars undergo a supernova explosion at the end of their life cycle. The core collapses under its own gravity, resulting in an incredibly dense object with a diameter of about 20 kilometers but a mass several times that of our sun. Neutron stars possess extreme gravitational forces and intense magnetic fields, making them ideal candidates for scientific exploration.The concept of the Neutron Star School revolves around using these unique properties to provide a platform for acquiring knowledge. Scientists propose sending specially designed spacecraft to orbit around a neutron star, utilizing its immense gravitational pull to maintain a stable position. These spacecraft would serve as mobile laboratories, enabling researchers and students to conduct experiments and study the mysteries of the universe.One of the main advantages of the Neutron Star School is the opportunity for hands-on learning in an extraordinary environment. Students would have the chance to observe and analyze the behavior of matter under extreme conditions. Neutron stars are known for their rapid rotation, producing intense magnetic fields. By studying the interactions between matter and these extreme conditions, scientists hope to gain insights into fundamental physics and advance our understanding of the universe.Furthermore, the Neutron Star School could provide a unique perspective on astrophysics. Neutron stars are cosmic laboratories, where phenomena such as gravitational waves, X-ray emissions, and high-energy particles can be observed and studied. Students participating in the Neutron Star School would have the chance to contribute to cutting-edge research and potentially make groundbreaking discoveries.In addition to scientific exploration, the Neutron Star School could also offer a new perspective on education itself. Traditional classrooms often limit learning to textbooks and theoretical concepts. By taking education to space and utilizing the natural wondersof the universe, students would be encouraged to think outside the box and develop a deeper appreciation for the mysteries of the cosmos.However, it is important to acknowledge the challenges associated with the Neutron Star School concept. The extreme conditions near a neutron star pose significant risks to spacecraft and human occupants. Radiation, intense gravitational forces, and the potential for unpredictable events make it a formidable endeavor. Extensive research, advanced technology, and rigorous safety measures would need to be in place before such a mission could be considered feasible.In conclusion, the Neutron Star School represents an exciting prospect for scientific exploration and education. By utilizing the unique properties of neutron stars, we could create an unprecedented learning environment that pushes the boundaries of human knowledge. While many challenges lie ahead, the potential rewards in terms of scientific discovery and educational advancement make the Neutron Star School a concept worth exploring further.。

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a r X i v :a s t r o -p h /0505007v 1 30 A p r 2005On the viability of neutron star black hole binaries as centralengines of gamma-ray burstsS.Rosswog 1School of Engineering and Science,International University Bremen,GermanyABSTRACTI discuss three-dimensional SPH simulations of neutron star black hole (BH)encounters.The calculations are performed using a nuclear equation of state and a multi-ﬂavor neutrino treatment,general relativistic eﬀects are mimicked using the Paczynski-Wiita pseudo-potential and gravitational radiation reaction forces.Most of the explored mass range (14to 20M ⊙)has not been considered before in numerical simulations.The neutron star is always disrupted during the ﬁrst approach after most of its mass has been transferred directly into the hole.In none of the analyzed cases episodic mass transfer is found.For the lower end of the mass range (M BH ≤16M ⊙)an accretion disk of moderate density (ρ∼1010g cm −3)and temperature (T <2.5MeV)forms around the hole;the rest of the material forms a rapidly expanding tidal tail,up to 0.2M ⊙of which are unbound.For higher mass black holes (M BH ≥18M ⊙)almost the complete neutron star disappears in the hole without forming any accretion disk.In these cases a small fraction of the star (between 0.01and 0.08M ⊙)is spun up by gravitational torques and dynamically ejected.None of the investigated systems of this study yields conditions that are promising to launch a GRB.While we cannot completely exclude that a subset of neutron star black hole binaries,maybe black holes with low masses and very large initial spins,can produce a GRB,this seems to happen -if at all-only in a restricted region of the available parameter space.I argue that the diﬃculty to form promising disks together with the absence of any observed neutron star black hole binary may mean that they are insigniﬁcant as central engines of the observed,short-hard GRBs and that the vast majority of the latter ones is caused by double neutron star coalescences.Subject headings:black hole physics—hydrodynamics—methods:numerical—nuclear reactions,nucle-osynthesis,abundances—gamma rays:bursts—1.IntroductionNeutron star binary systems have been recog-nized as potential central engines of gamma-ray bursts (GRBs)already two decades ago,they have been mentioned in Paczynski (1986)and Good-man et al.(1987)and discussed in more detail by Eichler et al.(1989)(for a more complete bibliog-raphy we refer to existing reviews,e.g.Meszaros 2002or Piran 2005).Paczynski (1991)discussed systems containing a neutron star (NS)and a stellar mass black hole (BH)as a possible GRB engine.These days,compact binary systems are considered the ’standard model’for the subclass of short gamma-ray bursts,that last typically forabout 0.3s (Kouveliotou et al.1993).While NSBH binaries are usually just considered to be a minor variation on the topic of double neu-tron star merger (DNS),it has been pointed out recently (Rosswog et al.2004)that it is not ob-vious,that such a coalescence will automatically produce a hot and massive accretion disk around the hole.Therefore,its role for gamma-ray bursts needs further investigations.During the disruption process tidal torques are expected to eject material into highly eccentric,possibly unbound orbits.This debris is extremely neutron rich,Y e ∼0.1,and therefore (if ejected at appropriate rates)holds the promise to be oneof the still much debated sources of r-process ele-ments(Lattimer and Schramm1974and1976). Moreover,NSBH systems are generally considered promising sources for ground-based gravitational wave detectors such as LIGO(Abramovici et al.1992), GEO600(Luck et al.2001),VIRGO(Caron et al. 1997)and TAMA(Tagoshi et al.2001).It is worth pointing out in this context that thereis a controversy about the rates at which NSBH mergers do occur.Bethe and Brown(1998)ar-gued that NSBH should merge about an orderof magnitude more frequently than DNS,while a recent study by Pfahl et al.(2005)comes to the conclusion that the number of NSBH systems inthe Galaxy should be below1%of the number of double neutron star systems.The current obser-vational status is that there are8observed DNS (Stairs2004),while not a single NSBH binary has been discovered yet.Neutron star black hole merger simulations have been performed by several groups.Janka et al. (1999)used a grid based hydrodynamics code to-gether with a nuclear equation of state(EOS)anda neutrino leakage scheme to explore the role of these mergers in GRB context.Lee(2000,2001) and Lee and Kluzniak(1999a,b)used smoothed particle hydrodynamics with polytropic equationsof state to explore the sensitivity of the resultson the adiabatic exponent of the EOS.Lee and Ramirez-Ruiz(2002)have analyzed theﬂow pat-tern within an accretion disk around a BH and,ina recent paper(2004),they included neutrino pro-cesses in their simulations.Setiawan et al.(2004) constructed disks around stellar mass black holes and followed their evolution including explicit vis-cosity,Rosswog et al.(2004)investigated the dynamics of the accretion process and the forma-tion of a disk during the merger.Stellar mass black holes formed in core collapse su-pernovae are thaught to be born with masses rang-ing from about3to20M⊙(Fryer and Kalogera 2001).Numerical simulations have so far only ex-plored black hole masses up to14M⊙(Janka et al.1999and Lee and Kluzniak1999a,b and Lee 2000,2001used black holes up to10M⊙,Rosswoget al.2004explored masses up to14M⊙).In this paper we will focus on black holes with masses ranging from14to20M⊙.The14M⊙case has been explored previously(Rosswog et al.2004) using the same microphysics but a purely New-tonian BH-potential and may therefore serve to gauge the eﬀect of the Paczynski-Wiita pseudo-potential.A simple estimate for the radius where a star around a BH is disrupted is the tidal radius, R tid= M BHrelativistic solutions in a Schwarzschild space time show that the pseudo potential is able to capture the essentials of general relativity and can repro-duce accretion disk structures to an accuracy of better than10%(see e.g.Artemova et al.1996).I restrict myself to initially corotating systems as the corresponding equilibrium conﬁgurations can be constructed accurately using the hydrocode it-self(see Rosswog et al.2004).The simulations presented here use up to3·106SPH particles and therefore are currently the best resolved models of neutron star black hole encounters(Rosswog et al. (2004)used up to106particles,Lee(2001)used slightly more than80000particles).The neutron star always has a mass of1.4M⊙and a radius of16km,the black hole masses vary from14to20M⊙,see Table1.3.ResultsThe neutron star is always completely disrupted during theﬁrst encounter.In all of the cases a large portion of the neutron star is transferred di-rectly into the hole without any accretion disk for-mation.The corresponding peak accretion rates exceed1000M⊙/s for about1ms,after this short episode they drop by at least two orders of mag-nitude,see panel one in Figure1.It is instructive to compare the14M⊙case to the corresponding case of our previous study(Ross-wog et al.2004),where we had used a New-tonian BH potential.In the purely Newtonian case we found episodic mass transfer with a low-mass,“mini neutron star”surviving throughout the whole simulation or about eight close encoun-ters.In the Paczynski-Wiita case about1.15M⊙(see panel two in Figure1)are transferred directly into the hole,the rest forms a rapidly expanding tidal tail.The tidal tail still contains an outward-moving density maximum(corresponding to the mini neutron star of the Newtonian case),but its self-gravity is not strong enough to form a spheri-cal object.The motion around the hole always has a strong radial velocity component and is far from being Keplerian.The matter fraction that is not swallowed during theﬁrst orbit collides with the accretion stream forming a spiral shock(see Figure 2).In this shock the temperatures slightly exceed 2MeV,the other disk regions are substantially colder.The disk is substantially diminished on timescales of a few orbital periods.The densities never exceed6·1010g cm−3,the neutrino luminosi-ties reach peak values of only2·1050erg/s and are thus about three orders of magnitude lower than in our simulations of neutron star binary merg-ers(see Rosswog and Liebend¨o rfer2003)where the same microphysics was used.The results are well converged,runs I and II show excellent agree-ment in the BH masses and peak mass transfer rates.Some minor deviations are visible at low mass transfer rates(see panel one in Fig.1and the distance,R MT,where numerically resolvable mass transfer sets in;see column six in Table1). The case with16M⊙BHs behaves qualitatively very similar to the14M⊙BHs:about1.2M⊙are transferred into the hole,the disk is slightly less massive,hot and dense than the14M⊙case. Again,the two diﬀerent resolutions yield nearly identical results.The systems containing BHs of18M⊙or more (runs V and VI)do not form accretion disks at all.Almost the complete neutron starﬂows via the inner Lagrange point directly into the hole, only a small fraction of the star is spun up enough by tidal torques to be dynamically ejected,see last column in Table1.In these cases the remnant con-sists of the black hole(without any accretion disk) and a rapidly expanding,concentric(half-)ring of neutron-rich debris material(0.08M⊙for the18 and0.01M⊙for20M⊙BH).The ejected mass fraction found in these simula-tions is near the range estimated by Lattimer and Schramm(1974and1976),they estimated0.05±0.05M⊙.Our nucleosynthetic calculations for such debris material for the neutron star merger case(Freiburghaus et al.1999)yielded excellent agreement with the observed r-process abundances from around Barium up to beyond the platinum peak.If large parts of the disrupted neutron star should form r-process material,a conﬂict with the observed element ratios in metal-poor halo stars might arise(Argast et al.2004),if their coalescence rates are similar to those of double neutron stars(DNS).The problem is avoided if NSBH coalesce much less frequently than DNS. This would be consistent with the non-observation of any NSBH-system(currently8DNS systems are known,see Stairs2004)and the result of re-cent studies(Pfahl et al.2005)that estimate their number in the Galactic disk to be less than0.1-1% of the number of DNS.It is worth pointing out that in some of the investi-gated cases mass transfer sets in only at distances considerably smaller than R isco(e.g.run VI,see Table1).This however,does not mean that the star is swallowed as a whole(keep in mind that R isco refers to the case without self-gravity and to circular motion;both conditions are not satisﬁed here).In the16M⊙BH case still a tidal tail and accretion disk forms,in the higher mass cases at least some material escapes from being drawn into the hole.4.DiscussionWe consider all the approximations made to be valid to a high degree.If an accretion disk forms at all(i.e.for the BH masses at the lower end of the explored range)it is of only moderate density (∼1010g cm−3)and completely transparent to neutrinos.Therefore the neutrino emission results cannot be inﬂuenced by ourﬂux-limited diﬀusion treatment.Moreover,the results are numerically converged,diﬀerent numerical resolution yields for the gross properties almost identical results.The BHs are massive enough to dominate the space-time completely and as they are spun up to spin parameters of only0.2(see Table1),we consider the use of PW-potentials a very good approxima-tion(note that for a=0.2the event horizon moves from2to1.98and the last stable orbit from6to 5.33gravitational radii).None of the investigated NSBH systems yields disks that are promising as GRB engines.The disks formed in the low mass BH cases are rela-tively cold and of low density,the neutrino lumi-nosities are more than two orders of magnitude be-low our results from the neutron star merger case (Rosswog and Liebend¨o rfer,2003).In the latter case the GRBs launched viaν¯ν-annihilation were rather weak by GRB standards and,as the neu-trino luminosities enter quadratically in the energy deposition rate,ν¯ν-annihilation does not seem a viable GRB mechanism for the investigated NSBH systems.Due to the lower densities the magnetic ﬁelds that can be anchored in the disk are substan-tially lower that in the DNS case,whether they still can launch a GRB remains to be explored in the future.BHs beyond∼18M⊙do not lead to any accretion disk formation at all and can there-fore be ruled out as sources of GRBs.We still cannot generally rule out NSBH-systems as central engines of GRBs.One might specu-late,for example,about about an extremly high disk viscosity.Another possibility is the nuclear EOS.Our previous investigations(Rosswog et al. 2004)showed that the dynamics of the merger is sensitive to the EOS.Here,I used a relativistic meanﬁeld EOS with neutrons and protons as the only baryonic constituents of matter.This EOS is certainly on the stiﬀside of the possible range of nuclear equations of state.Maybe a substantially softer EOS could make the outcome of the merger more promising to launch a GRB.The possibly most robust way out,however,are BHs that are already from the beginning spinning very rapidly and that are spun up during the merger to val-ues very close to the maximum spin parameter of a=1.In this case both the position of the last stable orbit and the event horizon move to 1M BH and thus closer to the hole.Therefore, much higher temperatures and densities might be reached in the inner disk regions.It seems that a large part of the parameter space does not yield conditions that are promising to launch GRBs.This diﬃculty to form promising disks together with the absence of any observed NSBH system may mean that NSBH binaries are insigniﬁcant as central engines of the observed, short-hard GRBs and that the majority of the lat-ter ones is caused by double neutron star coales-cences.NSBH mergers may just manifest them-selves as sources of gravitational waves and tran-sient X-rays.It is a pleasure to thank Jim Lattimer,William Lee,Enrico Ramirez-Ruiz,Roland Speith and Christophe Winisdoerﬀer for useful discussions and the INFN in Catania for their hospital-ity.The calculations reported here have been performed on the JUMP supercomputer of the H¨o chstleistungsrechenzentrum J¨u lich. 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