The relation between black hole mass and velocity dispersion at z~0.37

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Black Hole Thermodynamics from String Theory

a r X i v :h e p -t h /9405185v 1 28 M a y 1994EDO-EP-1May 1994Black Hole Thermodynamics from String Theory Ichiro Oda Edogawa University,474Komaki,Nagareyama City,Chiba 270-01,JAPAN ABSTRACTIn this note we consider a stringy description of black hole horizon.We start with a nonlinear sigma model deﬁned on a two dimensional Euclidean surface with background Rindler metric.By solving the ﬁeld equations,we show that to the leading order the Bekenstein-Hawking formula of black hole entropy can be produced.We also point out a relation between the present formalism and the ’tHooft formalism.To construct a theory of quantum gravity in four dimensions is one of the most diﬃcult and challenging subjects left in the modern theoretical physics since we have so far neither useful informations from experiments nor consistent quantum ﬁeld theory.Under such a circumstance,it seems to be an orthodox attitude to attack concrete problems with logical conﬂicts and then learn the fundamental principle from which in order to construct a full-ﬂedged theory.In the case of quantum gravity,as one of such unsolved problems,we have quantum black holes1. In particular,it is widely known that there are at least three problems which remain to be clariﬁed in quantum black hole,those are,the endpoint of Hawking radiation, the information loss paradox and the statistical origin of black hole entropy2.Recently,there have been some progresses on the last problem3−9.Among them,the authers of Ref.[6]made an interesting observation that superstring theory might play an important role in deriving the Bekenstein-Hawking formula of the black hole entropy1,10.On the other hand,in previous works11,’tHooft has stressed that black holes are as fundamental as strings,so that the two pictures are really complementary.In fact,he has demonstrated that by properly taking account of a leading gravitational back-reaction of the black hole horizon,the gravitational shock wave,from hard particles,his S matrix which describes the dynamical properties of a black hole can be recast in the form of functional integral over the Nambu-Goto string action. Although his formalism has some weaknesses,it is extremely interesting from the physical viewpoint since quantum incoherence never be lost and all information of particles entering into a black hole is transmitted to outgoing particles owing to the Hawking radiation through the quantumﬂuctuations of the black hole horizon.As it is expected that superstring has many degrees of freedom and hairs associated with its many excited states,the’tHooft formalism might also give us a clue to understanding of a huge entropy10and quantum hairs2of a black hole.In this note,we shall simply assume that the dynamics of the event hori-zon of a black hole can be described by the world sheet swept by a string in the Schwarzschild background,and then would like to discuss what physical conse-quences can be derived from this assumption.However,the Schwarzschild metric is rather complicated,so that we shall conﬁne ourselves to the case of the Rindler spacetime.The case of the Schwarzschild metric will be reported in a separate pa-per.We will see that a nonlinear sigma action leads to the well-known Bekenstein-Hawking formula of black hole entropy,S=12 d2σ√gµν(X)can be identiﬁed as the background spacetime metric in which the string is propagating.Note thatα,βtakes values0,1andµ,νdoes values0,1,2,3.The classicalﬁeld equations give us that0=Tαβ=−2√δhαβ,=∂αXµ∂βXνgµν(X)−1hhαβgµν∂βXν)−1hhαβ∂αXρ∂βXσ∂µgρσ.(3)In this note we consider the case that the background spacetime metric gµν(X) takes a form of the Euclidean Rindler metricds2=gµνdXµdXν=+g2z2dt2+dx2+dy2+dz2,(4)where g is given by g=1are the two dimensional diﬀeomorphisms and the Weyl rescaling byx(τ,σ)=τ,y(τ,σ)=σ,G(τ,σ)=1.(6) At this stage,let us impose an”axial”symmetryr(τ,σ)=r(τ),t(τ,σ)=t(τ).(7) From Eq.s(5),(6)and(7),the world sheet metric hαβtakes the formhαβ= g2z2˙t2+˙z2+1001 ,(8) where the dot denotes a derivative with respect toτ.And the remainingﬁeld equations(3)become∂τ(z2˙th)=0,(9)∂τh=0,(10)∂τ(˙zh)−1hg2z˙t2=0,(11)whereh=g2z2˙t2+˙z2+1.(12)Now it is straightforward to solve the aboveﬁeld equations.We have two kinds of solutions.One solution is a trivial one given byz=˙z=¨z=0,t(τ)=arbitrary.(13)which corresponds to a world-sheet surface of the Euclidean string just lying on the black hole horizon.The next solution is the solution of”world sheet instanton”described byz (τ)=c 2,t −t 0=1gc 1(τ−τ0),(14)where c 1,c 2,τ0,and t 0are the integration constants,in other words,”the moduli parameters”.To understand the physical meaning of this solution more vividly,it is convenient to rewrite z in terms of the time coordinate variable t .From Eq.(14),we obtainz (t E )=gc 1c 21time t Lz (t L )=gc 1c 21g whose inverse gives us nothingbut the Hawking temperature T H =12π=1¯h ,(17)where S E denotes the Euclidean action,and the path integral is performed under the boundary condition of being periodic in the Euclidean time with periodβ¯h. Then the black hole thermodynamics can be recovered in the limit¯h→0by expanding S E around its saddle point.Thus evaluating the free energyβto the leading term equals to substituting a classical solution into the Euclidean action.In the model just considered,it is easy to calculate the free energy.To do so we shall consider the solution(14)since this solution gives us the thermal temperature whose situation should be contrasted to the case of the other solution(13).The result isF=−1c2+1T A H,(18)where A H= dxdy which corresponds to the area of the black hole horizon if we consider the Schwarzschild black hole.By the formula which gives us the entropyS=β2∂Fc2+1T A H.(20) Note that the black hole entropy is proportional to the horizon area.Moreover,by selecting the string tensionT=1c2+1G,(21)we arrive at the famous Bekenstein-Hawking entropy formula1,10S=1duced by hard particles having a large amount of momenta.Thus let us introduce ”vertex operator”in the original action(1)S E=−Thhαβ∂αXµ∂βXνgµν(X)+ d2σ√√hhαβ∂βXµ)+Pµ,(24)where we have replaced gµνwith theﬂat metricηµν.This approximation would become good when the black hole mass is large compared to the Planck mass. Moreover,we haveﬁxed the world sheet metric hαβ(τ,σ)to be the metric on S2. Therefore we obtainT∆tr Xµ+Pµ=0,(25) where∆tr=1h∂α(√δXµ(σ).(28)From(25)and(27),we haveXµ(σ),Xν(σ′) =iNotes addedDuring the preparation of this article,we noticed that there is a recent work where the black hole is described by the membrane theory16.AcknowledgementWe are grateful to K.Akama,N.Kawamoto,A.Sugamoto and Y.Watabiki for valuable discussions.REFERENCES1.S.W.Hawking,Comm.Math.Phys.43,199(1975)2.J.Preskill,Physica Scripta T36,258(1991)3.L.Bombellli,R.K.Koul,J.Lee and R.D.Sorkin,Phys.Rev.D34,373(1986)4.G.’tHooft,Nucl.Phys.B256,727(1985)5.M.Srednicki,Phys.Rev.Lett.71,666(1993)6.L.Susskind and J.Uglum,Stanford preprint SU-ITP-94-1,hep-th/94010767.C.Callan and F.Wilczek,IAS preprint IAS-HEP-93/87,hep-th/94010728.D.Kabat and M.J.Strassler,Rutgers preprint RU-94-10,hep-th/94011259.T.Jacobson,Maryland preprint,gr-qc-940403910.J.D.Bekenstein,Nuovo Cim.Lett.4,737(1972);Phys.Rev.D7,2333(1973);ibid.D9,3292(1974);Physics Today33,no.1,24(1980)11.G.’tHooft,Nucl.Phys.B335,138(1990);Physica Scripta T15,143(1987);ibid.T36,247(1991);Utrecht preprint THU-94/02,gr-qc/940203712.L.Susskind,L.Thorlacius and J.Uglum,Phys.Rev.D48,3743(1993);L.Susskind and L.Thorlacius,Phys.Rev.D49,966(1994)13.W.G.Unruh,Phys.Rev.D14,870(1976)14.G.Gibbons and S.W.Hawking,Phys.Rev.D15,2752(1977);S.W.Hawking,From General Relativity:An Einstein Centenary Survey,Cambridge Univ.Press197915.I.Oda,Int.J.Mod.Phys.D1,355(1992)16.M.Maggiore,preprint IFUP-TH22/94,hep-th/940417211。

专业英语考点

一. 翻译重点1、事实上，他们协调工程中每个人的活动。

答：They coordinate the activities of virtually everyone engaged in the work.2、建筑物的结构是建筑物的功能、环境、及各种社会经济因素共同作用的产物。

答：The form of a building is an outgrowth of its function, its environment, and various socioeconomic factors.3、因为所需墙体的厚度很大，承重墙结构限制了建筑物的高度。

答：Bearing-wall construction limited the height of buildings because of the enormous wall thickness required.4、该体系由间距很小的柱子构成的外框筒与围绕中心设备区的刚性剪力墙内筒组成。

答：The system consists of an outer framed tube of very closely spaced columns and an interior rigid shear wall tube enclosing the central service area.1、The Employer, the Contractor, the Project Manager and the Supervisor shall act as stated in this contract and in a spirit of mutual trust and co-operation.答：雇主、承包商、项目经理和监理工程师应按本合同的规定，在工作中相互信任、相互合作。

2、All soils beneath the surface are in a state of compaction; that is, they are under a pressure that is equal to the weight of the soil column above it.答：所有地表以下的土都处于受压状态，说得更精确些，这些土承受与作用在其上的土柱重量相等的压力。

The Physics of Black Holes and their Properties

The Physics of Black Holes and theirPropertiesBlack holes have always been a subject of great curiosity and fascination for scientists and laymen alike. They are mysterious and intriguing, defying our understanding of the physical laws that govern the universe. But what exactly are black holes? How are they formed? What are their properties? These are the questions that physicists have been grappling with for decades, and although some answers have been found, much of their nature remains a mystery.One of the key features of black holes is their immense gravitational pull. This is because they are formed from the gravitational collapse of a massive object, such as a star, and their density is so high that their gravitational field becomes incredibly strong. In fact, the gravitational pull of a black hole is so powerful that even light cannot escape it, hence the name "black hole". This phenomenon is known as the event horizon, which marks the point of no return for any object that ventures too close to the black hole.But it's not just the gravitational pull of black holes that make them unique. They also have a number of other unusual properties, such as their temperature, their spin, and their size. Let's take a closer look at each of these characteristics.TemperatureIn the 1970s, physicist Stephen Hawking proposed that black holes emit radiation, which came to be known as Hawking radiation. This was a groundbreaking discovery, as it suggested that black holes are not entirely black after all, but rather emit a small amount of energy in the form of radiation. This radiation is due to quantum fluctuations near the event horizon, which cause particle-antiparticle pairs to be created. If one of the particles falls into the black hole, the other can escape, carrying energy away with it.The temperature of a black hole is proportional to its gravitational pull, so the more massive the black hole, the colder it is. This might sound counterintuitive, but it's becausea larger black hole has a larger event horizon, so it emits less radiation. Conversely, a smaller black hole has a smaller event horizon, so it emits more radiation and is therefore hotter.SpinAnother important property of black holes is their spin, which is determined by the angular momentum of the object that formed them. Like a spinning top, a black hole can spin either clockwise or counterclockwise, and its spin affects how it interacts with the surrounding matter. For example, a spinning black hole can drag nearby matter along with it, creating a swirling disk of gas and dust around itself.The spin of a black hole can also affect the characteristics of its event horizon. A non-spinning black hole has a spherical event horizon, whereas a spinning black hole has a flattened, donut-shaped event horizon known as an ergosphere. This region is where matter can enter the black hole, but also where energy and momentum can be extracted from it.SizeFinally, black holes come in a range of sizes, from the smallest "stellar" black holes, which have the mass of a few suns, to the largest "supermassive" black holes, which can have a mass billions of times greater than the sun. But size is not the only factor that determines the properties of a black hole - its spin and temperature also play a role.One interesting feature of black holes is that they have a maximum density, known as the Planck density. This is the point at which the laws of physics as we know them break down, and quantum effects become dominant. Beyond this density, we simply don't know what happens, and it's possible that new physical laws may need to be discovered to explain the behavior of matter in this extreme environment.ConclusionIn conclusion, black holes are fascinating objects that challenge our understanding of the universe. Their immense gravitational pull, temperature, spin, and size make themunique, and studying them can help us learn more about the fundamental laws of physics. However, much of their nature remains a mystery, and it will likely take many more years of research to unlock their secrets.。

The Theory of Black Holes

The Theory of Black HolesBlack holes have long fascinated scientists and the public alike, with their mysterious and seemingly paradoxical properties. They are defined as regions of space where the gravitational force is so strong that nothing, not even light, can escape. This means that anything that falls into a black hole is lost forever, trapped in a singularity at the center of the hole.The concept of black holes was first proposed in the early 20th century, but it was not until the 1960s that the theory was fully developed. The key idea is that the gravitational force near a massive object can be so strong that it warps space and time. This means that particles and light are forced to move along curved paths, just as if they were on a rollercoaster.The theory of general relativity, developed by Albert Einstein, is the foundation for our understanding of black holes. It describes how the force of gravity is caused by the curvature of space and time, rather than as a mysterious "force" that pushes objects together. This theory is still considered one of the most important discoveries in physics, and has been used to explain everything from the bending of light around massive objects to the behavior of the whole universe.The first observational evidence for black holes came in the 1970s, with the discovery of several X-ray sources that were too compact to be anything other than black holes. Observations of stars orbiting around a central object in our own galaxy, the Milky Way, have also provided strong evidence for a supermassive black hole at the center of the galaxy. These observations have allowed us to study black holes in more detail, and to understand some of their most fascinating properties.One of the most surprising aspects of black holes is their size. Despite being known for their immense gravitational forces, black holes are actually incredibly small. A supermassive black hole at the center of a galaxy can be millions or even billions of times more massive than our Sun, but it can still fit within its own event horizon - the point beyond which nothing can escape.Another important property of black holes is the way they interact with matter. Anything that falls into a black hole is lost forever, but as it does so, it heats up and emits a tremendous amount of energy in the form of X-rays and other radiation. This process, called accretion, is what makes black holes visible in the first place. By studying the radiation emitted by black holes, scientists can learn about the matter that is falling into them.Black holes have also been used to test some of the most fundamental principles of physics, such as the laws of thermodynamics and the nature of space and time. For example, studies of the radiation emitted by black holes have shown that they behave like thermal objects, with a temperature and entropy that can be described by the laws of thermodynamics. This has led to the development of some of the most exciting ideas in modern physics, such as the holographic principle and the information paradox.Despite all of these fascinating discoveries, there is still much we do not know about black holes. Theories about what happens to matter beyond the event horizon, or what happens when two black holes collide, are still the subject of much debate and research. Some scientists even believe that black holes could be the key to understanding some of the most mysterious phenomena in the universe, such as dark matter and dark energy.In conclusion, the theory of black holes has revolutionized our understanding of the universe and the fundamental laws that govern it. Through observation and experimentation, scientists have been able to unravel some of the most puzzling aspects of these mysterious objects, and to develop new and exciting ideas about the nature of space and time. Although there is still much we do not know, one thing is certain: black holes will continue to fascinate and inspire us for generations to come.。

Black holes in the Brans-Dicke-Maxwell theory

The other example comes from the black holes in the BD theory. More recently, many authors have investigated the gravitational collapse and black hole formation in the BD theory [3,4,5,6,7]. It turned out that the dynamic scalar ﬁeld in the BD theory plays an important role in the process of collapse and critical phenomenon. Hawking [8] proved ﬁrst that in the four dimensional vacuum BD theory, the black hole solution is just the Schwarzschild solution with a trivial constant scalar ﬁeld (hereafter the black holes in this paper mean the static, asymptotically ﬂat, and spherically symmetric solutions with horizon). Further the stability of black holes in the BD theory has been investigated in Ref. [9]. On the other hand, the vacuum BD theory can be transformed into the Einstein-massless scalar theory by using a conformal transformation. In Ref. [10], the solution to Einsteinmassless scalar equations was given. Although this solution has an asymptotically ﬂat region and the scalar ﬁeld approaches zero at spacelike inﬁnity, it exhibits a naked

常规英语850基本词汇列表

850基本词汇列表学习英语需要学习和背诵多少单词词汇合适呢？理论上自然是多多益善，但是事实上心急吃不了热豆腐，人无法一口吃成个胖子。

所以从最基础的，最常用的词汇开始背诵，才是正道。

下面列表中的850个最基本词汇，是英语中最常使用的英语基础单词。

在日常生活和日常用语中最经常用的基础词汇，要想学习英语，首先检查自己是否完全掌握了这些单词的拼写和发音，以及词义。

如果没有掌握，那么就需要抓紧时间背诵和学习了。

aableaboutaccountacidacrossactaddition adjustment advertisementafteragainagainstagreementairallalmostamongamountamusementandangleangryanimalanswerantanyapparatusappleapprovalarchargumentarmarmyartasatattackattemptattentionattraction authority automaticawake babybackbadbagbalanceballbandbasebasinbasketbathbebeautifulbecausebedbeebeforebehaviorbeliefbellbentberrybetweenbirdbirthbitbitebitterblackbladebloodblowblueboardboatbodyboilingbonebookbootbottleboxboybrainbrakebranchbrassbreadbreathbrickbridgebrightbrokenbrotherbrownbrushbucketbuildingbulbburnburstbusinessbutbutterbuttonbycakecameracanvascardcarecarriagecartcatcausecertainchainchalkchancechangecheapcheesechemicalchesschiefchinchurchcirclecleanclearclockclothcloudcoalcoatcoldcollarcolorcombcomecomfortcommitteecommoncompanycomparisoncompetitioncompletecomplexconditionconnectionconsciouscontrolcookcoppercopycorkcoughcountrycovercowcrackcreditcrimecruelcrushcrycupcurrentcurtaincurvecushioncutdamagedangerdarkdaughterdaydeaddeardeathdebtdecisiondeepdegreedelicatedependentdesigndesiredestructiondetaildevelopmentdifferentdigestiondirectiondirtydiscoverydiscussiondiseasedisgustdistancedistributiondivisiondodogdoordoubtdowndraindrawerdressdrinkdrivingdropdrydustearearlyeartheastedgeeducationeffecteggelasticelectricendengineenoughequalerroreveneventeverevery exampleexchange existence expansion experience experteyefacefactfallfalsefamilyfarfarmfatfatherfear feather feeble feeling female fertile fiction fieldfightfingerfirefirstfishfixedflagflameflatflightfloorflowerflyfoldfoodfoolishfootforforceforkform forward fowlframe freefrequentfriendfromfrontfruitfullfuturegardengeneralgetgirlgiveglassglovegogoatgoldgoodgovernmentgraingrassgreatgreengreygripgroupgrowthguidegunhairhammerhandhanginghappyharborhardharmonyhathatehaveheheadhealthyhearingheartheathelpherehighhistoryholehollowhookhopehornhorsehospitalhourhousehowhumoriiceideaifillimportantimpulseinincreaseindustryinkinsectinstrumentinsuranceinterestinventionironislandjellyjeweljoinjourneyjudgejumpkeepkettlekeykickkindkisskneeknifeknotknowledgelandlanguagelastlatelaughleadleaflearningleatherleftlegletletterlevellibraryliftlightlikelimitlinelinenlipliquidlistlittlelivinglocklonglooklooselossloudlovelowmachinemakemalemanmanagermapmarkmarketmarriedmassmatchmaterialmaymealmeasuremeatmedicalmeetingmemorymetalmiddle military milkmindmineminutemistmixed money monkey monthmoon morning mother motion mountain mouthmovemuch muscle musicnailnamenarrow nation natural near necessary neckneedneedle nervenetnewnewsnightnonoise normal northnosenotnotenownumbernut observation ofoffoffer officeoiloldononlyopenoperationopinionoppositeororangeorderorganizationornamentotheroutovenoverownerpagepainpaintpaperparallelparcelpartpastpastepaymentpeacepenpencilpersonphysicalpicturepigpinpipeplaceplaneplantplateplaypleasepleasureploughpocketpointpoisonpolishpoliticalpoorporterpositionpossiblepotpotatopowderpowerpresentpriceprintprisonprivateprobableprocessproduceprofitpropertyproseprotestpublicpullpumppunishmentpurposepushputqualityquestionquickquietquiterailrainrangeratraterayreactionreadingreadyreasonreceiptrecordredregretregularrelationreligionrepresentativerequestrespectresponsiblerestrewardrhythmricerightringriverroadrodrollroofroomrootroughroundrubrulerunsadsafesailsaltsamesandsayscaleschoolsciencescissorsscrewseaseatsecondsecretsecretaryseeseedseemselectionselfsendsenseseparateseriousservantsexshade shake shamesharp sheep shelf ship shirt shock shoe short shut side sign silk silver simple sister size skin skirt sky sleep slip slope slow small smash smell smile smoke smooth snake sneeze snowsosoapsocietysocksoftsolidsomesonsongsortsound soup south space spade specialspongespoonspringsquarestagestampstarstartstatementstationsteamsteelstemstepstickstickystiffstillstitchstockingstomachstonestopstorestorystraightstrangestreetstretchstrongstructuresubstancesuchsuddensugarsuggestionsummersunsupportsurprisesweetswimsystemtabletailtaketalktalltastetaxteachingtendencytestthanthatthethentheorytherethickthinthingthisthoughthoughtthreadthroatthroughthumbthundertickettighttilltimetintiredtotoetogethertomorrowtonguetoothtoptouchtowntradetraintransporttraytreetricktroubletrouserstrueturntwistumbrellaunderunitupusevalueverseveryvesselviewviolentvoicewaitingwalkwallwarwarmwashwastewatchwaterwavewaxwayweatherweekweightwellwestwetwheelwhenwherewhilewhipwhistlewhitewhowhywidewillwindwindowwinewingwinterwirewisewithwomanwoodwoolwordwork worm wound writing wrong year yellow yes yesterday you young850个基本英语词汇分类表OPERATIONS(最常用的100 词)1．表示动作的词：词：come get come get give go keep let make put seem take be do have say see send may will 2.2.介词：介词：介词：about about across after against amongat before between by down from in off on over through tounder up with as for of till than3.3.代词：代词：代词：a the a the all any every no other some such that this I he you who4.4.连接词：连接词：连接词：and and because but or if thoughwhile how when where why5.5.副词：副词：副词：again again ever farforward here near now out still then theretogether well almost enough even little much not only quite so very tomorrowyesterday north south east westplease yes.最常用的400普通名词（400general words ）account act additionadjust advertisement agreement air amountamusement animal answer apparatus approvalargument art attackattempt attention attraction authority back balance base behavior belief birth bit bite bloodblow bodybrass breadbreathbrother building burn burst business butter canvascare causechalk chance change clothcoal color comfort committee companycomparisoncompetitioncondition connectioncontrol cook copper copy cork cotton cough country cover crack credit crime crush cry current curve damage danger daughter day death debt decision degree design desire destruction detail developmentdigestion directiondiscovery discussion disease disgustdistancedistributiondivisiondoubt drinkdriving dustearth edgeeducationeffect enderror eventexampleexchangeexistenceexpansionexperienceexpert factfall familyfather fearfeelingfiction fieldfight fireflame flightflower foldfood forceform friendfront fruitglass goldgovernmentgrain grassgrip groupgrowth guideharborharmony hatehearing heathelp historyhole hope hourhumor ice ideaimpulseincreaseindustry inkinsectinstrumentinsuranceinterestinventioniron jellyjoin journeyjudge jumpkick kissknowledgeland languagelaugh law leadlearningleatherletter levellift lightlimit linenliquid listloss lovemachine manmanager markmarket massmeal measuremeat meetingmemory metalmiddle milkmind mineminute mistmoney monthmorningmother motionmountain movemusic namenation neednews nightnoise notenumber observationoffer oil operation opinion order organization ornament owner page pain paint paper part paste payment peace person place plant play pleasure point poison polish porter position powder power price printprocess produceprofit propertyprose protest pullpunishmentpurpose pushqualityquestion rainrange rate rayreactionreadingreason recordregretrelationreligionrepresentative requestrespect restreward rhythmrice riverroad roll roomrub rule runsalt sandscale sciencesea seatsecretaryselectionself senseservant sexshade shakeshame shockside sign silksilver sistersize sky sleepslip slopesmash smellsmile smokesneeze snowsoap societyson song sortsound soupspace stagestartstatementsteam steelstep stitchstone stopstory stretchstructuresubstancesugarsuggestionsummersupportsurprise swimsystem talktaste taxteachingtendency testtheory thingthoughtthunder timetin top touchtradetransporttrick troubleturn twistunit use valueverse vesselview voicewalk war washwaste waterwave wax wayweather weekweight windwine winterwoman woodwool word workwound writing year最常用的200个形象名词（200 Picturable words ） angle antapple arch arm army baby bag ball bankbasin basket bath bed bee bell berry bird blade board boatbone book boot bottle box boy brain brakebranch brick bridge brush bucket bulb button cake camera cardcart carriage cat chain cheese chest chin churchcircle clock cloud coat collar combcord cow cup curtaincushion dog door drain drawer dress drop ear egg engine eye face farm feather finger fishflag floor fly foot fork fowl frame garden girl glove goat gun hair hammer handhat head heart hook hornhorsehospital house island jewel kettle key knee knife knot leaf leg library line lip lock map match monkey moon mouth muscle nailneck needlenerve net nose nut office orange oven parcel pen pencilpicture pigpin pipe plane plateplough/plowpocket pot potato prison pump rail rat receipt ring rod roof rootsail schoolscissors screw seedsheep shelf ship shirt shoe skinskirt snake sock spade sponge spoon spring square stamp starstation stem stick stocking stomach store street sun table tailthread throat thumb ticket toe tongue tooth towntrain traythree trousersumbrella wall watch wheel whip whistle window wingwire worm最常用的100个普通形容词（QUALITIES -100 GeneralWords ）able acid angry automatic beautifulblack boiling bright broken brown cheap chemical chief cleanclear common complex conscious cut deep dependent early elastic electric equal fat fertile first fixed flatfree frequent full general good great grey/gray hanging happy hard healthy high hollow important kind like living longmale married material medical military naturalnecessary new normal open parallel past physicalpoliticalpoor possible presentprivateprobable quick quietready read regularresponsibleright roundsame secondseparate serious sharpsmooth sticky stiffstraightstrong sudden sweet tallthick tight tired true violentwaiting warm wet wide wiseyellow young最常用的50个反义形容词（QUALITIES -50 Opposites ）awake bad bent bitter bluecertain cold complete cruel dark dead dear delicate differentdirty dry false feeblefemale foolishfuture greenill last late left looseloud low mixednarrow oldoppositepublic roughsad safesecret shortshut simple slow smallsoft solid special strange thin white wrong。

Understanding the Physics of Black Holes

Understanding the Physics of BlackHolesIntroduction:Black holes are one of the most fascinating objects in the universe that have been explored by scientists for decades. Almost every scientist in the field of astrophysics has studied black holes to try to understand their amazing properties and behaviors. It is impossible to ignore the physics of black holes since they offer valuable information on how our universe began, how galaxies and stars form, and how time and space work. Understanding the physics of black holes will expand our knowledge of the universe in the most fantastical way.What are Black Holes?A black hole is a region in space that has an extreme gravitational pull from which no particles or radiation can escape. Black holes are formed when a massive star (at least 10 times the mass of the sun) collapses under its gravity and becomes a singularity- a point in space where all the matter that once made up the star is compressed into an infinitely small and dense point.The Physics of Black Holes:The properties of a black hole are defined by two factors: its mass and its spin. One of the factors that astrophysicists use to measure a black hole’s mass is through its Schwarzschild radius. The Schwarzschild radius is the point of no return - the event horizon - surrounding the black hole, beyond which nothing can escape.The spin of a black hole, on the other hand, affects its properties such as how it absorbs material and how it impacts the surrounding galaxies. The spin of a black hole is determined by how it was formed, and the accretion disk surrounding the black hole can provide more details on the spin.Black holes also emit radiation known as Hawking radiation, which is the result of virtual particle/antiparticle pairs becoming real near the event horizon of the black hole. One particle may fall into the black hole while the other escapes, carrying with it energy in the form of radiation. The smaller the black hole, the faster it evaporates, and the higher the temperature of the radiation emitted.The physics of black holes also explains how black holes create ripples in spacetime, known as gravitational waves. When two black holes orbit each other, they create ripples in spacetime that travel outward, similar to how waves travel through water. The waves can be detected by LIGO (Laser Interferometer Gravitational-Wave Observatory).Conclusion:The physics of black holes is a complex and fascinating field of study, offering insights into the behavior of our universe. To understand the physics of black holes, scientists must explore concepts such as the properties of mass, spin, and event horizons, as well as the creation of Hawking radiation and the creation of gravitational waves. Through continued exploration and study, we can expand our understanding of the universe in ways we never thought possible.。

SAT真题0601S6

SAT真题0601S61. Black Americans in Flight, a mural honoring several aviation pioneers, also ______ the 1992 spaceflight of astronaut Mae Jemison.A. discernsB. introducesC. approximatesD. commemoratesE. asserts2. The new antifungal has such ______ uses from treating Dutch elm disease to rescuing water-damaged works of art from molds, that it is considered one of the more ______ antibiotics.A. disturbing…explicitB. innova tive…precipitou sC. mysterious…recognizedD. varied…versatile3. The child had a tendency toward aggressive behavior, a ______ fighting rather than resolving differences amicably.A. propensity forB. confusion aboutC. disregard ofD. hostility towardE. compunction about4. Physical exercise often has a ______ effect, releasing emotional tension and refreshing the spirit.A. pejorativeB. debilitatingC. catharticD. retentiveE. tenacious5. Because rap and hip-hop offer such ______ commentary on contemporary issues, they are often said to be sharp-edged musical genres.A. nebulousB. trenchantC. circumspectD. prosaicE. benignEach passage below is followed hy questions based on its content. Answer the questions on the basis of what is stated or implkxl in each passage and in any introductory material that may be provided.Questions 6-7 are based on the following passage."Mechanical pencils rule,'" my fifteen-year-old grandniece, Genevieve, declared when I invited her to be her generation's voice on school supplies. "Nobody Line sharpens anymore." Then, continuing with a fashion maven's hyperbole and arbitrary imperatives, she gave a passionate disquisition on types of clickers, new grips, smaller lead sizes, and other niceties of pencil selection. As she consigned the yellow-painted wooden pencil to the wastebasket of history. I felt a rush of nostalgia for the perfumed sharpener shavings of my youth.6. In lines 4-5, the author refers to a "fashion maven's" tone primarily in order to(A) imply that Genevieve has only a superficial appreciation of mechanical pencils(B) suggest that Genevieve is excessively concerned about her clothing(C) illustrate some of the exaggerated claims made bymechanical pencil manufacturers(D) emphasize the unpredictability of trends in consumer tastes(E) indicate that Genevieve expresses her opinions with authority and flair7. The author mentions "sharpener shavings" (line 10) in order to portray a mood of(A) unrestrained joy(B) sentimental reminiscence(C) bitter disappointment(D) cautious optimism(E) dark forebodingQuestions 8-9 are based on the following passage.Black holes are the most efficient engines of destruction known to humanity. Their intense gravity is a one-way ticket to oblivion, and material spiraling into them can heat up to millions of degrees and glow brightly. Yet, they are not all-powerful. Even supermassive black holes are minuscule by cosmic standards. They typically account for less than one percent of their galaxy's mass. Accordingly, astronomers long assumed that supermassive holes, let alone their smaller cousins, would have little effect beyond their immediate neighborhoods. So it has come as a surprise over the past decade that black hole activity is closely intertwined with star formation occurring farther out in the galaxy.8. Which best describes the function of the statement in lines 10-13 ("So it. . . galaxy") ?(A) It summarizes the points made in the first four lines of the passage.(B) It provides support for the argument asserted in thepreceding statement.(C) It introduces a new view of information presented earlier in the passage.(D) It challenges recent scientific findings.(E) It offers examples to support a theory.9. Which of the following most resembles the relationship between "black hole activity" and "star formation" (lines 11-12) as described in the passage?(A) A volcanic eruption on one continent results in higher rainfall totals on another continent.(B) Industrial emissions in one region lead to an increase in airborne pollutants in ceut regions.(C) A drought in a wilderness area causes asignificant loss of vegetation in that area.(D) Decreased oil production in one country results in higher gas prices in oil-dependent countries.(E) Overfishing in a gulf leads to an increase in the population of smaller aquatic organisms.Questions 10-15 are based on the following passage.The following passage is an excerpt from a 1909 novel. Georgia, the main character, is a reporter in an otherwise all-male newsroom.Georgia was to be married. It was the week before Christmas, and on the last day of the year she would become Mrs. Joseph Tank. She had told Joe that if they were to be married at all they might as well get it over with this year, and still there was no need of being married any earlier in the year than was necessary. She assured him that she married him simply because she was tired of having paper bags waved before her eyes every where she went and she thought if she were once officially associated withhim people would not flaunt his idiosyncrasies at her that way. And then Ernestine, her best friend, approved of getting married, and Ernestine's ideas were usually good. To all of which Joe responded that she certainly had a splendid head to figure it out that way. Joe said that to his mind reasons for doing things weren't very important anyhow; it was doing them that counted.Yesterday had been her last day on the paper. She had felt queer about that thing of taking her last assignment, though it was hard to reach just the proper state, for the last story related to pork-packers, and pork-packing is not a setting favorable to sentimental regrets. It was just like the newspaper business not even to allow one a little sentimental harrowing over one's exodus from it. But the time for gentle melancholy came later on when she was sorting her things at her desk just before leaving, and was wondering what girl would have that old desk—if they cared to risk another girl, and whether the other poor girl would slave through the years she should have been frivolous, only to have some man step in at the end and induce her to surrender the things she had gained through sacrifice and toil.As she wrote a final letter on her typewriter—she did hate letting the old machine go—Georgia did considerable philosophizing about the irony of working for things only to the end of giving them up. She had waded through snowdrifts and been drenched in pouring rains, she had been frozen with the cold and prostrated with the heat, she had been blown about by Chicago wind until it was strange there was any of her left in one piece, she had had front doors—yes, and back doors too—slammed in her face, she had been the butt of the alleged wit of menials and hirelings, she had been patronized by vapid women as the poor girl who must make her living some way, she hadbeen roasted by—but never mind—she had had a beat* or two! And now she was to wind it all up by marrying Joseph T ank, who had made a great deal of money out of the manufacture of paper bags. This from her—who had always believed she would end her days in New York, or perhaps write a realistic novel exposing some mighty evil!* the area regularly covered by a reporter10. Based on information presented in the passage, which best describes w hat Georgia was "tired of” (line 8)?(A) Being forced to earn a living(B) Being leased about Joseph Tank(C) Being considered a hack writer by some of her colleagues(D) Being betrayed by her supposed friends(E) Being the only woman in the newsroom11.The second paragraph suggests that Georgia believes the "proper state" (line 19) would be one of(A) excitement(B) wistfulness(C) amusement(D) annoyance(E) relief12. In line 27, “poor” most nearly means(A) pitiable(B) indigent(C) inferior(D) humble(E) petty13. Which most resembles the "irony" mentioned in line 34?(A) A worker moving to a distant state to take a job, only to be fired without warning(B) An executive making an important decision, only to regret it later(C) An athlete earning a starting position on a good team, only to quit in midseason(D) A student studying for a major exam, only to learn that it has been postponed(E) A person purchasing an expensive umbrella, only to lose it on the first rainy day14. The description in lines 35-45 (“She . . . two!") primarily serves to(A) suggest that Georgia envied those women who did not have to work(B) imply that Georgia would be unlikely ever to consider working as a reporter again(C) indicate the role that weather plays in the everyday life of a reporter(D) exaggerate Georgia's reluctance to relinquish her job(E) show the adversities Georgia had to overcome as a reporter15. In context, the phrase "This from her" (lines 47-48) helps to suggest that a(A) specific feeling is quite heartfelt(B) stated viewpoint is highly personal(C) certain decision is out of character(D) particular behavior is extremely upsetting(E) given attitude is unsurprisingQuestions 16-24 are based on the following passage.The following passage is adapted from a book about television and popular culture.Ridiculing television, and warning about its inherent evils, isnothing new. It has been that way since the medium was invented, and television hasn't exactly been lavished with respect as the decades have passed. I suspect, though, that a lot of the fear and loathing directed at television comes out of a time-honored, reflexive overreaction to the dominant medium of the moment. For the past several decades, television has been blamed for corrupting our youth and exciting our adults, distorting reality, and basically being a big, perhaps dangerous, waste of time. Before TV radio and film were accused of the same things. And long before that—in fact, some 2.500 years earlier—philosophers were arguing that poetry and drama should be excluded from any ideal city on much the same grounds.In Book 10 of the Republic, Plato (428-348 B.C.) attacks epic poet Homer (c. 850 B.C.) and the tragedians on several grounds, all of which have a familiar ring. "Their productions are appearances and not realities," he gripes. "Drawing, and in fact all imitation . . . [is] quite removed from the truth." The audience, as well as the art form, troubled Plato, whose remarks are colored by an implied disdain for the popularity of public performances. The "common people," as Plato so charitably calls them, are drawn to "peevish and diverse" characters—such as Odysseus and other heroes in the Iliad and the Odyssey— who (to Plato, anyway) engage in such questionable displays of emotion as "spinning out a long melancholy lamentation" or "disfiguring themselves in grief." To Plato, baring such intimate sorrows is not to be condoned. (Clearly, he would have given thumbs down to the central characters of Shakespeare's Hamlet and Macbeth.) "If you receive the pleasure-seasoned Muse' of song and epic," Plato warns, "pleasure and pain will be kings in your city, instead of law." Finally, Plato sums up his anti-arts argument with the cold,sweeping pronouncement that "poetry is not to be taken seriously." One academic who has studied and written extensively about both Plato and television suggests that Plato, rather than being anti-arts, was merely an elitist. Plato wanted to ban poetry readings and live theater, the argument goes, because, being free and accessible and raucous and extremely popular, they were the mass entertainment of that era. "If, instead of 'tragedy' and 'poetry,' and 'Homer' and 'Aeschylus,'2 you read 'mass entertainment' or 'popular media,' you'll recognize Plato's arguments as the ancestor of all the reasons we have today for being suspicious of television."To wit: poetry, by which Plato means drama, confuses us between appearance and reality. The action it presents is too extreme and violent. Most important, it's a corrupting influence, perverting its audience by bombarding it with inferior characters and vulgar subjects—and con- stituting, in Plato's own words, "a harm to the mind of its audience."If Plato's Republic had become reality, it would have been a republic with a lot of empty libraries, theaters, and museums—if, indeed, those repositories of the arts would have survived at all. Plato's personal utopia never came to pass—but throughout the centuries, wherever and whenever a new medium of artistic expression attracted a lot of people, someone has been ready, waiting, and eager to attack its content and fear its impact.1 The Muses inspired poetry and song in Greek mythology.2 Aeschylus (525-456 B.C.) was a Greek tragic dramatist.16. The opening paragraph primarily serves to(A) criticize the way television distorts the truth(B) examine the evolution of television as a medium(C) place contemporary criticism of television in a historicalcontext(D) directly compare television and drama as art forms(E) explain why television, radio, and drama appeal to the masses17. Which of the following television shows would be LEAST vulnerable to the criticism expressed in lines 8-11 ("For. . . time") ?(A) A melodrama in which police detectives attempt to solve crimes(B) A soap opera depicting interpersonal conflicts in a fictional law firm(C) A comedy whose primary characters are supernatural(D) A documentary on the state of education in the nation(E) A talk show that encourages people to confront each other in front of a studio audience18. In line 26, "drawn" most nearly means(A) brought(B) depicted(C) selected(D) attracted(E) shaped19. Which of the following best characterizes Plato's view of the heroes mentioned in line 27?(A) Admiration(B) Curiosity(C) Distrust(D) Disappointment(E) Contempt20. The "'academic'" (line 39) indicates that Plato was primarily characterized by his(A) insight(B) artistry(C) cynicism(D) irreverence(E) snobbishness21. The primary purpose of the statements in lines 39-45 ("One . . . that era") is to(A) provide an interpretation of a viewpoint described in the previous paragraph(B) show how Plato's view of politics should be understood in today's terms(C) put divergent interpretations of Plato into historical perspective(D) acc ount for the appeal of Plato’s writings(E) signal a digression in the passage22. The fourth paragraph (lines 50-56) indicates that Plato's principal objection to "poetry" (line 50) was its(A) confusing language(B) widespread popularity(C) depiction of turbulent events(D) influence on people's morals(E) misrepresentation of historical figures、23. The author of the passage would probably agree with which of the following statements about the "Utopia" referred to in line 60 ?(A) It would have encouraged new artistic ventures.(B) It would have stifled human creativity.(C) It is an ideal that we should continue to work towards.(D) It may come to pass because of the popularity of television.(E) It was a notion rejected by Greek philosophers.24. The comment about "a new medium of artistic expression" (line 62) primarily suggests that(A) the author holds a fatalistic view of the future for artistic expression(B) certain societies in the past have been slow to accept new art forms(C) people often disguise their true feelings when it comes to art(D) the popular response to a new art form will often overcome opposition to it(E) a popular new art form will always receive some form of negative response。

The M-sigma Relation in Local Active Galaxies

a r X i v :a s t r o -p h /0512461v 1 17 D e c 2005T OAPPEAR INThe Astrophysical Journal (Letters).Preprint typeset using L A T E X style emulateapj v.26/01/00THE M BH −σ∗RELATION IN LOCAL ACTIVE GALAXIESJ ENNY E.G REENEHarvard-Smithsonian Center for Astrophysics,60Garden St.,Cambridge,MA 02138ANDL UIS C.H OThe Observatories of the Carnegie Institution of Washington,813Santa Barbara St.,Pasadena,CA 91101To appear in The Astrophysical Journal (Letters).ABSTRACTWe examine whether active galaxies obey the same relation between black hole mass and stellar velocity dis-persion as inactive systems,using the largest published sample of velocity dispersions for active nuclei to date.The combination of 56original measurements with objects from the literature not only increases the sample from the 15considered previously to 88objects,but allows us to cover an unprecedented range in both stellar velocity dispersion (30–268km s −1)and black hole mass (105−108.6M ⊙).In the M BH −σ∗relation of active galaxies we ﬁnd a lower zeropoint than the best-ﬁt relation of Tremaine et al.(2002)for inactive galaxies,and an intrinsic scatter of 0.4dex.There is also evidence for a ﬂatter slope at low black hole masses.We discuss potential con-tributors to the observed offsets,including variations in the geometry of the broad-line region,evolution in the M BH −σ∗relation,and differential growth between black holes and galaxy bulges.Subject headings:galaxies:active —galaxies:kinematics and dynamics —galaxies:nuclei —galaxies:Seyfert1.INTRODUCTIONBlack holes (BHs)are a basic component of galaxies,and the existence of a tight correlation between the stellar velocity dis-persion of bulges (σ∗)and the BH mass (the M BH −σ∗relation;Gebhardt et al.2000a;Ferrarese &Merritt 2000)suggests that the growth of the BH plays a fundamental role in the growth of the bulge,although exactly how remains unclear (e.g.,Silk &Rees 1998;Kauffmann &Haehnelt 2000;Di Matteo et al.2005).The M BH −σ∗relation for inactive galaxies,in so far as it represents the ﬁnal state of the BH-bulge system,represents a boundary condition for various evolutionary scenarios,and some clues are embedded in the scatter and possible skewness in the local M BH −σ∗relation (Robertson et al.2005).Unfortu-nately,the number of available points in the relation for inactive galaxies is limited,and statistics are poor.Currently,our only recourse is to rely on BH masses from active galactic nuclei (AGNs).To the extent that the BHs in AGNs continue to gain mass,the relation of BH masses in AGNs to their host bulges may carry additional information about the establishment of the relation for inactive sources.Since the majority of BH mass was assembled at high redshift (e.g.,Yu &Tremaine 2002),we might expect to ﬁnd the strongest evidence for evolution in the M BH −σ∗relation at large cosmological distances (Shields et al.2003;Treu et al.2004;Walter et al.2004;Peng et al.2005).While undoubtedly this is a vital direction to pursue,there are a number of compelling reasons to study the local AGN M BH −σ∗relation as well.For one thing,while various methods are available to char-acterize the bulge potential,virial mass estimation (e.g.,Ho 1999;Wandel et al.1999;Kaspi et al.2000),where the dense broad-line region (BLR)gas is assumed to be on Keplerian or-bits around the central BH,is currently the most widely uti-lized tracer of BH mass.In the absence of a detailed model of the BLR,the zeropoint for the virial BH mass scale is set through a direct comparison with stellar velocity dispersionsfor a small sample of local AGNs (Gebhardt et al.2000b;Fer-rarese et al.2001;Nelson et al.2004;Onken et al.2004).The virial BH masses considered in these studies are remarkably consistent with the M BH −σ∗relation of inactive galaxies,sug-gesting virial masses are reliable.But we must be cautious.For instance,there are compelling reasons to believe the BLR is actually a disk-wind (e.g.,Murray &Chiang 1997;Proga et al.2000;Proga &Kallman 2004)whose kinematics depend on both the mass and the accretion rate onto the BH.In this sce-nario,the virial mass calibration would depend systematically on BH mass and luminosity.We require objects spanning a wide range of AGN properties to properly calibrate the primary rung in our AGN BH “mass ladder.”At the same time,we may hope to learn about evolution of the M BH −σ∗relation by look-ing at the full distribution of local BHs (Robertson et al.2005),and AGNs in particular (e.g.,Yu &Lu 2004),in the M BH −σ∗plane.2.SAMPLE SELECTION AND METHODOLOGYOur goal is to directly compare M BH with σ∗for a large sam-ple of AGNs.As outlined in Greene &Ho (2005c),we selected spectroscopically identiﬁed AGNs from the Third Data Release of the Sloan Digital Sky Survey (SDSS DR3;Abazajian et al.2005)with z ≤0.05and signal-to-noise (S/N)ratios per pixel ≥18in the region surrounding the Ca II λλ8498,8542,8662triplet (CaT).Here we consider the 32objects from Greene &Ho (2005c)with resolved σ∗measurements and robust H αline widths.To increase the sample,we have relaxed the z require-ment and included an additional 24galaxies to satisfy the cri-teria established by Greene &Ho for use of the “Fe region”(5250–5820Å):S/N ≥20( S/N =40±8),estimated Ed-dington ratios [L bol /L Edd ,where L Edd ≡1.26×1038(M BH /M ⊙)ergs s −1] 0.5,and AGN contamination <80%.In addition to the 56objects from the SDSS,we include 15intermediate-mass BHs (IMBHs;M BH ≤106M ⊙)from Greene &Ho (2004)with σ∗measurements from Barth et al.(2005),resulting in a total12GREENE&HOof71objects(see Table1).The stellar velocity dispersions are measured using aTable1.Sample PropertiesName zσ∗FWHM Hαlog L Hαlog M BH(1)(2)(3)(4)(5)(6) SDSS J000805.62+145023.40.0454140±277610±38041.13±0.047.7±0.1 SDSS J004236.86−104921.80.041978.4±101960±9741.58±0.14 6.7±0.1 SDSS J011703.58+000027.30.045698.8±162270±11041.45±0.08 6.8±0.1Note.—Col.(1):Name.Col.(2):Redshift.Col.(3):σ∗(km s−1)measured from Ca triplet, unless otherwise noted.Col.(4):FWHM Hα(km s−1).Col.(5):L Hα(ergs s−1).Col.(6): M BH=(2.0+0.4−0.3)×106M⊙(L Hα/1042ergs s−1)0.55±0.02(FWHM Hα/103km s−1)2.06±0.06 (Greene&Ho2005b).Note that these are formal uncertainties;actual uncertainties in M BH are probably dominated by systematics in BLR geometry.Table1is available in its entirety via the link to the machine-readable version above.A portion is shown here for guidance regarding its form and content.direct pixel-ﬁtting algorithm described in detail in Greene& Ho(2005c).The uncertainties are derived from simulations in which the AGN contamination and S/N ratio are varied for a grid of model galaxy spectra.Virial masses are based on reverberation mapping(Bland-ford&McKee1982),which uses the measured lag between variability in the photoionizing continuum and emission lines to estimate BLR radii.Currently there are35reverberation-mapped AGNs in the literature(Peterson et al.2004).These,in turn,are used to calibrate the radius-luminosity relation,R BLR∝L51000.64(Greene&Ho2005b;see also Kaspi et al.2005),from which it is possible to infer a radius from the AGN bining the radius with an estimate of the velocity dis-persion of the BLR yields a virial mass estimate for the BH, M BH=f R v2/G,where f is a factor that accounts for the geom-etry of the BLR.We assume f=0.75for a spherical BLR(Net-zer1990).Because our sample is selected to have strong stellar continua,virial BH mass estimation requires special care.Un-der these circumstances the most robust virial mass estimator is that based on the width and luminosity of the broad Hαemis-sion line,as advocated by Greene&Ho(2005b).The emission-lineﬁtting is described in Greene&Ho(2004,2005b).Brieﬂy, the stellar continuum is modeled and removed using a prin-cipal component analysis designed for the SDSS data by Lei Hao(Hao et al.2005).We then construct a multi-component Gaussian model of the[S II]λλ6716,6731doublet,which is shifted and scaled toﬁt the narrow Hα+[N II]λλ6548,6583 complex.The remaining(broad)Hαﬂux isﬁt with as many Gaussian components as needed to provide a statistically ac-ceptableﬁt,although we attach no physical signiﬁcance to the individual components.As described in Greene&Ho(2005b), we measure both FWHM Hαand the true second moment(σHα) from the multi-component Gaussianﬁts.The uncertainties in the luminosities and line widths are derived using simulations, although we set a minimum uncertainty of∼5%on the line width.3.RESULTSWe present the largest single collection ofσ∗measure-ments in active galaxies.The single-epoch M BH values for the SDSS and Barth et al.(2005)samples are estimated us-ing FWHM Hα(rather thanσHα;e.g.,Peterson et al.2004). In our full sample,we also include the15reverberation-mapped AGNs considered by either Onken et al.(2004)or Nelson et al.(2004),using the weighted-meanσ∗from the two works.Weighted-mean virial products for this sample are computed using the Hβlag and FWHM measurements presented in Peterson et al.(2004;the weights are calculated taking into account the asymmetric error bars),and BH masses areF IG.1.—The M BH−σ∗relation for active and inactive galaxies.Open cir-cles are measurements from this work using CaT,open squares are measure-ments using the5250–5820ÅFe region(see Greene&Ho2005c),and open triangles represent the Keck data from Barth et al.(2005)but with M BH re-calculated using FWHM Hαvalues from DR3.Literature data include those of Onken et al.(2004)and Nelson et al.(2004;crosses;BH masses from Peterson et al.2004),NGC4395and POX52(Filippenko&Ho2003;Peterson et al. 2005;Barth et al.2004;asterisks),and the primary sample of inactive galax-ies with dynamically determined values of M BH(Tremaine et al.2002;ﬁlled squares).Representative error bars are shown in the upper left for the SDSS and Keck measurements.The dashed line represents theﬁt for the M BH−σ∗relation of inactive galaxies as given by Tremaine et al.(2002).The solid line is our bestﬁt for the AGN sample with aﬁxed slope ofβ=4.02and α=7.96±0.03;the dotted lines show the measured intrinsic scatter of0.4 dex.We display histograms of theσ∗(top)and M BH(right)distributions for the Keck(shaded),SDSS(open),literature(ﬁlled),and inactive(dash-dot line) samples.studied intermediate-mass BHs in NGC4395(reverberation mass M BH=3.6×105M⊙,Peterson et al.2005;virial mass M BH=1.4×104M⊙,Filippenko&Ho2003)and in POX52 (virial mass M BH=1.6×105M⊙,Barth et al.2004).The full sample of88objects covers a range in mass of105−108.5M⊙, and a corresponding range inσ∗of30−268km s−1(see Table 1).Consistent with previous work,Figure1shows that active galaxies apparently follow the M BH−σ∗relation deﬁned by in-active systems,even with a sample size increased by a factor of nearly6.In detail,however,we doﬁnd signiﬁcant differences in zeropoint and slope compared to the inactive sample,which we describe below.Assuming a log-linear form for the M BH−σ∗relation, log(M BH/M⊙)=α+βlog(σ∗/σ0),withσ0=200km s−1,we can formally quantify deviations of AGNs from the M BH−σ∗relation of inactive systems.We use the Levenberg-Marquardt algorithm as implemented by mpﬁt to minimizeχ2,deﬁned, following Tremaine et al.(2002),asχ2≡Ni=1(y i−α−βx i)2The M BH−σ∗Relation for AGNs3selected to reﬂect the sign of y i−α−βx i.In the simpliﬁed case of symmetric errors,we recover the results of the Numerical Recipes routineﬁtexy(Press et al.1992)as implemented in IDL.We begin byﬁxing the slopeβto the best-ﬁt value of4.02 from Tremaine et al.and investigate potential offsets in zero-point.Weﬁnd,for our sample alone,a best-ﬁtα=7.96±0.03, which corresponds to an offset of−0.17±0.07from the value of α=8.13±0.06of Tremaine et al.(consistent with Gebhardt et al.2000b;Nelson et al.2004;Onken et al.2004;see summary in Table2).The offset increases to−0.21±0.06when the litera-ture values are included(using either the reverberation-mapped or virial mass for NGC4395).Note that we are using formal uncertainties in M BH,while the true uncertainties are probably dominated by our ignorance of the BLR geometry and the cor-responding uncertainty in how to extract the velocity dispersion of the virialized BLR from the observed line proﬁle.Following Tremaine et al.and Gebhardt et al.(2000a),we estimate the intrinsic scatter as the valueǫ0that,when added toǫy,results in a minimumχ2r of1.For both our sample alone and includ-ing the literature sample,weﬁnd an intrinsic scatter1ofǫ0=0.4 (dotted lines in Fig.1).This is to be compared with the esti-mated scatter of0.25-0.3dex for the inactive sample(Tremaine et al.2002).While there is probably intrinsic scatter in the un-derlying M BH−σ∗relation,we conservatively adopt0.4dex as the systematic uncertainty in the single-epoch M BH measure-ments,so that we bracket the full range in possible uncertainty. If we repeat theﬁtting above increasing the uncertainties in the single-epoch BH masses by0.4dex in quadrature,the results for our sample alone are virtually unchanged,while weﬁnd α=7.86±0.04for the full sample,which corresponds to an offset of−0.27±0.07.This offset is similar to that advocated by Onken et al.,but it is statistically much more robust,being based on aﬁnal sample that is nearly6times larger.When weﬁt both the zeropoint and slope,we obtainα= 7.84±0.04andβ=3.65±0.13(α=7.89±0.05,β=3.74±0.17)if we include(exclude)literature values,corresponding to slopesﬂatter than the value ofβ=4.02±0.32for inac-tive sources by−0.37±0.35(−0.28±0.36).Including the 0.4dex scatter to the single-epoch measurements yields an evenﬂatter slope,withα=7.79±0.04andβ=3.49±0.18 (α=7.68±0.10,β=2.95±0.32).It appears that much of theﬂattening is driven by objects with BH masses<106M⊙, which rely on an extrapolation of the radius-luminosity relation and thus may be suspect.[As pointed out by Barth et al.(2005), these objects also may be biased by selection toward large M BH at a givenσ∗.]When we remove the Barth et al.objects,as well as POX52and NGC4395,but include all other data,weﬁnd β=4.19±0.22with the formal errors,orβ=3.85±0.25with the additional0.4dex uncertainty added.The fact that the slope is still shallower when the(more realistic)uncertainties are in-cluded gives us some conﬁdence that theﬂattening is real.4.IMPLICATIONS AND CONCLUSIONSWe have established,with statistical conﬁdence for theﬁrst time,that the M BH−σ∗relation of local AGNs,while gener-ally similar to that of inactive galaxies,shows some signiﬁcant differences.Weﬁnd evidence for a lower zeropoint,shallower slope,and(probably)larger scatter.There are many competing effects,relating both to BLR physics and galaxy evolution,Table2.Fit ParametersSample Uncertaintiesαβ(1)(2)(3)(4)Our Formal7.96±0.03 4.02Full Formal7.92±0.02 4.02Our Systematic7.97±0.06 4.02Full Systematic7.86±0.04 4.02Full Formal7.84±0.04 3.65±0.13Our w/o IMBH Formal8.02±0.08 4.61±0.37Full w/o IMBH Formal7.89±0.04 4.19±0.22Our Systematic7.68±0.10 2.95±0.32Full Systematic7.79±0.04 3.49±0.18Our w/o IMBH Systematic7.66±0.13 2.88±0.54Full w/o IMBH Systematic7.81±0.05 3.85±0.25Note.—Col.(1):Data set considered;the sample“w/oIMBH”excludes the Barth et al.(2005)objects,POX52,andNGC4395.Col.(2):Adopted uncertainties.Col.(3):Zeropointassuming log(M BH/M⊙)=α+βlog(σ∗/200km s−1).Col.(4):M BH−σ∗slope,ﬁxed to4.02for theﬁrst4entries.that may contribute to the observed differences.If we positthat AGNs obey the relation of inactive galaxies exactly,thenthe scatter and zeropoint offset may be attributed to variations in the geometry of the BLR.This is the assumption made byOnken et al.(2004),who derive a statistical offset in the factorf that scales all BH masses upwards relative to the case of a spherical BLR.If,however,as suggested by disk-wind models(e.g.,Proga&Kallman2004),the geometry of the BLR de-pends on physical properties of the AGN such as the BH mass and the Eddington ratio,then virial mass estimates will not scat-ter randomly about oneﬁxed value of f.Rather,f will changesystematically with the state of the system,and its average value for any given sample will depend on the range of parameterspace spanned by the objects used to derive it.It is important to recognize that all work so far—including ours—has considereda rather limited range in M BH and L bol/L Edd,and so may lead to a biased value of f.Apart from the Greene&Ho(2004) objects studied by Barth et al.(2005),the practical challenge ofdetecting stellar absorption features to measureσ∗inevitablybiases theﬁnal sample toward relatively low Eddington ratios and BH masses.Excluding the Barth et al.objects,the samplesummarized in Figure1has a median L bol/L Edd=6×10−2and 106∼<M BH∼<108M⊙.While we expect that secondary param-eters(e.g.,L bol/L Edd)may ultimately help to account for the overall scatter in the AGN M BH−σ∗relation,we refrain from discussing this issue here because we believe that a proper anal-ysis would require a larger and more complete sample than is currently available.Apart from systematic uncertainties in virial masses,evolu-tion of the M BH−σ∗relation with cosmic time(e.g.,Shields et al.2003;Treu et al.2004;Walter et al.2004;Peng et al.2005) also imprints scatter and skewness into the local relation as a function of M BH(Robertson et al.2005).However,it is unclear at this stage how much scatter can be attributed to the fact that BHs in AGNs,in so far as they are radiating and thus accret-ing,are still gaining mass.Any differential growth between BHs and bulges will introduce additional scatter to the AGN M BH−σ∗relation if AGN accretion and star formation are not precisely synchronized(Ho2005;Kim et al.2005).If we as-cribe all the observed scatter to differential growth(taking the observed scatter of∼0.27dex in the relation for inactive ob-1The intrinsic scatter increases to0.5dex whenσHα,rather than FWHM Hαis used to estimate M BH,partly because of the difﬁculty of measuring the low-contrast line wings.We therefore consider only masses derived using FWHM Hαin the following.We estimate that disk rotation contributes at most a small error toσ∗since weﬁnd no correlation between galaxy inclination angle and deviation from M BH−σ∗(78%probability of no correlation with Kendall’sτ),and typically only the inner∼20%of the galaxy light enters theﬁber.See further arguments in Greene&Ho(2005a).4GREENE&HOjects from Tremaine et al.),there can be no more than∼0.3dex scatter(factor of2)introduced by relative BH-bulge growth. This level of growth has only modest fuel requirements that are easy to sustain in nearby galaxies;a106M⊙BH requires only 0.022M⊙yr−1to double its mass in a Saltpeter time(4.5×107 yr).Finally,taking our entire data set at face value,we doﬁnd evidence for a shallower slope than the inactive M BH−σ∗rela-tion.Whether this is the result ofﬂattening at low mass or a different slope in AGNs is difﬁcult to determine at the present time,in the absence of more AGNs with M BH>108M⊙.In this regard,Wyithe(2005)argues that the slope for the inac-tive sample steepens considerably when the four smallestσ∗values are removed,independently suggestingﬂattening at low mass.Flattening at low mass may be a result of the changing efﬁciency in AGN feedback in low-mass halos.For instance, the formalism of Vittorini et al.(2005)ﬁnds that a combina-tion of decreased optical depth(proportional to galaxy radius) and cooling times shorter than a dynamical time(small,dense halos)allows these BHs to grow to larger relative masses with-out feedback limitations.Alternatively,different growth modes between spheroidal and disk-dominated systems may result in a differentﬁnal position on the M BH−σ∗plane.On the other hand,we cannot preclude the possibility that a change in slope in the BLR radius-luminosity relation at low luminosity is re-sponsible for the change in slope in the M BH−σ∗relation.How-ever,we note that a radius-luminosity slope closer to the theo-retically preferred value of0.5(e.g.,Kaspi et al.2000)would only increase the observed discrepancy in slope.Reverberation mapping of low-mass BHs would be required to address this issue.In summary,although we have increased the population of AGNs withσ∗measurements by a factor of nearly6,we do not yet have a large enough sample,or adequate coverage of param-eter space,to uniquely identify the cause or causes responsible for the observed differences between the M BH−σ∗relation of local active and inactive galaxies.Future effort should focus on(1)further enlarging the sample of AGNs with robustσ∗measurements,(2)pushing the samples to the extremes of the mass distribution,particular above108M⊙,(3)extending the luminosity coverage to include objects with a wider range in Eddington ratios,and(4)better characterizing the BLR radius-luminosity relation over a broader range of AGN properties than is currently available.We thank L.Hao for providing her PCA code,D.Proga for useful discussion,and the SDSS collaboration for providing the extraordinary database and processing tools that made this work possible.We thank an anonymous referee for a prompt and pos-itive review.REFERENCESAbazajian,K.,et al.2005,AJ,129,1755Barth,A.J.,Greene,J.E.,&Ho,L.C.2005,ApJ,619,L151Barth,A.J.,Ho,L.C.,Rutledge,R.E.,&Sargent,W.L.W.2004,ApJ,607, 90Blandford,R.D.,&McKee,C.F.1982,ApJ,255,419Di Matteo,T.,Springel,V.,&Hernquist,L.2005,Nature,433,604 Ferrarese,L.,&Merritt,D.2000,ApJ,539,L9Ferrarese,L.,Pogge,R.W.,Peterson,B.M.,Merritt,D.,Wandel,A.,&Joseph, C.L.2001,ApJ,555,L79Filippenko,A.V.,&Ho,L.C.2003,ApJ,588,L13Gebhardt,K.,et al.2000a,ApJ,539,L13——.2000b,ApJ,543,L5Greene,J.E.,&Ho,L.C.2004,ApJ,610,722——.2005a,ApJ,627,721——.2005b,ApJ,630,122——.2005c,ApJ,in pressHao,L.,et al.2005,AJ,129,1783Ho,L.C.1999,in Observational Evidence for the Black Holes in the Universe, ed.S.K.Chakrabarti(Dordrecht:Kluwer),157——.2005,ApJ,629,680Kaspi,S.,Maoz,D.,Netzer,H.,Peterson,B.M.,Vestergaard,M.,&Jannuzi, B.T.2005,ApJ,629,61Kaspi,S.,Smith,P.S.,Netzer,H.,Maoz,D.,Jannuzi,B.T.,&Giveon,U.2000, ApJ,533,631Kauffmann,G.,&Haehnelt,M.2000,MNRAS,311,576Kim,M.,Ho,L.C.,&Im,M.2005,ApJ,submittedMurray,N.,&Chiang,J.1997,ApJ,474,91Nelson,C.H.,Green,R.F.,Bower,G.,Gebhardt,K.,&Weistrop,D.2004, ApJ,615,652Netzer,H.1990,in Active Galactic Nuclei,ed.R.D.Blandford,zer, L.Woltjer,T.Courvoisier,&M.Mayor,(Berlin:Springer),57Onken,C.A.,Ferrarese,L.,Merritt,D.,Peterson,B.M.,Pogge,R.W., Vestergaard,M.,&Wandel,A.2004,ApJ,615,645Peng,C.Y.,Impey,C.D.,Ho,L.C.,Barton,E.J.,&Rix,H.-W.2005,ApJ,in press(astro-ph/0509155)Peterson,B.M.,et al.2004,ApJ,613,682——.2005,ApJ,632,799Press,W.H.,Teukolsky,S.A.,Vetterling,W.T.,&Flannery,B.P.1992, Numerical Recipes in C(Second ed.;Cambridge:Cambridge Univ.Press), 660Proga,D.,&Kallman,T.R.2004,ApJ,616,688Proga,D.,Stone,J.M.,&Kallman,T.R.2000,ApJ,543,686 Robertson,B.,Hernquist,L.,Cox,T.J.,Di Matteo,T.,Hopkins,P.F.,Martini, P.,&Springel,V.2005,ApJ,submitted(astro-ph/0506038)Shields,G.A.,Gebhardt,K.,Salviander,S.,Wills,B.J.,Xie,B.,Brotherton, M.S.,Yuan,J.,&Dietrich,M.2003,ApJ,583,124Silk,J.,&Rees,M.J.1998,A&A,331,L1Treu,T.,Malkan,M.A.,&Blandford,R.D.2004,ApJ,615,L97Vittorini,V.,Shankar,F.,&Cavaliere,A.2005,MNRAS,363,1376 Walter,F.,Carilli,C.,Bertoldi,F.,Menten,K.,Cox,P.,Lo,K.Y.,Fan,X.,& Strauss,M.A.2004,ApJ,615,L17Wandel,A.,Peterson,B.M.,&Malkan,M.A.1999,ApJ,526,579 Wyithe,S.2005,MNRAS,submitted(astro-ph/0503435)Yu,Q.,&Lu,Y.2004,ApJ,610,93Yu,Q.,&Tremaine,S.2002,MNRAS,335,965。

Black Hole entropy in D=2+1 dimensions from extended Chern-Simons term in a gravitational b

a rX i v :h e p -t h /0006126v 1 16 J u n 2000Black Hole entropy in D =2+1dimensions from extended Chern-Simons term in a gravitationalbackgroundbyCarlos Pinheiro ∗1and F.C.Khanna ∗∗2∗Universidade Federal do Esp´ırito Santo,UFES.Centro de Ciˆe ncias Exatas Av.Fernando Ferrari s/n 01fcpnunes@cce.ufes.br/maria@.br 2khanna@phys.ualberta.caIntroductionThe topologicaly theory like Chern-Simons in D=2+1dimensions has been studied in various diﬀerent approaches in quantum Field theory,in particularly in perturbative quantum gravity[6].In general,topological action such asεµναAµ∂νAαwhere Aµmeans the abelian poten-tial vector,or the actionεµνα Γλµβ∂νΓβαλ+2where I and I ECS are respectively the action for the three dimensional gravity with a2negative cosmological constantΛ=−R+216πG√−8MG+r2ℓ2 dt2+√√√andxα=(x0,x1,x2)=(t,r,ϕ)and that the electric and magneticﬁeld are pseudo vector and scalar respectively.Thus,we introduce deﬁnitions for magnetic and electricﬁelds asE=− ∇ϕ+∂ A√√√√∂r +g11−g ∂Eϕ√∂t −g00−g ∂B√∂t − g00ℓ2 B−g00−g ∂Bα(11) withαa parameter given byα=1dr r=r+,α=0.(12)Here the function f(r)is equal to g00,and is given byf(r)=−8MG+r2where r=r+,the event horizon given byr=r+=√√M√r2−2β2r −rβ2r−3∂β(ln Z T)S=ln Z T−β∂βln Z T.(21)The contribution to entropy is calculated from each term using(10).For instance,for the second term in(10.a)we may write the partition function Z T asZ T∼eπ2ℓ2/2Gβe−π2ℓ2∂r)B+r2∂r)B(22) Then the average entropy isS∼π2ℓ2β2 ∂E rℓ2∂E rGβ−2π2ℓ2∂r r=r+·B(r=r+)(24)where theﬁrst part comes from Einstein-Hilbert action,together with eq.(6)and the second part comes from extension of Chern-Simons action in a gravitational background.Again for simplicity the contribution to entropy only for static conﬁguration,is consid-ered in eq.(10).The other terms have a non zero contribution for entropy,in particular a contribution as given by eq.(20)and eq.(24).The reason why we have a non zero contribution for entropy in the present case is because in constrast with the abelian Chern-Simons theory for electromagnetic theory or Chern-Simons for gravitational theory where the energy momentum tensor is zero,here weﬁnd the energy-momentum tensor is not zero and is given asTµνECS =2−gδI ECS2εαµνFµν,(27)In accordance with[2],this cannot be done here since our metric(5)is a particular caseof the anti de-Sitter space.Conclusions and Look out:In contrast to the abelian Chern-Simons term for the electromagnetic theory or the Chern-Simons term associated with the gravitational theory in D=2+1dimensions there is a contribution to the entropy of black holes due to higher derivative Chern-Simons extensions in a gravitational background.Appropriate vector fαfor an extension of a topologically term such as Chern-Simons [2,6]is deﬁned and we have shown that the source of entropy for black holes in D=2+1 dimension is the stress tensor which is not zero(TµνECS=0).The entropy using(21)in combination with(17)is diﬀerent than S=A4π d3xεµνρ 13! f abc f aµf bνf cρwheref aµ=(−g)1/2gµαεαλγA aγ.This goal will be hopefully realised in the next letter.Aknowledgments:I would like to thank the Department of Physics,University of Alberta for their hospital-ity.This work was supported by CNPq(Governamental Brazilian Agencie for Research).I would like to thank also Dr.Don N.Page for his kindness and attention with me at Univertsity of Alberta.References[1]Black Holes PhysicsBasic Concepts and News DevelopmentsValeri P.Frolov and Igor D.NovikovKluwer Academic Publishers.[2]Higher Derivative Chern-Simons Extensions.S.Deser–R.Jackiew–hep-th9901125V2,Jan.1999.[3]Notes on black holes and three dimensional gravity M´a ximo Ban˜a doshep-th/9903244,Mar.1999.[4]M.Ban˜a dos,T.Brotz and M.Ortiz,“Boundary dynamics and the statistical me-chanics of the2+1dimensional black hole”,hep-th/9802076.[5]J.Maldacena,A.Strominger,“ADS(3)black Holes and a stringy exclusion principle”hep-th/9804985.[6]C.Pinheiro and G.O.Pires,“Extending the Barnes-Rivers operators to D=3topo-logical gravity”.Phys.Lett.B301(1993)339-344.。

The Physics of Black Holes

The Physics of Black HolesBlack holes are one of the most mysterious and fascinating objects in the universe. They are objects so dense that nothing, not even light, can escape their gravitational pull. In this article, we will delve into the physics of black holes and explore some of the fascinating phenomena that take place in and around them.What is a black hole?A black hole is a region of space-time where the gravitational pull is so strong that nothing, not even light, can escape. This occurs because the black hole is so dense that it distorts space-time, creating a gravity well from which nothing can escape.The boundary around a black hole, beyond which nothing can escape, is called the event horizon. Once an object crosses this boundary, it is inevitably pulled into the black hole.The three types of black holesThere are three types of black holes: stellar, intermediate, and supermassive.Stellar black holes are formed from the collapse of a massive star, typically over 10 times the mass of the Sun. Intermediate black holes are more massive than stellar black holes, but less massive than supermassive black holes, which can be billions of times the mass of the Sun.How are black holes formed?Black holes are formed when a massive star runs out of fuel and can no longer support its own weight. The star collapses in on itself, creating a region of space-time where the gravitational pull is so strong that nothing can escape.Other ways black holes can be formed include the collision of two neutron stars or the accretion of matter onto a dense object, such as a neutron star, in a binary system.The singularityAt the center of a black hole lies a singularity, a point of infinite density and zero volume. Our current understanding of physics breaks down at the singularity, and it is impossible to predict what happens beyond it.The event horizonThe event horizon is the boundary around a black hole beyond which nothing can escape. The size of the event horizon is determined by the mass of the black hole. The larger the mass, the larger the event horizon.Gravity near a black holeThe gravitational pull near a black hole is so strong that it distorts space-time, causing time to slow down. The closer you get to the black hole, the stronger the gravitational pull and the slower time appears to run.This phenomenon is known as time dilation and has been observed by scientists using atomic clocks on Earth and in space orbiting a black hole.The influence of black holes on their surroundingsBlack holes have a profound influence on their surroundings. They can disrupt the orbits of nearby stars, causing them to speed up or slow down, and even fling them out of the galaxy entirely.Black holes can also accrete matter from nearby stars or gas clouds, leading to the formation of accretion disks and powerful jets of plasma that are visible across the electromagnetic spectrum.ConclusionBlack holes are fascinating objects that challenge our understanding of physics. They have a profound influence on their surroundings and can create some of the most extreme phenomena in the universe. While there is still much we don't know about black holes, the study of their physics continues to be an important area of research. So, the deeper we dive into the physics of black holes, the more fascinating and intriguing they become.。

Black Hole Mass Formula Is a Vanishing Noether Charge

δˆL = LξL = d(ξ · L).
1
thermodynamics and the diﬀeomorphism invariance of the gravitational theories. They have also claimed that the black hole entropy is a Noether charge [2],[3],[4]. But, some problems are still open even for the classical black hole thermodynamics such as how to relate the formula for mass itself with the conservation current with respect to the diﬀeomorphism invariance, in what sense the black hole entropy is a Noether charge and so on so forth.
f ∗(L(gab)) = L(f ∗(gab)),
(1)
where f ∗ is the induced map by f . The horizontal variation of L with respect to the diﬀeomorphism is deﬁned as
δˆL
=
d dλ L(fλ∗gab)|λ=0
It is easy to show the following formal equation (see, for example, [1),
(3)
where E = 0 gives rise to the Euler-Lagrange equation for the gravitational ﬁeld theory and Θ the symplectic potential. In addition, from the diﬀeomorphism invariance of the Lagrangian it follows

高级英语课后习题答案

Unit11.An inblance between the rich and poor is the oldest and most fatal ailment of republics贫富不均乃共和政体最致命的宿疾2.Their poverty is a temporary misfortune,if they are poor and meek,they eventually will inherit the earth他们的贫穷只是一种暂时性的不幸，如果他们贫穷但却温顺，他们最终将成为世界的主人3.Couples in love should repair to R H Macy‟s not their bedroom热恋的夫妇应该在梅西百货商店过夜，而不是他们的新房4.The American beauty rose can be produced in the splendor and fragrance which bring cheer to its beholder only by sacrificing the early buds which grow up around it.and so is in economic life.It‟s merely the working out of the a law of the nature and a law of god美国这朵玫瑰花以其华贵与芳香让观众倾倒，赞不绝口，而她之所以能被培植就是因为在早期其周围的花蕾被插掉了，在经济生活中情况亦是如此。

这是自然规律和上帝的意志在起作用5.(it has become) an economically not unrewarding enterprise. （它已成为）经济上收入不菲的行业6.There is~~no form of oppression that is quiet so great,no constriction on thought and effort quiet so comprehensive,as that which come from having no money at all没有哪种压迫比身无分文更厉害，也没有哪种对思想和行为的束缚比一无所有来得更全面彻底7.Freedom we rightly cherish,cherishing it,we should not use it as a cover for denying freedom to those in need 我们珍惜自由式对的。

窄线赛弗特I型星系中可能具有吸积盘热辐射起源的软X射线超

窄线赛弗特I型星系中可能具有吸积盘热辐射起源的软X射线超李晔【摘要】理论上,低质量高吸积率活动星系核的标准吸积盘黑体热辐射有可能形成软X射线波段的超出.然而,活动星系核的软X射线超温度为0.1 keV左右,显著高于标准吸积盘理论预言的最高有效温度.只有Yuan等人在2010年报道的RXJ1633+4718是一个例外,其软超温度为32.5±-8.06.0eV,显著小于0.1 keV,并与吸积盘理论预言的温度相符；此外,其光度也符合吸积盘的理论预期.因此该软X射线超很可能起源于吸积盘的热辐射.这一类源对于吸积盘理论和软X射线超的研究都有重要意义.文中使用ROSAT PSPC数据,在所有已知的窄线赛弗特I型星系(Narrow Line Seyfert I galaxies,NLSIs)中寻找类似于RXJ1633+4718的源,即软X射线超可能起源于吸积盘热辐射的源.分析了150个源的245条光谱,其中58个源的90条光谱具有显著的软X射线超.样本中软X射线超温度分布的平均值-Tsoft为0.10 keV,标准偏差为0.03 keV.除了RX J1633+4718外,只有3个源的软X射线超温度小于60 eV,而且温度接近吸积盘最高温度.这个结果表明,类似于RX J1633+4718的具有低温软X射线超的源很稀少.最后,在具有黑洞质量估计的26个源中,软超温度与黑洞质量MBH、爱丁顿比L/LEdd及预期吸积盘最高温度Tmax都没有明显的关联性,与前人的结果一致.%It is theoretically expected that the thermal radiation from accretion disks of Active Galactic Nuclei (AGNs) with low black hole mass would contribute to the soft X-ray band and result in an excess emission. However, the temperatures of the observed soft X-ray excess of AGNs are typically around 0.1 keV, significantly higher than those predicted by the standard disk model. There is only oneexception found so far, R.X J1633+4718, which has a significantly low soft excess temperature of 32.5l+8.0-6.0 eV, consistent with the maximum temperature as well as the luminosity of the predicted disk emission(Yuan et al. 2010).rnIn this paper, we search for RX J1633 like AGNs, whose soft X-ray excess temperature is close to the maximum temperature of accretion disk, in all known Narrow Line Seyfert I galaxies (NLSIs) observed with ROSAT PSPC in the archive. We analyzed the PSPC spectra of 150 NLSIs (245 observations) in total, 58 (90 observations) of which show significantly soft X-ray excess emission. In addition to RX J1633+4718, only 3 objects (4 observations) show soft X-ray excess temperatures less than 60 eV and close to the theoretical prediction of the disk emission. They form a sample of candidates for future follow-up studies. Our result indicates that RX J1633+4718 like objects are very rare. The correlations between the temperature of the soft X-ray excess and black hole mass as well as the Eddington ratio are also investigated, and no correlation is found. This confirms the previous results, and implies that the soft X-ray excess of most AGNs should originate from other mechanisms rather than the thermal emission of the accretion disk.【期刊名称】《天文学进展》【年(卷),期】2013(031)001【总页数】14页(P110-123)【关键词】活动星系核;吸积盘X射线热辐射;软X射线超【作者】李晔【作者单位】中国科学院国家天文台/云南天文台,昆明650011;中国科学院大学,北京100049;中国科学院国家天文台,北京100012【正文语种】中文【中图分类】P157.6活动星系核中心存在超大质量黑洞，物质落入中心黑洞的过程中形成吸积流，并产生辐射[1-3]。

Black Hole, White Hole and Worm Hole(黑洞,白洞和虫洞)

Fantastic Holes in the Universe
Black Hole, White Hole and Worm Hole
Song, Kaiwen School of Civil Engineering and Architecture
CONTENTS 1. What is a Black Hole 2. How are Black Holes Formed 3. White Hole & Worm Hole
called an Event Horizon(事件视界).
3
Escape Speed:
the lowest velocity that a body must have, in order to escape the gravity attraction of a particular planet or other object.
• It is theoretically possible to enter a rotating black hole, avoid the singularity, and travel into a rotating white hole and travel into another univHole
According to the general theory of relativity, a black hole is ——
a region of space from which nothing, including light, can escape.
Thank you
Song, Kaiwen School of Civil Engineering and Architecture

黑洞英文简介

Do you know a black hole do?General relativity predicts a particularly dense dark objects. Evolution of massive stars in their late collapse occurs, the dense material in particular, it has one called "event horizon" of the closed border, a black hole hidden in a huge gravitational field, due to the gravitational field so strong, including in particular photon (ie the composition of light particles, the speed c = 3.0 × 10 ^ 8m / s), including any material can only be entered could not escape. The formation of a black hole minimum mass star's core is about three times the solar mass, of course, this is the last star of nuclear quality, rather than main sequence stars in the period of quality. In addition to this stellar-class black hole, there are other sources of black holes - the so-called micro-black holes may be formed in the early universe, the so-called supermassive black holes may exist in the central galaxy. A black hole can be found through the concept of electronic equipment. The black hole within its borders to prevent any outsiders to see anything, which is the object known as the "black hole" of the reason. We were unable to observe the reflection of light it can only be affected indirectly understand the objects around the black hole. Having said that, but the black hole still has its borders, namely "event horizon (horizon)." It is assumed that the evolution of stellar black hole of death matter, is in a special super-massive stars collapse generated. In addition, the quality of a black hole must be larger than the Chandrasekhar limit of stellar evolution to the end of the form, quality, smaller than the Chandrasekhar limit of the star is unable to form a black hole。

“金工实习”课程思政教学设计

总第213期2021年第1期机械管理开发MECHANICAL MANAGEMENT AND DEVELOPMENTTotal213No.l,2021专题与综述DOI:10.16525/l4-1134/th.2021.01.105“金工实习”课程思政教学设计苟建军（内蒙古大学交通学院，内蒙古呼和浩特010000）摘要：殳足高校“止德树人”的根本任务，深入分析金工实习课程思政建设的必要性与紧迫性,探讨了基于创新授课方式、挖掘思政元素、完善考核评价三位一体的课程思政建设思路，设计了课程思政的育人目标、教学实现与考核方法，为高校进行课程思政教学优化设计、推进实践类课程思政建设进程提供新的思路。

关键词：金工实习课程思政教学设计中图分类号:G641文献标识码：A文章编号：1003-773X（2021）01-0248-02引言习总书记在全国高校思政会议上明确指出：“要用好课堂教学这个主渠道，思想政治理论课要坚持在改进中加强，提升思想政治教育亲和力和针对性，满足学生成长发展需求和期待，其他各门课都要守好一段渠、种好责任田，使各类课程与思想政治理论课同向同行，形成协同效应。

”新工科建设大潮中，我们必须紧紧扭住课程思政这个牛鼻子，不断在理论、实践实训课程教学内容中深入挖掘思政元素、在教学手段和方式上不断寻找专业教学与思政教育二者之间的结合点，互相渗透、互相促进、同向同行。

金工实习作为一门实践课程，在工科专业认证这一背景下，其面向专业范围广、学习人数比较多的特点更加凸显，如何充分挖掘金工实习教学内容中的思政育人元素,并巧妙运用其来激发、培养学生技能立身、报效祖国，运用好每一个鲜活、温暖、有力的思政教育元素,软化原本坚硬、冰冷的专业知识点，让金工实习达到过程有温度、内容有深度、效果有高度，实现实践教学所具备的“传道、立德、树人”的根本任务,十分必要也十分紧迫。

1建设思路1）创新授课方式，增强课程吸引力。

充分运用好翻转课堂、案例教学、线上线下混合教学等多种教学手段，吸引学生参与其中，增强学生间的交流分享，凸显学生的主体学习地位。

江西高考英语试卷真题

江西高考英语试卷真题在江西高考英语试卷真题中, 通常会包含阅读理解、完型填空、选词填空、短文改错、书面表达等题型。

以下是一份典型的江西高考英语试卷真题：第一部分阅读理解（共20小题，每小题2分，共40分）阅读下列短文，并根据短文内容从每题所给的A、B、C、D四个选项中选出最佳选项。

AWalking tours are back in fashion. The idea of taking a leisurely stroll while learning about a city’s history or architecture is gaining popularity.One international company is offering US$1 walking tours in 124 cities worldwide. The guided tours usually take two to three hours. The idea is that tourists pay what they think the tour is worth once they’ve made it to the end.This form of touring has been booming in popularity recently. It was reported that the tour’s app had been downloaded more than 80 million times.“I would never have come out and followed a map of the city. But, during the walking tour, I received so much information about the city, and now I’m in love with it,” said one tourist following a tour of Sydney in Australia.Walking tours are contributing to growth in many cities as they encourage tourists to learn and explore places they woul dn’t have on theirown. These tours are also popular in cities across Asia, where people often follow the guide through the busy streets and learn about local customs and historical events that shape the city.Some people are wondering whether or not the trend is going to last.“I think this is a new way of traveling. People don’t want to be a tourist anymore; they want to be a traveler,” said one tour guide.21. How long do the US$1 walking tours usually take?A. One hour.B. Two hours.C. Three hours.D. Four hours.22. What do we know about the company mentioned in the text?A. It provides free walking tours.B. It requires tourists to pay after the tour.C. It has branches in 80 different countries.D. It offers walking tours in 124 cities.BWhen you think of wild animals in Florida, you probably think of alligators or panthers. But the latest animal craze(爱好) there is something much more fearsome.They’re called “shark dogs,” and they’re actually an invasive species. They started showing up in 1999, after a hurricane hit the state. The sharkswere set free from aquariums by people who didn’t want the animals facing the storm. The sharks survived and began swimming in local waters.“Shark dogs” get their name from the mix of dogfish and sharpnose sharks. The species produces up to 94 young in a year and can get to be over two feet long.So what’s so scary about these creatures? For one, they have been known to attack humans, even though the last attack was more than 100ye ars ago. “Shark dogs” are also a danger to local wildlife. They have been spotted eating alligators in the area, as well as endangering the local manatee population.This invasive species is a major concern for Florida wildlife protectors. The “shark dogs” are destroying the local balance of wildlife and posing a risk to humans in the area.23. When did “shark dogs” start to appear in Florida?A. In 1999.B. In 1990.C. In 1989.D. In 2000.24. Why are “shark dogs” a danger to local wildlife in Florida?A. They can grow up to over two feet long.B. They produce up to 94 young in a year.C. They live in aquariums instead of local waters.D. They have been spotted eating other animals.CImagine being able to see the world in more detail than ever before. That’s exactly what happened when scientists, working with the Event Horizon Telescope (EHT), captured the image of a black hole for the first time in history.The black hole, named Powehi, is located in the galaxy M87. Powehi is 55 million light-years away from Earth and has a mass 6.5 billion times that of our sun. The EHT is a network of eight radio telescopes located around the world. When they worked together, they were able to create an image of the black hole at the center of the galaxy.This breakthrough is significant because it provides evidence for some of Einstein’s theories related to black holes and gravity. It is also a huge step forward in astrophysical research and our understanding of the universe.Now that scientists have achieved something once thought impossible, what’s next? Researchers are looking at other black holes and hoping to take more images that will expand our knowledge even further. The EHT has big plans for the future and is excited to continue pushing the limits of our understanding of the universe.25. What is the importance of the image captured by the Event Horizon Telescope?A. It offers proof of Einstein’s theories about gravity.B. It shows a detailed image of the galaxy M87.C. It proves the existence of the black hole named Powehi.D. It explains the relationship between black holes and the sun.26. What could be a possible next step for the Event Horizon Telescope?A. To look at other galaxies besides M87.B. To discover another black hole in the universe.C. To take more images of black holes for research.D. To focus on studying the sun and its mass.第二部分完型填空（共20小题，每小题1.5分，共30分）阅读下面短文，掌握其大意，然后从每题所给的A、B、C、D四个选项中选出最佳选项。

短语shutup的中文是什么意思

短语shutup的中文是什么意思短语shut up的中文是什么意思英语单词的产生是汉英两种语言双向交流的产物，一些带有中国特色的名称和概念进入了英语词汇，同时还有一些英语词汇进入了汉语，在文化环境中衍生出新的含义，形成了英语词汇的语义文化特征。

下面是是店铺收集短语shut up的中文是什么意思，欢迎大家阅读参考。

英语短语shut up的中文意思安静，闭嘴; 关严; 憋1. Can't you shut your friend up?你不能叫你朋友闭嘴吗?英语短语shut up的单语例句1. Local residents expressed outrage over the beefed up security, with some 3000 CIA agents standing by and Cairo's main roads shut down.2. Authorities will step up measures to shut down substandard organic food businesses, cracking down on illegal activities such as certification misuse and counterfeiting of organic food products.3. It ordered local authorities to " clean up " such sites and shut down those with " serious violations ".4. Wuxi ordered the rest to clean up by coming June or be permanently shut down.5. The coal supply has shrunk as the government has stepped up efforts to shut down coal mines this year after a series of fatal accidents.6. Zeng urged more efforts to shut up unqualified SMEs and intensify monitoring on market admittance and financing of SMEs.英语短语shut up的双语例句1. After the failure last time he shut himself up in the room reading insanely.上次惨败之后，他就开始闭门苦读，并且发誓要一雪前耻。

Basic English Vocabulary

Basic English VocabularyFor Global Communication25% of all that is spoken, read, or written. (10)Ten Words, they are:and, be, have, I, it, me, of, the, will, you.50% of all words used by adults (51)a, about, all, are, as,but,can, come,day, dear, do,for, from,get, go, good,had, he, hear, her,if, in, is,letter,much, my,no, not,on, one, our,put,say, she, so, that, there, they, this, time, though, to,verywas, we, when, with, would , write, your, yours.200 most used nouns (pictured things)angle, ant, apple, arch, arm, army, baby, bag, ball, band, basin, basket, bath, bed, bee, bell, berry, bird, blade, board, boat, bone, book, boot, bottle, box, boy, brain, brake, branch, brick, bridge, brush, bucket, bulb, button,cake, camera, card, carriage, cart, cat, chain, cheese, chest, chin, church, circle, clock, cloud, coat, collar, comb, cord, cow,, cup, curtain, cushion,dog, door, drain, drawer, dress, drop,ear, egg, engine, eye,face, farm, feather, finger, fish, flag, floor, fly, foot, fork, fowl, frame,garden, girl, glove, goat, gun, hair, hammer, hand, hat, head, heart, hook, horn, horse, hospital, house,island,jewel,kettle, key, knee, knife, knot,leaf, leg, library, line, lip, lock,map, match, monkey, moon, mouth, muscle,nail, neck, needle, nerve, net, nose, nut,office, orange, oven,parcel, pen, pencil, picture, pig, pin, pipe, plane, plate, plough, pocket, pot, potato, prison, pump,rail, rat, receipt, ring, rod, roof, root,sail school, scissors, screw, seed, sheep, shelf, ship, shirt, shoe, skin, skirt, snake, sock, spade, sponge, spoon, spring, square, stamp, star, station, stem, stick, stocking, stomach, store, street, sun, table, tail, thread, throat, thumb, ticket, toe, tongue, tooth, town, train, tray, tree, trousers, umbrella,wall, watch, wheel, whip, whistle, window, wing, wire, worm. Words describing "operations".(96) a, about, after, again, against, all, almost, among, and, any, as, at,be, because, before, between, but, by,come,do, down,east,, enough, even, ever, everyfar, for, forward, from,get, give, go,have, he, here, how,I, if, in,keep,let, little,make, may, much,near, no, north, not, now,of, off, on, only, other, out, over,please, put,quite,say, see, seem, send, so, some, south, still, such,take, than, that, the, then, there, this, though, through, till to, together, tomorrow,under, up,very,well, west, when, where, while, who, why, with,yesterday, you.Words describing "qualities" (General). (100)able, acid, angry, automatic, beautiful, black, boiling, bright, broken, brown,cheap, chemical, chief, clean, clear, common, complex, conscious, cut, deep, dependent,early, elastic, electric, equal,fat, fertile, first, fixed, flat, free, frequent, full,general, good, great, grey, hanging, happy, hard, healthy, high, hollow,important,kind,like, living, long,male, married, material, medical, military,natural, necessary, new, normal, open, parallel, past, physical, political, poor, possible, present, private, probable,quick, quiet,ready, read, regular, responsible, right, round,same, second, separate, serious, sharp, smooth, sticky, stiff, straight, strong, sudden, sweet,tall, thick, tight, tired, true, violent,waiting, warm, wet, wide, wise, yellow, young.Words describing "opposites". (50)awake,bad, bent, bitter, blue,certain, cold, complete, cruel, dark, dead, dear, delicate, different, dirty, dry,false, feeble, female, foolish, future,green,ill,last, late, left, loose, loud, low,mixed,narrow,old, opposite,public,rough,sad, safe, secret, short, shut, simple, slow, small, soft, solid, special, strange, thin,white, wrong.Nouns describing "general things" (392)account, act, addition, adjustment, advertisement, agreement, air, amount, amusement, animal, answer, apparatus, approval, argument, art, attack, attempt attention, attraction, authority, back, balance, base, behaviour, belief, birth, bit, blood, blow, body, brass, bread, breath, brother, building, burn , burst, business, butter,canvas, care, cause, chalk, chance, change, cloth, coal colour, comfort, committee, company, comparison, competition, condition, connection control, cook, copper, copy, cork, cotton, cough, country, cover crack, credit, crime, crush, cry, current, curve, damage, danger, daughter, day, death, death, debt, decision, direction, discovery, discussion, disease, disgust, distance, distribution, division, doubt, drink, driving, dust,earth,, edge, education, effect, end, error, event, example, exchange, existence, expansion, experience, expert,fact, fall, family, father, fear, feeling, fiction, field, fight, fire, flame,, flight, flowers, fold, food, force, form, friend, front, fruit,glass, gold, government, grain, grass, grip, group, growth, guide,harbour, harmony, hate, hearing, heat, help, history, hole, hope, hour, humour,ice, idea, impulse, increase, industry, ink, insect, instrument, insurance, interest, invention, iron, jelly, join, journey, judge, jump,kiss, knowledge,land, language, laugh, law, lead, learning, leather, letter, level lift, light, limit, linen, liquid, list look, loss, love,machine, man, manager, mark, market, mass, meal, measure, meat, meeting, memory, metal, middle, milk, mind, mine, minute, mist,money, month, morning, mother, motion, mountain, move, music, name, nation, need, news, night, noise, note, number, observation, offer, oil, operation, opinion, order, organization, ornament, owner,page, pain, paint, paper,, part, paste, payment, peace, person, place, plant, play,, pleasure, point, poison, polish,, porter, position, powder, power, price, print, produce, profit, property, prose, protest, pull, punishment, purpose, push,quality, question,rain, range, rate, ray, reaction, reading, reason, record, regret, relation, religion, representative, request, respect, rest, reward, rhythm, rice, river, road, roll, room,, rub, rule, run,salt, sand, scale, science, sea, seat, secretary, selection, self, sense, servant, sex, shade, shake, shame, shock, side, sign, silk, silver, sister, size, sky, sleep, slip, slope, smash, smell, smile, smoke, sneeze, snow, soap, society, son, song, sort, sound, soup, space, stage, start, statement,, steam, steel, step, stitch, stone, stop, story, stretch, structure, substance, sugar, suggestion, summer, support, surprise, swim, system, talk, taste, tax, teaching, tendency, test, theory, thing, thought, thunder, time, tin, top, touch, trade, transport, trick, trouble, turn twist,unit, use,value,, verse, vessel, view, voice,walk, war, wash, waste, water, wave, wax, way, weather, week, weight, wind, wine, winter, woman, wood, wool, word, work, wound, writing, year.These basic rules apply:Plurals add 's'Derivatives add 'er', 'ing'.Adverbs end in 'ly' from qualifiers.Add degrees with 'more' and 'most'Question by inversion and 'do'.Measurement, numerals, currency,calendar, and international terms in English form.From this basic list of almost 900 words, a rich, effective English vocabulary can be developed.。

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2.2. Observations and data reduction
High signal-to-noise (Table 1) spectra were obtained using the Low Resolution Imaging Spectrograph (Oke et al. 1995) at the Keck-I telescope on 2003 March 6 (S99) and 2003 Sep 3. Two exposures were obtained for each object, with total exposure times ranging between 1200s and 5280s. The 900/5500 grating with a 1′.′5 slit provided a resolution of σs = 55 ± 5 kms−1 around Mg5175 and Fe5270, as measured from sky lines and arc lamps. Internal ﬂat ﬁelds were obtained after each object exposure, to correct the fringing pattern of the red CCD. A set of A0V stars from the Hipparcos catalog1 to be 15 degrees from each target was observed during the night as ﬂux calibrators, and to measure the B-band atmospheric absorption. Spectrophotometric standards were observed during twilights. Internal tests, and comparison with SDSS spectra, show that this procedure corrects the B-band absorption to a level of a few parts in a thousand and relative ﬂux calibration to a few percent. The data reduction was similar to that in Treu et al. (2001).
Interesting clues can be obtained from the cosmic evolution of empirical relations. Different scenarios – all reproducing the local BHS relation – predict diﬀerent evolution. For example, in a pure luminosity evolution scenario of spheroids, σ would not change with time, while MBH would increase as a result of accretion. A typical 107M⊙ BH accreting at an average rate 0.01M⊙yr−1 (e.g., Sun & Malkan 1989), would double its mass in a Gyr. This would predict the MBH at given σ to increase with time, possibly changing the slope of the BHS relation if the accretion rate is a function of MBH (e.g. Small & Blandford 1992). In contrast, if spheroids grew faster than BH, σ at ﬁxed MBH could increase with time.
1Based on data collected at Keck Observatory, operated by Caltech and the University of California. 2University of California at Los Angeles, CA 90095; ttreu@, malkan@ 3Hubble Fellow 4California Institute of Technology. Pasadena, CA 91125 5Kavli Institute for Particle Astrophysics and Cosmology Stanford, CA; rdb@
In this Letter we present the ﬁrst results from an observational program aimed at measuring the cosmic evolution of the BHS relation. We measure the BHS relation for a sample of 7 Seyfert 1s at z ∼ 0.37. This redshift is high enough to provide a time baseline over which we might expect evolution, yet low enough to be observationally practical.
2. Observations and analysis
2.1. Experiment Design and Sample Selection
The sphere of inﬂuence of supermassive BHs in galaxies at cosmological distances cannot be resolved even with the Hubble Space Telescope (HST). Therefore we target active galaxies, where MBH can be obtained from the integrated properties of the broad emission-line region. In this paper, we will combine an empirically calibrated photo-ionization estimate of the size of the broad line region (hereafter ECPI; Wandel et al. 1999) with its kinematics measured from the rms width of Hβ, to deduce the central BH mass. To measure simultaneously the stellar velocity dispersion from absorption lines, requires nuclei of relatively low luminosity, so that the fraction of stellar light in the integrated spectrum is substantial. Seyfert 1s provide the right balance between the two components: absorption features typical of old stellar populations such as Mg5175 and Fe5270 are clearly visible in their high signal-to-noise integrated spectra. In order to minimize the uncertainties from sky subtraction and atmospheric absorption corrections, it is convenient to select speciﬁc redshift windows where the relevant emission and absorption lines fall in clean regions of the atmosphere. Accordingly, we selected the “clean window” z ∼ 0.37, which corresponds to a look-back time of ∼ 4 Gyrs, for H0 = 70 km s−1 Mpc−1, Ωm = 0.3, and ΩΛ = 0.7.
–3–
objects was selected according to the following criteria: 0.35 < z < 0.37, Hβ equivalent width and rms width greater than 5 ˚A. These are suﬃcient to select only broad Hβ galaxies, but are loose enough that they should not introduce signiﬁcant bias in MBH. The relevant properties of the observed objects are listed in Table 1.
ABSTRACT
The velocity dispersion of 7 Seyfert 1 galaxies at z ∼ 0.37 is measured using high signal-to-noise Keck spectra. Black hole (BH) mass estimates are obtained via an empirically calibrated photoionization method. We derive the BH mass velocity dispersion relationship at z ∼ 0.37. We ﬁnd an oﬀset with respect to the local relationship, in the sense of somewhat lower velocity dispersion at a ﬁxed BH mass at z ∼ 0.37 than today, signiﬁcant at the 97% level. The oﬀset corresponds to ∆ log σ = −0.16 with rms scatter of 0.13 dex. If conﬁrmed by larger samples and independent checks on systematic uncertainties and selection eﬀects, this result would be consistent with spheroids evolving faster than BHs in the past 4 Gyrs and inconsistent with pure luminosity evolution.