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a rXiv:as tr o-ph/34514v129Apr23Carnegie Observatories Astrophysics Series,Vol.1:Coevolution of Black Holes and Galaxies,2003ed.L.C.Ho (Pasadena:Carnegie Observatories,/ociw/symposia/series/symposium1/proceedings.html)Abstract Radio emission from early–type (E and S0)galaxies usually signals the presence of a central supermassive black hole.If radio luminosity and black–hole mass are correlated,then we can use the large sample of radio galaxies observed in the 2dF Galaxy Redshift Survey (2dFGRS)to estimate the local (z <0.1)black–hole mass function for early–type galaxies.Integrating over this mass function yields a local black–hole mass density of ρBH =1.8+0.4−0.6×105M ⊙Mpc −3(H 0=50km s −1Mpc −1,Ω0=1),in good agreement both with the local value derived from galaxy velocity dispersions and with the high–redshift value de-rived from QSOs.This supports earlier suggestions that local radio galaxies are the direct descendants of most or all of the high–redshift QSOs.1.1Does Radio Luminosity Scale with Black Hole Mass?The relationship between black–hole mass and radio luminosity in nearby galaxies is currently a topic of much debate.Auriemma et al.(1977)first showed that (optically)brighter elliptical galaxies are more likely to be radio sources,so the discovery of a corre-lation between black–hole mass and bulge luminosity (Magorrian et al.1998)means that some correlation between black–hole mass and radio luminosity must exist for early–type galaxies,at least in a statistical sense (there may still be considerable scatter for individual objects).Franceschini,Vercellone &Fabian (1998)found a remarkably tight relationship between black–hole mass and radio power (P radio ∝M 2.5BH )in nearby galaxies,implying that the totalradio power emitted by a galaxy is both an excellent tracer of the presence of a supermassive black hole and a good estimator of its mass.However,analysis of larger data sets by Laor (2000)and Ho (2002)found a much larger scatter in the M BH –P radio correlation.All these authors used data sets which contained a mixture of galaxy types (e.g.spirals,ellipticals,Seyfert galaxies,radio galaxies and quasars).More recently,Snellen et al.(2003)have investigated the correlation between black–hole mass and radio power for the large sample of nearby elliptical galaxies with stellar velocity dispersions measured by Faber et al.(1989).They found that that most optically–selected (i.e.‘relatively passive’)elliptical galaxies obeyed the Franceschini et al.(1998)relation between black–hole mass and radio luminosity.Black hole mass is clearly not the only variable which determines radio luminosity —weE.M.Sadlerknow that radio galaxies were more powerful and/or more numerous in the past,whereas the mass of their central black holes can only increase with cy et al.(2001)suggest that radio power scales with both black–hole mass and accretion rate,which provides a plausible mechanism for time–varying radio emission.1.2The2dF Galaxy Redshift SurveyThe recently-completed2dF Galaxy Redshift Survey(2dFGRS;Colless et al.2001) obtained optical spectra and redshifts for over220,000galaxies in the local(z<0.3)universe. Cross-matching these galaxies with sensitive all–sky radio imaging surveys like the NRAO VLA Sky Survey(NVSS;Condon et al.1998)makes it possible to assemble samples of several thousand radio-galaxy spectra which can be used to derive accurate radio luminosity functions for both AGN and star-forming galaxies(Sadler et al.2002).Cross-matching the2dFGRS and NVSS surveys provides a data set which is both large and very homogeneous in quality.Although only about1.5%of2dFGRS galaxies are matched with radio sources above the NVSS detection limit of2.5mJy at1.4GHz,this still represents one of the largest and most uniform set of radio–galaxy spectra so far obtained. The high quality of most of the2dFGRS spectra means that it is usually straightforward to determine whether the radio emission arises mainly from an AGN,or from processes related to star formation.Thefinal data set(work in progress)will be a factor of four larger.Most2dFGRS–NVSS radio galaxies(at least90%of those classified as AGN)show either an absorption–line spectrum typical of giant ellipticals or LINER–like emission lines superimposed on a stellar continuum,i.e.they fall into the class of‘relatively passive’radio galaxies discussed by Snellen et al.(2003).It therefore seems reasonable to use the relation between black–hole mass and radio power from Franceschini et al.(1998)together with the accurate local radio luminosity function from the2dFGRS–NVSS sample to estimate the local mass function for massive black holes.This calculation only requires that the Franceschini et al.(1998)relation holds in a statistical sense(there can still be some scatter for individual objects)for early–type galaxies with relatively quiescent optical spectra.1.3The Local Radio Luminosity Function for2dFGRS Radio GalaxiesFigure1.1shows the local radio luminosity function for active galaxies at1.4GHz, as derived by Sadler et al.(2002).The values are in good agreeement with earlier determina-tions,but have much lower error bars in the luminosity range1022–1025W Hz−1.Remark-ably,the space density of radio–emitting AGN is extremely close to a simple power–law of the form(1.1)Φ(P1.4)∝P−0.62±0.031.4over almostfive decades in luminosity from1020.5to1025W Hz−1,before turning down above1025W Hz−1.1.4The Local Black Hole Mass Function for Early-type GalaxiesFollowing the precepts of Franceschini et al.(1998),the1.4GHz radio luminosity function in Figure1.1can be converted to a black hole number density assuming log10M BH(M⊙)=0.376log10P1.4(WHz−1)+0.173.(1.2)E.M.SadlerFig.1.1.Local radio luminosity function for active galaxies at1.4GHz.Filled circles are points from the2dFGRS–NVSS data set,while open triangles are the Sadler et al.(1989)values for nearby E/S0galaxies,converted from5GHz assum-ing a spectral index ofα=−0.7.The solid line shows the best–fitting value of an analyticfitting function as described by Saunders et al.(1990).Luminosities are calculated using H0=50km s−1Mpc−1andΩ0=1.Figure1.2shows the results—the downturn in the radio luminosity function above1025 W Hz−1implies a corresponding steeper downturn in the space density of black holes more massive than about5×109M⊙.The derived number densities mostly agree well with the values derived by Franceschini et al.(1998),though the2dFGRS–NVSS points are system-atically higher at the high–mass end.This may be the result of luminosity evolution within the relatively large volume(to z∼0.2)probed by the2dFGRS for powerful radio sources.Figure1.3shows the mass density distribution,i.e.the number density of black holes of a given mass multiplied by that mass.Again,there is a stronger downturn above a few times 109solar masses.At the low–mass end,the mass density of black holes continues to increase down to the lowest values(a few times107M⊙)probed by radio surveys.Integrating overE.M.SadlerFig.1.2.Black hole number density,in mag−1Gpc−3for radio galaxies in the local universe.Thefilled circles and solid line are converted from the data points and analyticfit shown in Figure1.1.Crosses show values from Franceschini et al.(1998).the curve in Figure1.4gives the total mass density of massive black holes(M BH>7.6×107M⊙)in nearby galaxies:×105M⊙Mpc−3(1.3)ρBH=1.8+0.4−0.6This is clearly a lower limit,since the derived black–hole mass density is still increasing at the lowest values of M BH we can measure.However,our value forρBH agrees well with the values recently derived by Yu&Tremaine(2002)and Aller&Richstone(2002)from optical measurements of galaxy velocity dispersions.It is also within the range1.4−2.2×105derived by Chokshi&Turner(1992)from the optical luminosity function of QSOs,implying that local radio–emitting AGN are the direct descendants of most or all of the high–z QSOs.Similar conclusions have been reached by others(e.g.Franceschini et al.1998;Salucci et al.1999;Merritt&Ferrarese2001).E.M.SadlerFig.1.3.Local black–hole mass density(in M⊙mag−1Mpc−3).As in Figure1.2, thefilled circles and solid line correpond to the data points andfit from Figure1.1.1.5ConclusionsBoth massive black holes and low–power radio sources are common in nearby el-liptical galaxies.If radio luminosity is a good estimator of black–hole mass in these galaxies, then a comparison of the black–hole mass density in nearby early–type galaxies and distant QSOs suggests that local radio-emitting AGN(i.e.luminous elliptical galaxies)are the di-rect descendants of most or all of the distant QSOs.AcknowledgementsMuch of this work was done in collaboration with members of the2dFGRS team,and is described in more detail in our joint paper.ReferencesAller,M.C.,&Richstone,D.2002,AJ,124,3035Auriemma,C.,Perola,G.C.,Ekers,R.D.,Fanti,R.,Lari,C.,Jaffe,W.J.,&Ulrich,M.H.1997,A&A,57,41E.M.SadlerChokshi,A.,&Turner,E.L.1992,MNRAS,259,421Colless,M.,et al.2001,MNRAS,328,1039Condon,J.J.,Cotton,W.D.,Greisen,E.W.,Yin,Q.F.,Perley,R.A.,Taylor,G.B.,&Broderick,J.J.1998,AJ, 115,1693Faber,S.M.,Wegner,G.,Burstein,D.,Davies,R.L.,Dressler,A.,Lynden-Bell,D.,&Terlevich,R.J.1989, ApJS,69,763Franceschini,A.,Vercellone,S.,&Fabian,A.C.1998,MNRAS,297,817Ho,L.C.2002,ApJ,564,120Lacy,M.,Laurent-Muehleisen,S.A.,Ridgway,S.E.,Becker,R.H.,&White,R.L.2001,ApJ,551,L17 Laor,A.2000,ApJ,543,L111Magorrian,J.,et al.1998,AJ,115,2285Merritt,D.,&Ferrarese,L.2001,MNRAS,320,L30Sadler,E.M.,Jenkins,C.R.,&Kotanyi,C.G.1989,MNRAS,240,591Sadler,E.M.,McIntyre,V.J.,Jackson,C.A.,&Cannon,R.D.1999,PASA,16,247Sadler,E.M.,et al.2002,MNRAS,329,227Salucci,P.,Szuszkiewicz,E.,Monaco,P.,&Danese,L.1999,MNRAS,307,637Saunders,W.,Rowan-Robinson,M.,Lawrence,A.,Efstathiou,G.,Kaiser,N.,Ellis,R.S.,&Frenk,C.S.1990, MNRAS,242,318Snellen,I.A.G.,Lehnert,M.D.,Bremer,M.N.,&Schilizzi,R.2003,MNRAS,submitted(astro-ph/0209380) Yu,Q.,&Tremaine,S.D.,2002,MNRAS,335,965。
What is a black holeIntroductionA black hole is a mysterious and fascinating concept in the field of astrophysics. It is an area in space where gravitational forces are so strong that nothing, not even light, can escape its pull. In this article, we will explore the nature, formation, and properties of a black hole.DefinitionA black hole can be defined as a region in space-time with extremely strong gravitational forces, caused by a massive amount of matter packed into a small area. This compact mass creates a gravitational field that is so intense, even electromagnetic radiation cannot escape its gravitational pull.FormationBlack holes can form through different processes. One common formation scenario involves the collapse of massive stars. When a star that is several times more massive than our Sun exhausts its nuclear fuel, it undergoes a supernova explosion. If the remaining core of the star is above a certain critical mass, it collapses inward, forming a black hole.Another way black holes can form is through the merging of two smaller black holes. As they approach and eventually collide, their combined mass becomes concentrated into a single black hole.Properties1.Event Horizon: Every black hole has an event horizon, which is the boundary beyond which nothing can escape its gravitational pull. Once an object crosses the event horizon, it is trapped inside the black hole.2.Singularity: At the core of a black hole lies a singularity, a point of infinite density. The laws of physics, as we currently understand them, break down at this point. General relativity predicts that the singularity is a region of zero volume and infinite density.3.Spacetime Curvature: The immense mass concentrated in a black hole causes significant curvature of space and time in its vicinity. This curvature creates the strong gravitational forces that characterize a black hole.4.No Hair Theorem: According to the no hair theorem, black holes have no additional properties beyond mass, electric charge, and angular momentum. This means that all other information about matter that enters a black hole is lost, except for these three characteristics.5.Hawking Radiation: Despite their reputation for absorbing everything, black holes can actually emit radiation, known as Hawking radiation. This phenomenon occurs due to quantum effects near the event horizon, where particle-antiparticle pairs are spontaneously created. In some cases, one particle falls into the black hole, while the other escapes, resulting in the emission of radiation.Types of Black Holes1.Stellar Black Holes: These are formed from thecollapse of massive stars and typically have a mass of a few times that of our Sun.2.Intermediate Black Holes: Intermediate blackholes have masses ranging from thousands to millions of times that of our Sun. Their origins are still not entirelyunderstood.3.Supermassive Black Holes: These are the largestknown black holes, with masses millions or even billions of times greater than our Sun. They are believed to reside at the centers of most galaxies, including our own Milky Way.ConclusionBlack holes are extraordinary phenomena that captivate the imagination of scientists and the general public alike. They represent the extreme limits of nature’s principles, challenging our understanding of space, time, and the laws of physics. While much remains to be understood about black holes, the study of these enigmatic objects continues to shed light on the mysteries of the universe.。
重庆市第八中学校2024届高三下学期高考适应性月考（五）英语试卷学校：___________姓名：___________班级：___________考号：___________一、阅读理解DAY TRIP ITINERARY (行程)After a warm reception from your tour manager at your dedicated pick-up point in London, settle in your comfortable coach as we set off on our journey towards Stonehenge. The world's most famous prehistoric monument has inspired people to study and interpret it for centuries, yet many questions remain to be answered-about who built it, when, and why.After visiting Stonehenge, we drive to Windsor Castle, which is home to royalty and 1,000 years of royal history. The stunning 13-acre site is the largest and oldest occupied, working castle in the world. There are many famous, must-see moments within these spectacular rooms in the castle, like the grand Waterloo Chamber and the magnificent Crimson Drawing Room.In the early evening, we make our way towards London and proceed towards your respective drop off points and bid farewell to all friends you have made on the tour. ESSENTIALS TO CARRY WITH YOUWe recommend you wear comfortable clothing and carry essentials such as a jacket or jumper, dry snacks, water, tissues, chargers, power bank, ete., in your handbag as access to the luggage hold is only possible until a comfort stop or arrival at your destination. Hot foods are not allowed to be carried or consumed inside the coach.PICK-UP POINTSand travelling.1．How many tourist spots will the participants visit?A.Two.B.Three.C.Four.D.Five.2．It is advised to put your essentials in the handbag because _______.A.the luggage hold is inaccessible when the bus is in motionB.they are not allowed to be carried inside the coachC.it's convenient for you to enjoy hot foodsD.drivers are likely to access them3．Where is the text most probably taken from?A.A journal.B.A webpage.C.A travel brochure.D.A magazine.It all started with a simple question："Can I paint your portrait? "One day in the summer of 2015, Peterson was relaxing in his living room, reading the book Love Does, about the power of love in action, when his quiet was disturbed by a homeless man outside his apartment. Inspired by the book's compassionate message, Peterson made a decision：He was going to go outside and introduce himself.In that first conversation, Peterson learned that the man's name was Matt Faris. He'd moved to Southern California from Kentucky to pursue a career in music, but he soon fell on hard times and ended up living on the street for more than a decade. "I saw beauty on the face of a man who hadn't shaved in probably a year, because his story, the life inside of him, inspired me," Peterson recalled. Therefore, Peterson asked if he could paint Faris's portrait. Faris agreed.Peterson's connection with Faris led him to form Faces of Santa Ana, a nonprofit organization focused on befriending and painting portraits of members of the community who are unhoused. Peterson sells the paintings for money, splitting the proceeds and putting half into a "love account" for his model. He then helps people use the money to get back on their feet.Many of Peterson's new friends use the donations to secure immediate necessities medical care, hotel rooms, food. Faris used the funds from his portrait to record an album, fulfilling his musical dreams. Another subject, Kimberly Sondoval, had never been able to financially support her daughter. She asked, "Can I use the money to pay my daughter's rent? " When the check was delivered, "They both wept in my arms, "Peterson recalls.Peterson has painted 41 of these portraits himself. But there's more to the finished products than the money they bring to someone who's down and out. He's discovered that the buyers tend to connect to the story of the person in the painting, finding similarities and often friendship with someone they might have otherwise overlooked or stereotyped."People often tell me, 'I was the one that would cross the street, but I see homeless people differently now, ' " Peterson says. "I didn't know that would happen."4．What made Peterson start a conversation?A.The curiosity about strangers.B.The touching story of Matt Faris.C.The disturbance by a homeless man.D.The sympathetic message in Love Does.5．What do we know about Faces of Santa Ana?A.It pays the homeless salaries.B.It is an official nonprofit organization.C.It tries to restore the lives of Peterson's models.D.It spends all the money on helping the unhoused.6．After buying a portrait, a buyer might view the homeless as ______?zy and poorB.odd but inspiringC.disturbing and untidyD.pitiful but respectable7．Which of the following is the best title of this text?A.Art with Purpose: Love Account MattersB.Hope in Paintings: Help Knows No RaceC.Faces of Compassion: Painting a New PerspectiveD.Encounter with Strangers: Embracing New FriendsFilm Puts Justifiable Defense in SpotlightThe film, Article 20, directed by Zhang Yimou, draws its name from Article 20 of the Criminal Law, which focuses on the sometimes controversial legal concept of justifiable defense. Drawing inspiration from real-life cases of justifiable defense, the film gained widespread attention and struck a chord with the public during the Spring Festival holiday. The movie calls for a detailed interpretation of legal terms and urges against compromising on unlawful conduct.According to the Criminal Law, when a person, faced with an unlawful attack, takes action to protect his or her own rights or interests or those of others, and the attacker is thereby harmed, the defender will be considered to have acted in justifiable defense and will not bear criminal responsibility. For some time, justifiable defense has been regarded as a "dormant clause" (沉寂条款) , due to the influence of misconceptions, such as "whoever is injured or killed is right".But the true meaning of the law should be to increase the responsibility for wrongdoers, rather than burdening good people. Recent cases have shown that, for ordinary citizens, justifiable defense is no longer a pipe dream. A high-profile case in Kunshan, Jiangsu province, in 2018 served as a wake-up call and caught the attention of authorities regarding such cases. In that case, a traffic argument led to a motorist who took a knife with him confronting another man.The motorist was killed, and police and judges determined that the defender's actions constituted justifiable defense. Since then, the justifiable defense clause has been applied in several places across the nation. The concern over justifiable defense reflects the public's demand for fairness, justice, security and rule of law.Luo Xiang, a renowned professor of criminal law at China University of Political Science and Law, said in a recent comment about the film Article20 that the public and judges should avoid taking a "godlike" perspective. Instead, they should consider the situation in which the defender was involved, empathize with the defender's position, and stop themselves from making excessive demands on the defender, Luo said.8．Why did the film Article 20 attract the audience's attention?A.It was released during the Spring Festival holiday.B.It is named after one article in the Criminal Law.C.It explores real-life cases of justifiable defense.D.It was directed by Zhang Yimou.9．According to the Criminal Law, the victim will be free from criminal responsibility when ______.A.the victim gave up his legal rightsB.the robber kept silent about the robberyC.the robber was hurt worse than the victimD.the victim knifed the armed robber to stop the ongoing crime10．What is the function of the case in Kunshan in Paragraph 3?A.Making comparisons.B.Listing reasons.C.Explaining misconceptions.D.Providing evidence.11．What does Luo Xiang suggest judges do?A.Take a “godlike” viewpoint with the public.B.Put oneself in the defender's shoes.C.Demand more from the defender.D.Side with the attacker.Researchers have discovered the oldest black hole ever observed, dating from the dawn of the universe, and found that it is "eating" its host galaxy to death.The international team, led by the University of Cambridge, used the James Webb Space Telescope (JWST) to detect the black hole, which dates from 400 million years after the big bang. The results, which lead author Professor Roberto Maiolino says are "a giant leap forward", are reported in the journal Nature.This surprisingly massive black hole even exists so early in the universe challenges our assumptions about how black holes form and grow. The size of this newly-discovered black hole suggests that they might form in other ways: they might be 'born big' or they can eat matter at a rate that's five times higher than had been thought possible. Like all black holes,According to standard models, supermassive black holes form from the remains of dead stars, which collapse and may form a black hole about a hundred times the mass of the Sun. If it grew in an expected way, this newly-detected black hole would take about a billion years to grow to its observed size. However, the universe was not yet a billion years old when this black hole was detected.The young host galaxy, called GN-z11, is a compact galaxy, about one hundred times smaller than the Milky Way, but the black hole is likely harming its development. When black holes consume too much gas, it pushes the gas away like an ultra-fast wind. This "wind" could stop the process of star formation, slowly killing the galaxy, but it will also kill the black hole itself, as it would cut off the black hole's source of "food".Maiolino says that the gigantic leap forward provided by JWST makes this the most exciting time in his career. "It's a new era: the giant leap is like upgrading from Galileo's telescope to a modern telescope overnight," he said. "The universe has been quite generous in what it's showing us, and this is just the beginning."12．What does the underlined word "devours" mean in Paragraph 3?A.Changes.B.Swallows.C.Observes.D.Forms.13．According to Paragraph 5, why is GN-z11 likely to be harmed?A.Because the host galaxy is too small.B.Because the black hole is killing itself.C.Because the “wind” ceases star formation.D.Because black holes produce too much gas.14．What is Maiolino's attitude to the new discovery about the black hole?A.Favorable.B.Intolerant.C.Doubtful.D.Ambiguous.15．What can we learn from this passage?A.The black hole took a billion years to achieve its size.B.Supermassive black holes are assumed to form overnight.C.The new discovery of the host galaxy is a giant leap forward.D.The host galaxy and the black hole can be destroyed by the "wind".二、七选五16．The Failed New Year's Resolution: Three Tips to Get on Track January is officially over, and many people are taking stock of their progress towards New Year's resolutions. The fact is that you probably haven't kept up with them as much as you hoped. But that's not your fault. ①______.If you feel like you have already failed, here are three tips before you let go.Practice self-compassionMany people talk to themselves in harsh ways when struggling with new habits, believing self-criticism will help them reach their goals. Research shows, however, that the opposite is true. Self-compassion is more effective for personal improvement, especially when facing failure. ②______, try to be kind and gentle with yourself, just as you would with a loved one.③______Resolutions are often phrased as definitive goals. I will exercise daily. I will kick desserts. ④______. But setting all-or-nothing goals can lead to all-or-nothing decisions that one gives up when faced with challenges. In contrast, intentions focus more on your values than specific actions. For example, the resolution "I will exercise daily" may become an intention of "I want to move my body because it feels good." This approach allows for more flexibility when unexpected stress arises.Solve problems by overcoming barriersIf you are struggling to maintain your desired habits, there are evidence-based techniques available to help you. ⑤______. This involves identifying the specific barriers that lead to your quitting something that you want to do. Perhaps you keep forgetting the new habit, or perhaps you don't understand how to do it. Whatever it is, identify the barrier and cope with it specifically.A. Set all-or-nothing goalsB. Change your resolutions into intentionsC. One such skill is called missing links analysisD. Setting specific behavioral goals can be effectiveE. If you're persuaded to give up on your resolutionsF. Old habits tend to die hard, and new habits tend to die easyG. When you are upset about yourself for not keeping resolutions三、完形填空（15空）My son asked me months ago if he could switch from his mainstream high school to aanother learning environment to complete his study. But my heart hurt a little that he wouldThen, we decided the vocational school (职业学校) was an option with the same generalcarry over, and he could graduate early.17．pulsory B.technical C.unprofessional D.academic18．A.heartbroken B.nervous C.angry D.confused19．A.apply B.adapt C.transfer D.talk20．A.ceremony B.moment C.dilemma D.stage21．A.curriculum B.wellbeing C.friendship D.decision22．A.bald B.generous C.straightforward D.shy23．A.anxiety B.conduct C.responsibility D.awareness24．A.studied B.canceled C.required D.banned25．A.credits B.subjects C.medals D.reputations26．A.graduate B.worsen C.thrive D.suffer27．A.formed B.understood C.abandoned D.remembered28．A.got away B.made up C.lined up D.got along29．A.crying B.murmuring plaining D.smiling30．A.oversell B.learn C.share D.predict31．A.affordable B.suitable C.available D.sensible四、短文填空32．While there is growing consumer ①______ (realize) of the environmental impact of fast fashion, can the same be said about fast furniture? The chairs and tables that fill many of our homes and everyday spaces are manufactured on a mass scale, and the cheaper items often end up ②______ landfills.According to the Environmental Protection Agency (EPA) , in 2020 over 12 million tons of furniture ③______ (throw) out in America and some into the forest illegally. Buying furniture can be ④______ (incredible) expensive. Many of us switch over to cheaper, instant brands like IKEA, ⑤______ manufacturers use materials harder to recycle, which is likely to damage the environment.With growing calls for sustainability, many brands are announcing to change though it remains ⑥______ (see) whether they will keep these promises. In ⑦______ (it) current sustainability strategy, IKEA commits itself to using only recyclable materials in all its products in an effort to practice "circular" design and cut emissions to net-zero. The concept of circular design ⑧______ (win) increasing concern up to now. In ⑨______ circular system, furniture products would be designed to last longer and be fully recyclable, thus forming a ⑩______ (close) loop (环) .五、书面表达33．假定你是高三学生李华。
a r X i v :0712.1036v 2 [a s t r o -p h ] 16 A p r 2008Draft version April 16,2008Preprint typeset using L A T E X style emulateapjTHE LOWEST-MASS STELLAR BLACK HOLES:CATASTROPHIC DEATH OF NEUTRON STARS INGAMMA-RAY BURSTSK.Belczynski 1,R.O’Shaughnessy 2,V.Kalogera 3,F.Rasio 3,R.E.Taam 3,T.Bulik 41Los Alamos National Laboratory (Oppenheimer Fellow)2Penn State University 3Northwestern University 4Warsaw UniversityDraft version April 16,2008ABSTRACTMergers of double neutron stars are considered the most likely progenitors for short gamma-ray bursts.Indeed such a merger can produce a black hole with a transient accreting torus of nuclear matter (Lee &Ramirez-Ruiz 2007,Oechslin &Janka 2006),and the conversion of a fraction of the torus mass-energy to radiation can power a gamma-ray burst (Nakar 2006).Using available binary pulsar observations supported by our extensive evolutionary calculations of double neutron star formation,we demonstrate that the fraction of mergers that can form a black hole –torus system depends very sensitively on the (largely unknown)maximum neutron star mass.We show that the available observations and models put a very stringent constraint on this maximum mass under the assumption that a black hole formation is required to produce a short gamma-ray burst in a double neutron star merger.Specifically,we find that the maximum neutron star mass must be within 2−2.5M ⊙.Moreover,a single unambiguous measurement of a neutron star mass above 2.5M ⊙would exclude a black hole –torus central engine model of short gamma-ray bursts in double neutron star mergers.Such an observation would also indicate that if in fact short gamma-ray bursts are connected to neutron star mergers,the gamma-ray burst engine is best explained by the lesser known model invoking a highly magnetized massive neutron star (e.g.,Usov 1992;Kluzniak &Ruderman 1998;Dai et al.2006;Metzger,Quataert &Thompson 2007).1.INTRODUCTIONGamma-ray bursts (GRBs)have been separated into two classes:long-soft bursts,and short bursts (Nakar 2006,Gehrels et al.2007).The origin of long-soft bursts has been connected to the death of low-metallicity massive stars (Piran 2005,Gehrels et al.2007).However,while ob-servations support a binary merger origin for short bursts (Nakar 2006,Gehrels et al.2007),the exact nature of the progenitor remains uncertain:they could be either dou-ble neutron stars (NS–NS)or black hole –neutron star (BH–NS)binaries.The number of BH–NS binaries that both merge and produce GRBs is hard to estimate since (i)no such system has yet been observed;(ii)formation models are rather uncertain and predict very small BH–NS merger rates (likely too small to explain most of the short bursts);and (iii)theory suggests that the fraction of BH–NS mergers producing bursts depends sensitively on the black hole spin and spin–orbit orientation (Belczyn-ski et al.2007b),but black hole birth spins are not well constrained observationally or theoretically.On the other hand,NS–NS binaries are only observed in the Milky Way,but their properties and numbers are also in agreement with theoretical models,and their merger rate is sufficient to explain the present-day short burst population (Nakar 2006,Belczynski et al.2007a).We have performed an extensive theoretical study of high-mass binary stars (potential progenitors of NS–NS systems)using StarTrack ,a population synthesis code in-corporating the most up-to-date and detailed input physicsfor massive stars (Belczynski et al 2008).The code em-ploys state-of-the-art predictions for neutron star and black hole masses based on hydrodynamic core collapse simulations (Fryer &Kalogera 2001)and detailed stel-lar structure and evolution calculations for massive stars (Timmes,Woosley,&Weaver 1996).Our models predict a Galactic NS–NS merger rate in the range ∼10−100Myr −1(Belczynski et al.2007a),in good agreement with the em-pirical estimate of ∼3−190Myr −1(Kim,Kalogera,&Lorimer,2006).The spread in our predicted rates orig-inates from including the most significant model uncer-tainties associated with the treatment of dynamical mass transfer episodes (common envelope phases),which are in-volved in the formation of most double compact objects (Belczynski et al.2007a).2.RESULTSIn Figure 1we compare short GRB rates with NS–NS merger rates in the present-day (redshift 0)universe.Ex-trapolating the NS–NS merger rates to the local universe by assuming a star-forming density of 10−2Milky Way-equivalents per Mpc 31,we estimate the local universe NS–NS merger rate to be in the range ∼100−1000Gpc −3yr −1.By comparison,the estimated conservative lower limit on the short GRB rate is ∼10Gpc −3yr −1,based on the BATSE/SWIFT sample (Nakar 2006).This estimate re-lies on very conservative assumptions:(i)there is no colli-mation and (ii)there are no bursts dimmer than we have already observed,thus providing a true lower limit on the 1Introductionof different modes of star formation and redistribution of progenitors over old elliptical and younger spiral galaxies does notincrease the predicted merger rates by more than a factor of ∼3O’Shaughnessy et al.2007.12rate.Therefore,even adopting the most optimistic predic-tions for the NS–NS merger rate and the most pessimistic bound on the local short GRB event rate,the fraction of NS–NS mergers f grb that produce GRBs must be greater than at least10−2to explain the majority of known short bursts.In this paper we start with the assumption that all short GRBs are connected with NS-NS system mergers that pro-duce a black hole.We discuss the implications of relaxing this stringent assumption at the end of the paper.From our models we also derive physical properties of double neutron stars,with individual masses of neutron stars being of particular interest.Figure2shows the rela-tion between progenitor(single star)mass andfinal rem-nant mass used in our evolutionary calculations.Mass transfer and other binary interactions change this simple picture,through both accretion and mass loss,which can either increase or decrease an individual binary compo-nent mass.However,(Belczynski et al.2007b)argues that we do not expect significant mass accretion onto the components of NS–NS binaries.The population model we adopt for our discussion here produces NS mass distri-butions that appear consistent with the current observed NS-NS sample,at least in the extent of the mass ranges (Fig.3).While mass transfer does influence the remnant masses(e.g.,smearing the narrowly peaked mass distribu-tion implied by Fig.2),the qualitative structure is largely preserved,as one would expect from isolated stellar evo-lution combined with an initial mass function that falls steeply with increasing initial mass.The predicted neu-tron star mass distribution only very weakly depends on evolutionary model assumptions because the neutron star formation mass is almost independent of the progenitor mass(Timmes et al.1996)and mass accretion in NS-NS progenitor binaries is rather small(Belczynski et al. 2007a).Depending on the masses in the progenitor binary and the highly uncertain nuclear equation of state,thefinal remnant of a NS–NS merger may or may not collapse to a black hole.We estimate thefinal gravitational mass of the compact remnant asM rem=0.9(M ns,1+M ns,2−0.1M⊙),(1) where the initial neutron star masses are denoted by M ns,1,M ns,2and we have assumed that the torus mass is sufficiently large to power a GRB(i.e.,≃0.1M⊙)(Seti-awan,Ruffert,&Janka2004,Lee&Ramirez-Ruiz2007) and that10%of rest mass is lost in neutrinos(Lattimer &Yahli1989;Timmes et al.1996).Higher rest mass loss(e.g.,Metzger,Thompson&Quataert2007)would only strengthen our subsequent conclusions.Because stars more massive than18M⊙(progenitors of massive neutron stars with M ns≃1.8M⊙)are much rarer than those form-ing lighter neutron stars(M ns≃1.35M⊙)we a priori ex-pect that most remnants from NS–NS mergers will have rather low mass M rem≃2.3M⊙(see eq.1for two1.35M⊙neutron stars).Neither observations nor nuclear theory have yet pinned down the maximum neutron star mass M ns,max above which a black hole must form.Thus,the fraction of binary neutron stars which produce black holes and are able to power short GRBs is set by the fraction of mergers such thatM rem≥M ns,max.(2) We therefore calculate the fraction of our simulated NS–NS mergers that lead to black hole formation and a short GRB as a function of M ns,max;see Fig.4.Observations of the highest mass neutron stars(∼<2M⊙;(Barziv et al. 2001,Ransom et al.2005)and lowest mass black holes(∼> 3M⊙;(Orosz2003,Casares2006)only weakly constrain this parameter.Remnant masses from NS–NS mergers (M rem)obtained both from our simulations and from ob-servations all fall very close to the range2.2−2.5M⊙. Comparing Figs1and4we immediately deduce that, since the fraction f grb of NS–NS mergers that produce short GRBs must be greater than10−2(Fig.1),the neu-tron star maximum mass M ns,max must be less than2.5M⊙(Fig.4).Because we lack a robust lower bound on the mass of the residual torus surrounding the black hole,we have adopted a conservative upper limit on M ns,max obtained by assuming a negligible torus mass(i.e.,replace0.1M⊙with0in eq.1).This result has been obtained with the assumption that all(k=1.0)short GRBs are connected with NS-NS merg-ers.It is however possible that only a fraction of short GRBs is produced in NS-NS mergers.How does our result depend on the fraction k of short GRBs that are connected with NS-NS mergers?The lower limit on f grb is then de-creased by k,see Figure1.If k∼>0.1,then the limit lower limit becomes f grb>10−3,and as is clearly seen from Fig-ure3,the upper limit on the maximum mass of a neutron star remains unchanged.For the values of k∼<0.01the NS-NS mergers are not important for overall short GRB population,as the mergers would consist of only∼<1%of the short GRBs.Therefore,in this case short GRBs do not provide information about the merger product.3.DISCUSSIONOur proposed limit on the maximum neutron star mass is still above the maximum masses allowed by almost all proposed models for the nuclear equation of state(Lat-timer&Prakash2007).However,the proposed limit would remain unchanged even if a dramatic improvement in short GRB surveys led to a significantly larger lower bound on the local short GRB rate:because of the sharp decrease in f grb with M ns,max shown in Fig.4.If,however, electromagnetic observations could constrain the least lu-minous short GRBs and thus provide an upper bound on the short GRB rate,with gravitational wave obser-vations at the same time accurately determining the NS–NS merger rate,then f grb could also be constrained from above.If only a fraction of NS–NS mergers produce short bursts,because f grb depends so sensitively on M ns,max,the combination of upper and lower limits would constrain the maximum neutron star mass extremely tightly,even if the assumptions going into eq.1are relaxed.While our limit on the effective maximum neutron star mass is entirely empirical,detailed merger models in-cluding realistic relativistic dynamics,neutrino transport, magneticfields,and potentially even energy extraction from thefinal black hole remain under intense investi-gation(Janka&Ruffert1996;Oechslin&Janka2006). Many merger remnants are expected to be(temporarily) rotationally supported against collapse(Morrison,Baum-3garte&Shapiro2004),with a“hypermassive”remnant neutron star eventually spinning down and collapsing to a black hole(Faber et al.2006;Duez et al.2007;Shibata& Taniguchi2006).Our model only relies upon the current consensus on double neutron star mergers,as summarized by Oechslin&Janka(2006):sufficiently massive binary mergers produce a black hole and only mergers that pro-duce a black hole extract enough energy to power short GRBs.Known Galactic black holes extend in mass up to 10−15M⊙(Casares2006),while two recently discovered black hole candidates in other galaxies(Orosz et al.2007, Prestwich et al.2007)have even higher masses of≃16 and∼>24M⊙.Clearly black holes can form with rather high masses in different types of environments.The lower mass limit is not well constrained observationally,as the highest-mass neutron stars barely reach2M⊙,while the lowest-mass black holes are above3M⊙.In order to ex-plain the observed short GRBs with NS–NS mergers,un-der the assumption of black hole–torus central engine model,we have shown that the maximum neutron star mass must be lower than2.5M⊙.However,pulsar surveys (Ransom et al.2005)have discovered increasingly more massive neutron stars.So far in our analysis we have in-cluded only NS–NS systems formed in thefield.There is one known relativistic double neutron star system in the Galactic globular cluster M15,that has probably formed through dynamical interactions.This binary consists of two low-mass neutron stars(1.36and1.35M⊙;Jacoby et al.2006)very similar to those in the Galacticfield,so the results of our analysis are not changed by this isolated ob-servation.Moreover,it was estimated that no more than 10−30%short GRBs can originate from mergers of dou-ble neutron stars formed in globular clusters(Grindlay, Portegies Zwart,&McMillan2006).If any observation can be made that establishes unam-biguously a pulsar mass(either in thefield or a globular cluster)over2.5M⊙,this would exclude a black hole–torus short GRB central engine model for double neutron star mergers.We note that a tentative mass measurement for a pulsar of2.74±0.21M⊙was recently reported by (Freire et al.2007).If this measurement is confirmed,the double neutron star mergers may still be possible progen-itors for short GRBs.However,the central engine model will need to be reexamined.In particular,it was proposed that a merger of two neutron stars may lead to the forma-tion of a magnetar;a rapidly rotating highly magnetized and high mass neutron star(with or without a torus)that can lead to a short GRB(e.g.,Usov1992;Kluzniak&Ru-derman1998;Dai et al.2006;Metzger et al.2007).Grav-itational wave observatories(LIGO,VIRGO)may provide the direct evidence that NS-NS merger can produce a short GRB if there is a coincidence of the burst and the inspiral gravitational wave signal.It may also be possible to dis-tinguish a merger product(NS versus BH)from the shape of the merger and ringdown signal or from radio pulses if a magnetar was formed in a nearby gamma-ray burst event.We would like to thank Neil Gehrels,Duncan Lorimer, Scott Ransom,Ben Owen,Jerome Orosz,Chris Stanek, John Beacom,Paulo Freire,Chunglee Kim,Todd Thomp-son and an anonymous referee for very useful discussions.REFERENCESBarziv,O.,Kaper,L.,Van Kerkwijk,M.H.,Telting,J.H.,&Van Paradijs,J.2001,A&A,377,925Belczynski,K.,Kalogera,V.,Rasio,F.,Taam,R.,Zezas,A.,Mac-carone,T.,&Ivanova,N.2008,ApJS,174,223Belczynski,K.,Taam,R.E.,Kalogera,V.,Rasio,F.A.,&Bulik,T.2007,ApJ,662,504Belczynski,K.,Taam,R.E.,Rantsiou,E.,&Sluys,M.v.d.2007, ApJ,submitted(astro-ph/0703131)Casares,J.2006,IAU Symposium238:”Black Holes:From Stars to Galaxies-Across the Range of Masses”,in press (astro-ph/0612312)Dai,Z.,Wang,X.,Wu,X.,&Zhang,B.2006,Science,311,1127 Duez,M.D.,Liu,Y.T.,Shapiro,S.L.,Shibata,M.,&Stephens,B.C.2007,Proceedings of the Eleventh Marcel Grossmann Meet-ing,in 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short GRB event rate (Nakar 2006),based solely on the rate of detected bursts.Depending on the amount of beaming and the fraction of distant faint short GRBs that are missed,the true event rate is often estimated to be at least 10times larger (Nakar 2006).This lower limit is smaller than the double neutron star merger rate estimated for the Milky Way both from (i)observations of Galactic binary pulsars (filled blue region)and (ii)our population synthesis simulations (filled red region),when these two estimates are extrapolated to cosmological scales.Based on the maximum plausible double neutron star merger rate with the minimum plausible short GRB event rate,the fraction f grb of binary mergers that lead to short GRBs should be greater than 10−2if double neutron stars are the progenitors of short GRBs.557.51012.51517.52022.5Initial star mass MFig.2.—Initial(Zero Age Main Sequence)mass tofinal compact object mass relation for single stars.This represents our current understanding of compact object formation.Stars below about7.5M⊙form white dwarfs;stars in the narrow range around8M⊙can potentially form very light neutron stars through electron capture supernovae(Podsiadlowski et al.2004).More massive stars show a well defined bifurcation caused by different modes of energy transport in the stellar core:stars below18M⊙form light neutron stars(≃1.35M⊙),while stars above this mass form heavy neutron stars (≃1.8M⊙).Above≃20M⊙stars experience partial fallback of material that can turn nascent neutron stars into black pact objects originating from stars of∼20−22M⊙form either very heavy neutron stars or low-mass black holes depending on the unknown limiting mass between these two remnant types(expected to lie around2−3M⊙).6Fig. 3.—Predicted mass distribution for neutron stars in merging double neutron star binaries.First born neutron stars are slightly heavier as they can accrete some matter from their unevolved binary companions.Population synthesis models(red and blue lines)are shown along with measured neutron star masses for the known double neutron star binaries.Although more observations are needed to constrain the shape of this distribution,the mass ranges of observed and predicted systems are in agreement.We use direct mass estimates for B1913+16,B1534+12,J0737−3039and J1756−2251(O’Shaughnessy et al.2008),while for J1906+0746we assume that both neutron stars have masses of1.3M⊙(total system mass is2.6M⊙;Lorimer et al.2006).The few compact objects found in our simulations with masses as high as≃2.5M⊙may well be low-mass black holes(see also Fig.1).7Fig. 4.—Gamma Ray Burst production efficiency as a function of the maximum neutron star mass in the framework of the double neutron star model for GRBs involving the formation of a black hole.The mass of the merger product is plotted here as the blue (observations)and red (theory)lines.There is a sharp drop in number of NS–NS systems that can form a merger with mass over 2.5M ⊙.For example,only 1in 103NS–NS mergers can form a remnant with a mass of 2.5M ⊙or higher.Therefore,if short GRBs are connected to NS–NS mergers,the maximum neutron star mass is required to be M ns ,max <2.5M ⊙.For comparison we show observed masses of the lowest-mass black holes (GRO J0422−32,GRS 1009−45;Casares 2006)and highest-mass neutron stars (Vela X-1,Terzan 5I,and Terzan 5J;Barziv et al.2001,Ransom et al.2005).These observations,along with our findings,constrain the maximum mass of a neutron star to lie in the narrow range of 2−2.5M ⊙.。
a rXiv:075.1374v1[astro-ph]9May27Black hole mass estimates from soft X-ray spectra Roberto Soria a ,b ,1a Harvard-Smithsonian CfA,60Garden st,Cambridge,MA 02138,USA b Mullard Space Science Lab (UCL),Holmbury St Mary,Surrey RH56NT,UK Zdenka Kuncic c ,2c School of Physics,University of Sydney,NSW 2006,Australia1Standard disk in a thermal dominant stateDetermining the masses of the accreting black holes(BHs)in ultraluminous X-ray sources(ULXs)is a key unsolved problem in X-ray astrophysics.In the absence of direct kinematic measurements of their mass functions,indirect methods based on X-ray spectral modelling have sometimes been used,by analogy with Galactic BH X-ray binaries,whose spectra can be approximated, in the“canonical”0.3–10keV range,with a thermal component plus a power-law.The thermal component is consistent with disk-blackbody emission from an optically thick disk,while the power-law is generally attributed to inverse-Compton scattering of softer disk photons offhigh-energy electrons.The peak temperature and luminosity of the thermal component are good indicators of the size of the X-ray-emitting inner-disk region,which in turn is related to the BH mass.In the standard disk-blackbody approximation(Makishima et al.,1986,2000),L disk=4πσ(T in/κ)4(R in/ξ)2≡4πσT4in r2in(1) R in=R ISCO≡6αGM/c2,(2)where:L disk is the integrated(bolometric)disk luminosity;T in is the peak colour temperature,which can be directly inferred from X-ray spectralfit-ting3;T in/κis the peak effective temperature;κis the hardening factor (1.5<∼κ<∼2.6);R in is the true inner-disk radius,assumed to coincide with the innermost stable circular orbit R ISCO;r in is the apparent inner radius obtained from spectralfitting with the disk-blackbody approximation;αdepends on the spin of the BH(α=1for a Schwarzschild BH,α=1/6for an extreme Kerr BH).The numerical factorξwas introduced(Kubota et al.,1998)to obtain a correctly normalized bolometric disk luminosity,taking into account that the fitted peak temperature occurs at R=(49/36)R in because of the no-torque boundary conditions.With this approximation,and with the choice ofκ=1.7 (Shimura&Takahara,1995),the physical inner-disk radius is related to the fitted value by:R in≡(ξ1/2κ)2r in≈(1.09)2r in.(3) An alternative estimate ofξκ2,which takes into account relativistic correc-tions,suggests thatR in≈(1.35)2r in(4)(Fabian et al.,2004),which is equivalent to a choice ofκ≈2.1for the hard-ening factor in(3).A hardening factor as high asκ≈2.6was empirically estimated for some Galactic BHs in the high/soft state(Shrader&Titarchuk, 2003).The bolometric luminosity can be derived from the observedflux: L disk=2πd2f bol(cos i)−1,(5) where d is the source distance and i the viewing angle(the diskflux being higher in the direction perpendicular to the disk plane).In addition,the disk luminosity can be directly related to the accretion rate,from general energy-conservation priciples.Ignoring relativistic corrections,L disk=GM˙M12α˙Mc2≡η˙Mc2.(6)From(1),(2),and(6)we have:M≈c2ξκ2η0.1ξκ25×1038erg s−1 1/2 kT in2Spectral arguments for intermediate-mass BHs2.1Soft X-ray emission in ULXsULX X-ray spectra can also be modelled with a power-law plus a thermal com-ponent,much cooler than that observed from Galactic BHs—typically,with colour temperatures kT in∼0.12–0.20keV for the brightest sources(Miller et al.,2004;Feng&Kaaret,2005;Stobbart et al.,2006).If(7)is applied,with total0.3–10keV luminosities≈1–3×1040erg s−1,the inferred masses are ∼1000–2000M⊙,or a factor of two lower if we consider only the luminosity in the thermal component.This argument has been used in support of the intermediate-mass BH interpretation of ULXs(Miller et al.,2004). However,it is unclear whether this argument can be directly applied to ULXs. There is still little direct evidence that the“soft excess”in ULXs is due to disk emission,partly because of our limited observing band.Various alternative interpretations have been suggested(e.g.,Gon¸c alves&Soria,2006;Stobbart et al.,2006;Ebisawa et al.,2003).For example,analogous soft-excesses in AGN,and particularly in narrow-line Seyfert1galaxies,can be explained as blurred,ionized absorption(mostly in the∼0.5–2keV band)and reprocessing of the primary power-law-like spectrum in a fast outflow(Gierli´n ski&Done, 2004;Chevallier et al.,2006).Gon¸c alves&Soria(2006)showed that a similar interpretation can be applied to at least some ULXs,whose X-ray spectra are very similar to those of narrow-line Seyferts.Downscattering of harder photons by a cooler outflow is another mechanism proposed to explain the soft excess (King&Pounds,2003;Laming&Titarchuk,2004).Even if we accept that the soft excess is indeed thermal emission from a disk(as we shall do in the rest of this paper),we need to keep in mind that some of the disk-blackbody scaling relations summarized in Section1have been confirmed observationally for the thermal dominant state(Remillard&McClintock,2006),but have to be modified when a consistent fraction of the accretion power is not directly radiated by the disk(Section3).2.2Cool disks and power-law componentTwo key issues need to be addressed by any ULX spectral model.Thefirst is that the X-ray spectra of most ULXs are dominated by a broad,power-law-like component,at least in the limited energy range covered by Chandra and XMM-Newton.The thermal component represents only∼10–30per cent of the0.3–10keV emission(Stobbart et al.,2006;Feng&Kaaret,2005;Winter et al., 2006).Physically,this suggests that most of the accretion power is not directlyradiated by the disk,but is efficiently transferred in other forms(mechanical, thermal or magnetic energy)to an upscattering medium,and then partly radiated with a non-thermal(power-law-like)spectrum.In Galactic stellar-mass BHs,this happens more commonly when the system is in the low/hard state,accreting at less than a few percent of their Eddington rate.But for transient sources,it also happens briefly near the peak of their outbursts,when they are probably accreting above their Eddington rate(very high state). The second issue to be addressed is why the disk appears so cold for its lu-minosity.Even when we take into account only the luminosity in thefitted thermal component,ULX disks can radiate up to≈1040erg s−1with a much lower peak temperature than that observed from Galactic BHs in their high state,even though the latter are an order of magnitude less luminous.A stan-dard,truncated disk,replaced in the inner region by a radiatively-inefficient flow(Narayan&Yi1994),would produce a power-law-dominated spectrum with a cold disk component(low/hard state).However,if ULXs are in the low/hard state at luminosities≈1040erg s−1(and hence,at mass accretion rates>∼106M⊙yr−1),their BH masses should be>∼104M⊙.The formation of such massive remnants in the local Universe is difficult to explain with exist-ing models of stellar or star cluster evolution,and the existence of primordial intermediate-mass BHs is not yet supported by independent evidence.There-fore,we need to consider alternative scenarios,in which the accretion rate is high,but the disk is or appears cooler than a standard disk in a thermal dominant state,for the same accretion rate and BH mass.In the rest of this paper,we will discuss phenomenological corrections to the disk-blackbody equations,to estimate what physical effects may produce more luminous but cooler disks.We will also illustrate the effects that those correc-tions have on the BH mass estimates.3Parametrical modifications of the disk-blackbody equations3.1Constant removal of powerThefirst plausible scenario we consider is that a constant fraction of power ǫ>0is extracted from the disk at each radius(independent of radius);for example,to power a corona.The radiativeflux from the disk becomes3GM˙MσT eff(R)4≈(1−ǫ)As a result,the peak temperature T in→T′in=(1−ǫ)1/4T in,and L disk→L′disk=(1−ǫ)L disk.Neither R in nor r in changes.The emitted spectrum is still a disk blackbody.Asǫincreases,the disk becomes cooler and less luminous, for afixed accretion rate,and its parameters move downwards along the same L disk∼M2T4in track.This scenario is equivalent to changing the effective accretion rate˙M→˙M′=(1−ǫ)˙M.It follows from the previous argument that the BH mass is still given by(7),independent ofǫ.Hence,removal of a constant fraction of accretion power does make the disk cooler but does not explain the high BH masses inferred from ULX spectralfitting.3.2Hardening of the disk photonsAnother simple modification to the standard-disk scenario is to assume that an increasing fraction of the emitted disk photons are upscattered by rela-tivistic electrons at the disk photosphere.This is equivalent to increasing the hardening factorκ,typically from≈1.7to≈2.5(Davis et al.,2005;2006). Observationally,this spectral hardening occurs at accretion rates near or just above Eddington.In the(T in,L disk)plane,the effect is to move the source horizontally to the right:higher colour temperature T in but same effective temperature T in/κand same luminosity L disk.The true inner-disk radius R in does not change,while the apparent disk radius decreases:r in→r′in=[κ/(κ+∆κ)]2r in.This does not affect the mass estimate,if one has properly taken into account its dependence on T in/κ,as we did in(7).3.3Partial covering of the diskThe third effect that needs to be taken into account is a partial covering of the disk surface:a fraction X of photons may be absorbed or more gener-ally removed from the disk-blackbody spectrum by clouds or a moderately optically-thick corona.They are re-emitted in other spectral bands or com-ponents(e.g.,X-ray power-law,or infrared).In a self-consistent analysis,one must of course account for all upscattering,downscattering and absorption effects,redistributing the total available accretion power into the various com-ponents.But for the purpose of relating the disk emission parameters to the BH mass,we can simply consider those photons as being lost from the disk spectrum.The effect is to reduce the observed diskflux and consequently the inferred luminosity:L disk→L′disk=(1−X)L disk.The spectral shape is not altered.The peak colour temperature T in is not changed.R in stays the same but the apparent disk radius decreases:r in→r′in=(1−X)1/2r in,because r in is indirectly derived from theflux normalization.The BH mass inferred fromthe observed luminosity and temperature via(7)is a factor(1−X)1/2less than the true mass.The combined effect of the modifications described in Sections3.1,3.2and 3.3is to move the location of the source to the right-hand-side of its thermal track,in the(T in,L disk)plane(Figure1).The precise displacement depends on the relative importance of the parametersǫ,∆κand X.Physically,it leads to lower estimates for the radius r in(sometimes much lower than the innermost stable orbit),and may lead to an underestimate of the BH mass if not properly accounted for.These empirical corrections may be used to explain the very high state(or steep-power-law state)of accreting black holes(Remillard& McClintock,2006).They do not help explain the high masses and large radii inferred for ULXs.4A two-zone structure of the inflowFor high accretion rates,it is plausible to speculate that accretion power may not be uniformely removed from the whole disk(Section3.1)and/or disk pho-tons may not be uniformly“lost”independent of radius.More likely,those losses may be strongly concentrated in the inner disk region(Done&Kubota, 2006;Soria&Kuncic,2007b).For example,the inner disk may be disrupted or simply occulted by an optically-thick outflow(King&Pounds,2003).Or,all of its photons may be comptonized by an optically-thick corona and emerge as a power-law or broken power-law component(Stobbart et al.,2006).Alterna-tively,the inner disk may still be present and visible,but most of its accretion power is extracted via non-radiative processes,such as mechanical outflows or Poyntingflux(Kuncic&Bicknell,2004).Some of the power released through those channels is then converted to non-thermal photons.Hence,a possible phenomenological way to correct the standard disk equations is to assume the presence of a transition radius R c≫R ISCO.For R>R c,the inflow can be approximated by a standard disk,such thatL disk≈4πσT4c R2c,(9) where T c≡T(R c)is the maximum(observable)disk temperature.For R ISCO< R<R c,we assume that all the accretion power comes out in the power-law-like component,and the standard disk either is not directly visible or gives a negligible direct contribution.Regardless of the details,in this scenario,(2)no longer holds or is no longerrelevant to the observed spectrum.It is replaced byR c=F R ISCO(10) with F=F(˙M)>1.The visible disk radiates only the accretion power released from the outer radius to R c.The effective radiative efficiency of that part of the inflow∼M/R c∼1/(12αF)<0.1.Therefore,we have(cf.(6),(7)):L disk≈GM˙M12αF˙Mc2≡ηF η1.19L disk1keV −2M⊙≈7900.1ξκ25×1039erg s−1 1/2 kT inL Edd,(13)the bolometric disk luminosity integrated for R>R c can more usefully be expressed asL disk≈ ˙m0.1 L Edd.(14) 5Observational predictionsIt was suggested that the disk structure parameterized in Section4is applica-ble to sources with very high accretion rates,˙m>1(Done&Kubota,2006; Soria,2007;Soria&Kuncic,2007b).To estimate the BH mass and accretion rate of a source in that state,from the observed disk luminosity and temper-ature,we need to estimate F=R c/R ISCO,either by measuring it directly, or by understanding how it depends on˙m.The simplest way to estimate F, at least as an order of magnitude,is to recall that in this scenario,all of thelog L disk log TinFig.1.Evolution of the source parameters in the (T in ,L disk )plane,due to various competing effects at high accretion rates.Dashed line:thermal track,characterizedby L disk ∼T 4inM 2;A:effect of increasing the accretion rate;B:effect of injecting some of the accretion power into a corona or outflow (uniformly at all radii);C:effect of removing some of the disk photons via absorption or upscattering into the power-law component;D:effect of spectral hardening due to electron scattering near the disk photosphere (equivalent to increasing the colour temperature without changing the effective temperature).accretion power released at R >R c is radiated by the disk,and some or most of the power released at R ISCO <R <R c is eventually radiated as power-law photons,without contributing to the thermal disk component.Since the ac-cretion power liberated down to a radius R scales ∼1/R ,one can estimatethat F >∼L tot /L disk .The inequality sign takes into account the fact that the radiative efficiency of the non-thermal processes in the inner region is less than the efficiency of blackbody emission in a standard disk.For the most luminous nearby ULXs,extrapolating from the relative fluxes of the power-law and thermal components in the 0.3–10keV band,the luminosity ratio L tot /L disk ∼3–20;in a few other,more distant ULXs,there is only a lowerlimit >∼10for this ratio.Hence,we infer that F >∼10for typical ULXs.From the fitted luminosity and temperature of the disk (9),typical values of R c >∼5000km are found for many ULXs,i.e.,∼100times larger than typical inner-disk radii in stellar-mass BH.If F >∼10,it means that BH masses in those ULXs are only required to be <∼10times larger than typical BH massesin Galactic systems.This simple argument suggests that ULX masses are <∼100M⊙.The location or evolutionary track of a source in the(T c,L disk)plane provides another observational constraint.To predict the displacement of a source from its thermal track when F>1,we need to understand how F and T c vary as a function of˙m.For afixed BH mass,the radiativeflux equation of a standard disk tells us that T c∼R−3/4˙m1/4.It was suggested(Poutanen et al.,2007;cBegelman et al.,2007;Soria&Kuncic,2007b)that R c∼˙m,based on plausible physical processes that may form such a transition radius.If so,from(9)we expect that,as the accretion rate˙m increases,a source will move along a track defined by L disk≈constant,T c∼˙m−1/2(Figure2).The luminosity track is very sensitive to the radial temperature distribution on the disk,at R>R c.Disk models with a distributionflatter than R−3/4 are sometimes used.For example,it was found(Kubota et al.,2005)that T∼R−0.7may provide a more accuratefit to the X-ray spectral data of Galactic BHs.In that case,we expect L disk∼T−0.44,with T c∼˙m−0.45.Forca disk dominated by X-ray irradiation(as may be the case if R≫R ISCO), T∼R−0.5.In that case,L disk∼T−4c,with T c∼˙m−0.25.See Soria&Kuncic (2007b)for further discussions and a comparison with observations. Regardless of the precise functional forms of F(˙m)and T c(R c),the significant result is that we expect a source to move to the left-hand-side of its thermal track,as the accretion rate increases(Soria2007).Along that track,the lumi-nosity of the disk component stays constant or increases,even if the observed peak temperature decreases.We speculate that the effects described in Sec-tions3.1,3.2and3.3dominate when˙m>∼1,and the shift to larger transition radii and lower peak temperatures becomes the dominant term for˙m≫1. Thus,we predict that an accreting BH may initially move up along its thermal track,then slightly down and to the right,then cross the thermal track and move to the left,for increasing accretion rates(Figure2).As it does so,we also expect the source to become more and more dominated by non-thermal emission components(including Compton scattering).We also suggest that transient stellar-mass BHs are more likely to proceed in the opposite direc-tion:moving from the low hard state directly to the ultraluminous state on the left-hand-side of the diagram,at the beginning of the outburst,when the accretion rate is highest;then they may move to the right,spend some time in the very high state and high/soft state as the accretion rate declines,and finally return to the low/hard state.Thefitted X-ray properties of many bright ULXs are qualitatively consistent with this phenomenological scenario.Their disks are very luminous but have a low peak temperature.The total power output is dominated by a power-law component,perhaps in addition to other non-thermal and non-radiative mech-anisms(e.g.,outflows).Their characteristic variability timescales are consis-tent with large disk radii(Soria&Kuncic,2007b).For example,let us consider an accreting BH with M≈50M⊙,and a disk luminosity≈5×1039erg s−1≈L Edd.If˙m≈1and F=1,we expect its spectrum to be dominated by the disk component,with a peak temperature≈0.8keV and a characteristic size of the X-ray emitting region∼6GM/c2∼500km.Although the luminosity is consistent with an average ULX,its spectral properties are not.However,let us allow for˙m≈20,and consequently F≈20.In that case,we expect that the source will still have L disk≈L Edd≈5×1039erg s−1,but a peak temperature ≈0.8×20−0.5keV≈0.18keV,a characteristic radius∼20×6GM/c2∼10,000 km,and a dominant X-ray power-law component with a luminosity>∼5×1039 erg s−1.These are more typical ULX parameters.If we had observed such a source,determining only itsfitted values of L disk and T c,and inserting those values directly into(7)instead(9),we would have incorrectly interpreted the source as an intermediate-mass BH with M≈1000M⊙.6ConclusionsIt is now recognized that it may not be possible to estimate BH masses in ULXs using the standard disk-blackbody model.If we accept that the soft excess is the disk emission component(which at this stage is only one possible hypothesis),we need to account for the fact that ULX spectra are power-law dominated and their thermal component has a remarkably low peak tempera-ture.We briefly reviewed simple phenomenological corrections to the standard disk model,which have been used to explain the very high state of Galactic BHs.However,they do not help explaining the ULX spectral properties.We then discussed the effects of introducing a transition radius R c≫6GM/c2, such that for R>R c the accretionflow is a standard disk,while for R<R c the disk is either drained of all its power via non-thermal processes,or its pho-tons are completely reprocessed by an optically-thick comptonizing medium. In this case,the peak disk emission comes from R≈R c,while the inner part of the inflow emits with a power-law-like spectrum.We speculate that R c/R ISCO∼˙m,where˙m is the accretion rate in Edding-ton units.With this parameterization,for afixed BH mass,the peak colour temperature T c∼˙m p with p≈−0.5,and L disk∼T q c,with q≤0.The pre-dicted effect is to move the source to the left-hand-side of its thermal track in the(T c,L disk)plane.This behaviour may be incorrectly read as standard disk emission from a more massive BH.We argue that this had lead to the flawed intermediate-mass BH interpretation.In our scenario,if the accretion rate˙m∼20,the BH mass can be∼50–100M⊙;hence,perhaps still consistentlog L disklog TinFig.2.Suggested X-ray spectral evolution of BH accretion disks for accretion rates 0.1<∼˙m <∼20.Sources first move up the thermal track,until their disk luminosity L disk ≈L Edd (high/soft state).Then,they move to the very high state (or steep--power-law state),generally characterized by a higher peak temperature,lower disk luminosity and a dominant,steep power-law component.Finally,as ˙m increases further,they may move to the ULX region,characterized by a large transition radius between outer disk and inner non-thermal region,and a dominant,flatter power-law component.The location of the thermal track (high/soft state)is deter-mined by the BH mass;the horizontal shift towards lower apparent temperatures is mostly determined by the accretion rate.with their formation via stellar processes,in very special circumstances.On the other hand,the BH mass may not be much smaller than ∼50M ⊙,if weassume that L disk <∼L Edd and L tot <∼a few L Edd .In this scenario,the peak fluxcontribution from the disk may come from ∼100gravitational radii.The de-pendence of the transition radius on the accretion rate needs to be taken into account also when scaling the frequency of X-ray quasi-periodic oscillations between sources of different mass.Lower frequencies may be caused by either an increase of ˙m or an increase of M .In summary,we speculate that ULXs may be defined as accreting BHs with masses a few times higher than Galactic BHs,and persistent accretion rates at least an order of magnitude above their Eddington limit.None of them has been seen to move along its thermal track,typical of accretion rates ∼0.1–1Eddington.Perhaps this is due to the nature of their massive Roche-lobe-filling donor stars,which provide a consistently higher mass transfer rate.A physicalinterpretation of the transition radius,as well as a more detailed comparison with observed X-ray spectral and timing properties of some Galactic BHs and ULXs will be presented elsewhere(Soria&Kuncic,2007b). 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