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

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。

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 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 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.。

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 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。

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。

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.。