Supernova rates in Abell galaxy clusters and implications for metallicity
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Supernova rates in Abell galaxy clusters and implica-tions for metallicity Avishay Gal-Yam 1and Dan Maoz 11School of Physics and Astronomy and Wise Observatory,Tel Aviv University,Tel Aviv 69978,Israel Abstract.Supernovae (SNe)play a critical role in the metal enrichment of the intra-cluster medium (ICM)in galaxy clusters.Not only are SNe the main source for metals,but they may also supply the energy to eject enriched gas from galaxies by winds.However,measurements of SN rates in galaxy clusters have not been published to date.We have initiated a program to find SNe in 163medium-redshift (0.06<z <0.2)Abell clusters,using the Wise Observatory 1m telescope.Our program has already discovered 11spectroscopically confirmed SNe at z =0.1−0.24,and several unconfirmed SNe.We present the main scientific goals of this project,and discuss a novel explanation for the centrally enhanced metal abundances indicated by X-ray observations of galaxy clusters,based on the contribution of intergalactic SNe.1Scientific goals Our main scientific goal is to derive SN rates as a function of various parameters such as host galaxy type and cluster environment:position within the cluster,cluster richness and cluster vs.field.SN rates can then be used to determine the current and past star formation rates in galaxy clusters [8].Our measured SN rates can replace the assumed rates used so far in studies of metal abundances in the intracluster gas.We also intend to study the rate,distribution and properties of intergalactic SNe in galaxy clusters.We have already discovered one candidate,SN 1998fc (See fig.1).Our search is also sensitive to other optical transients,such as AGNs in the clusters and behind them,flares from tidal disruption of stars by dormant massive black holes in galactic nuclei and GRB afterglows.We may also detect the gravitational
lensing effect of the clusters on background SNe.
2Intergalactic SNe and metal abundances in clusters The existence of a diffuse population of intergalactic stars is supported by a grow-ing body of observational evidence such as intergalactic planetary nebulae in the Fornax and Virgo clusters [1],and intergalactic red giant stars in Virgo [5].Recent
Figure1:The Ia SN1998fc was detected78Kpc from the cD galaxy of Abell403,at the cluster redshift[6].This may be an intergalactic SN whose progenitor star was a member of the diffuse intergalactic stellar population. Alternatively,the host may be a faint dwarf galaxy.This question could be resolved with larger number statistics of such events.
imaging of the Coma cluster reveals low surface brightness emission from a diffuse population of stars[7],the origin of which is attributed to galaxy disruption[2]. Since type Ia SNe are known to occur in all environments,there is no obvious reason to assume that such events do not happen within the intergalactic stellar population.SN1998fc may well be such an event.The intergalactic stellar pop-ulation is centrally distributed[3].Therefore,metals produced by intergalactic Ia SNe can provide an elegant explanation for the central enhancement of metal abundances with type Ia characteristics,recently detected in galaxy clusters[4]. References
[1]Freeman,K.C.et al.1999,astro-ph/9910057,and references therein,Theuns,
T.,&Warren,S.J.1996,MNRAS,284,L11
[2]Dubinski,J.,Mihos,J.C.&Hernquist,L.,1996,ApJ,462,576,and also
Moore,B.,et al.1996,Nature,379,61
[3]Dubinski,J.,1999,astro-ph/9902331
[4]Dupke,R.A.&White,R.E.III,1999,ApJ,submitted,astro-ph/9902112
[5]Ferguson,H.C.,Tanvir,N.R.,&von Hippel,T.1998,Nature,391,461
[6]Gal-Yam,A.&Maoz,D.,1999,IAUC7093
[7]Gregg,M.D.&West,M.J.,1998,Nature,396,549
[8]Madau,P.,DellaValle,M.,&Panagia,N.1998,MNRAS,297,L17。
介绍宇宙英语作文
The universe is a vast expanse that has fascinated human beings for centuries.It is the collection of all existing matter and energy,including galaxies,stars,planets,and other celestial bodies.Here is a detailed introduction to the universe in an English essay format.Title:The Enigma of the UniverseIntroduction:The universe,a boundless and aweinspiring concept,has been a subject of wonder and study for as long as humanity has gazed upon the stars.It is the ultimate frontier,a testament to the infinite possibilities that lie beyond our terrestrial realm.Composition of the Universe:The universe is composed of billions of galaxies,each containing billions of stars.Our own galaxy,the Milky Way,is just one of these celestial bodies.Surrounding these stars are planets,some of which,like our Earth,are capable of supporting life.The universe also contains vast amounts of dark matter and dark energy,which,despite being invisible, play a crucial role in the expansion and structure of the cosmos.The Big Bang Theory:The most widely accepted explanation for the origin of the universe is the Big Bang Theory.According to this theory,the universe began as an infinitely dense and hot point, and has been expanding ever since.This event occurred approximately13.8billion years ago and set in motion the creation of all the matter and energy that we observe today.Galaxies and Stars:Galaxies are massive collections of stars,gas,and dust held together by gravity.They come in various shapes and sizes,from spiral galaxies like the Milky Way to elliptical galaxies that are more rounded.Stars,the powerhouses of galaxies,are born in nebulae and can live for billions of years,undergoing various stages of evolution before they die, sometimes in spectacular supernova explosions.Planets and Solar Systems:Planets are celestial bodies that orbit stars.They are diverse in nature,ranging from rocky terrestrial planets like Earth to gas giants like Jupiter.Our solar system,with its eight planets,is just one example of the many solar systems that exist within galaxies.Life in the Universe:The search for extraterrestrial life is an ongoing endeavor.While Earth is the only known planet to harbor life,the vastness of the universe suggests that the conditions necessaryfor life could exist elsewhere.Scientists are continually searching for signs of life on other planets,moons,and even in the interstellar medium.The Expansion and Fate of the Universe:The universe is not static it is in a state of constant expansion.This expansion is driven by dark energy,a mysterious force that is causing the universe to stretch at an accelerating rate.The ultimate fate of the universe is still a topic of debate among cosmologists,with possibilities ranging from a Big Freeze to a Big Rip.Conclusion:The universe is a complex and dynamic entity that continues to reveal its secrets to us.As our understanding of the cosmos grows,so too does our appreciation for the intricate balance of forces that govern its existence.The universe is a reminder of our place in the grand scheme of things and the boundless potential for discovery that lies ahead. Further Exploration:The study of the universe is a collaborative effort that spans disciplines and cultures. From the earliest stargazers to modern astronomers and astrophysicists,the quest to understand the universe is a testament to human curiosity and our desire to explore the unknown.As technology advances,we can expect to uncover even more about the cosmos and our place within it.。
自考英语(二)教材课文翻译
自考英语(二)课文翻译Unit One What Is a Decision ?何为决策 ?A decision is a choice made from among alternative courses of action that are available. The purpose of making a decision is to establish and achieve organizational goals and objectives. The reason for making a decision is that a problem exists, goals or objectives are wrong, or something is standing in the way of accomplishing them.决策是一种选择，来自可以获得的、任择其一的行动步骤。
作决策的意图是要确立和实现机构的目标和目的。
作决策的原因是有问题存在、目标和目的不正确、或者有某种东西妨碍目标或目的的实现。
Thus the decision-making process is fundamental to management. Almost everything a manager does involves decisions, indeed, some suggest that the management process is decision making. Although managers cannot predict the future, many of their decisions require that they consider possible future events. Often managers must make a best guess at what the future will be and try to leave as little as possible to chance, but since uncertainty is always there, risk accompanies decisions . Sometimes the consequence s of a poor decision are slight; at other times they are serious.因此，作决策的过程对管理人员来说至关重要。
外星人是否存在的英语作文
外星人是否存在的英语作文英文回答：The Existence of Extraterrestrial Life: A Scientific Inquiry.The question of whether extraterrestrial life exists has captivated humanity for centuries. From ancient myths and folklore to modern scientific inquiry, the search for intelligent beings beyond Earth continues to inspire awe and speculation.From a scientific perspective, the search for extraterrestrial life is guided by two fundamental principles: the Drake equation and the Fermi paradox. The Drake equation attempts to estimate the number of potentially habitable planets in the Milky Way galaxy based on factors such as the rate of star formation, the fraction of stars with planets, and the likelihood of those planets supporting life. While the estimates vary widely, theequation suggests that there could be a significant number of habitable planets in our galaxy.The Fermi paradox, on the other hand, poses the question: "If life is so common, why haven't we detected it yet?" Despite decades of radio telescope observations, space exploration missions, and SETI (Search for Extraterrestrial Intelligence) programs, we have yet to establish contact with extraterrestrial civilizations. This apparent contradiction has led to a range of hypotheses, including the Great Filter theory, which suggests that there are barriers that prevent most civilizations from advancing to a detectable level of intelligence.Recent astronomical discoveries have provided further impetus to the search for extraterrestrial life. The confirmation of exoplanets, planets outside our solar system, has shown that our Milky Way galaxy is teeming with planetary systems. Moreover, the discovery of potentially habitable exoplanets, such as TRAPPIST-1 and Proxima Centauri b, has raised the possibility that life may exist not only on Earth but also on nearby planets.中文回答：外星人是否存在，一个科学探究。
GRE阅读高频机经原文：冰川沉积物
GRE阅读高频机经原文：冰川沉积物GRE阅读高频机经原文：冰川沉积物GRE阅读高频机经原文：冰川沉积物14. 冰川沉积物Tills are commonly classi?ed according to the perceived process of deposition. However, it is increasingly recognised that this classi?cation, which is mainly based on macroscopic ?eld data, has severe limitations. At the same time the concept of the deforming glacier bed has become more realistic as a framework for discussing tills and their properties, and this (tectonic) concept is irreconcilable with the existing (depositional) till classi?cation scheme. Over the last 20 years large thin sections have been used to study tills, which has provided new insights into the textural and structural properties of tills. These results have revolutionised till sedimentology as they show that, in the main, subglacial tills possess deformational characteristics. Depositional properties are rare.Based on this new insight the process of subglacial till formation is discussed in terms of glacier/ice sheet basal velocity, clay, water and carbonate content and the variability of these properties in space and time. The end result of this discussion is: till, the deforming glacier bed. To distinguish subglacial till from depositional sedim ents the term ‘tectomict’ is proposed. Within the single framework of subglacial till as the deforming glacier bed, many textural, structural and geomorphological features of till beds can be more clearly and coherently explained and understood.GRE阅读高频机经原文及答案：云和气候变化预测15. 云和气候变化预测 1996年04月北美 D9604As of the late 1980’s, neither theorists nor large-scale computer climate models could accurately predict whether cloud systems would help or hurt a warming globe. Some studies suggested that a four percent increase in stratocumulus clouds over the ocean could compensate for a doubling in atmospheric carbon dioxide, preventing a potentially disastrous planetwide temperature increase. On the other hand, an increase in cirrus clouds could increase global warming.That clouds represented the weakest element in climate models was illustrated by a study of fourteen such models. Comparing climate forecasts for a world with double the current amount of carbon dioxide, researchers found that the models agreed quite well if clouds were not included. But when clouds were incorporated, a wide range of forecasts was produced. With such discrepancies plaguing the models, scientists could not easily predict how quickly the world’s climate would change, nor could they tell which regions would face dustier droughts or deadlier monsoons.15.1. The author of the passage is primarily concerned with(A) confirming a theory(B) supporting a statement(C) presenting new information(D) predicting future discoveries(E) reconciling discrepant findings15.2. It can be inferred that one reason the fourteen models described in the passage failed to agree was that(A) they failed to incorporate the most up-to-date information about the effect of clouds on climate(B) they were based on faulty information about factors other than clouds that affect climate(C) they were based on different assumptions about the overall effects of clouds on climate(D) their originators disagreed about the kinds of forecasts the models should provide(E) their originators disagreed about the factors other than clouds that should be included in the models15.3. It can be inferred that the primary purpose of the models included in the study discussed in the second paragraph of the passage was to(A) predict future ch anges in the world’s climate(B) predict the effects of cloud systems on the world’s climate(C) find a way to prevent a disastrous planetwide temperature increase(D) assess the percentage of the Earth’s surface covered by cloud systems(E) estimate by how much the amount of carbon dioxide in the Earth’s atmosphere will increase15.4. The information in the passage suggests that scientists would have to answer which of the following questions in order to predict the effect of clouds on the warming of the globe?(A) What kinds of cloud systems will form over the Earth?(B) How can cloud systems be encouraged to form over the ocean?(C) What are the causes of the projected planetwide temperature increase?(D) What proportion of cloud systems are currently composed of cirrus of clouds?(E) What proportion of the clouds in the atmosphere form over land masses?答案：B C A AGRE阅读高频机经原文及答案：Supernova16. Supernova D 89-12Astronomers observe a supernova that is dimmer than expected because of dust screening，If a supernova (the explosion of a massive star) triggered star formation from dense clouds of gas and dust, and if the most massive star to be formed from the cloud evolved into a supernova and triggered a new round of star formation, and so on, then a chain of star-forming regions would result. If many such chains were created in a differentially rotating galaxy, the distribution of stars would resemble the observed distribute in a spiral galaxy.This line of reasoning underlies an exciting new theory of spiral-galaxy structure. A computer simulation based on this theory has reproduced the appearance of many spiral galaxies without assuming an underlying density wave, the hallmark of the most widely accepted theory of the large-scale structure of spiral galaxies. That theory maintains that a density wave of spiral form sweeps through the central plane of a galaxy, compressing clouds of gas and dust, which collapse into stars that form a spiral pattern.。
超新星纪元词语
以下是90个超新星纪元的词语以及它们的译文：1.超新星纪元- Supernova Age2.星际物质- Interstellar Matter3.星云- Nebula4.恒星- Star5.黑洞- Black Hole6.脉冲星- Pulsar7.星系- Galaxy8.旋臂- Spiral Arm9.恒星系- Stellar System10.双星- Binary Star11.星团- Star Cluster12.星云团- Nebula Cluster13.星际空间- Interstellar Space14.星尘- Stardust15.星系团- Galaxy Cluster16.超星系团- Supercluster17.宇宙射线- Cosmic Ray18.反物质- Antimatter19.高能射线- High-energy Radiation20.量子力学- Quantum Mechanics21.引力波- Gravitational Wave22.宇宙微波背景辐射- Cosmic Microwave Background Radiation23.暗物质- Dark Matter24.暗能量- Dark Energy25.星系核- Galaxy Core26.黑洞吞噬- Black Hole Accretion27.恒星演化- Stellar Evolution28.核合成- Nucleosynthesis29.星系碰撞- Galaxy Collision30.恒星爆炸- Stellar Explosion31.引力透镜- Gravitational Lensing32.宇宙网- Cosmic Web33.反物质粒子- Antimatter Particles34.高纬宇宙模型- High-dimensional Cosmic Model35.宇宙常数- Cosmological Constant36.宇宙密度- Cosmic Density37.宇宙膨胀- Cosmic Expansion38.宇宙学红移- Cosmological Redshift39.大爆炸理论- Big Bang Theory40.弦理论- String Theory41.相对论- Relativity42.量子力学- Quantum Mechanics43.弦理论- String Theory44.卡鲁扎-克莱因理论- Kaluza-Klein Theory45.高维时空- Higher-dimensional Spacetime46.虚时间- Virtual Time47.宇宙微波背景辐射- Cosmic Microwave Background Radiation48.标准宇宙模型- Standard Cosmological Model49.星系团- Galaxy Cluster50.超星系团- Supercluster51.丝状结构- Filamentary Structure52.大尺度结构- Large-scale Structure53.哈勃常数- Hubble Constant54.引力波- Gravitational Wave55.黑洞信息悖论- Black Hole Information Paradox56.夸克星- Quark Star57.反物质星- Antimatter Star58.原子核- Atomic Nucleus59.量子纠缠- Quantum Entanglement60.高温高压状态方程- High-temperature and high-pressure equation ofstate61.星系演化- Galaxy Evolution62.星系动力学- Galaxy Dynamics63.星际物质循环- Interstellar Matter Cycle64.恒星形成- Star Formation65.分子云- Molecular Cloud66.星际空间气体- Interstellar Gas67.星际尘埃- Interstellar Dust68.星系核活动- Active Galactic Nucleus69.射电星系- Radio Galaxy70.光学星系- Optical Galaxy71.X射线星系- X-ray Galaxy72.恒星团- Star Cluster73.双星系统- Binary Star System74.变星- Variable Star75.新星- Nova76.超新星- Supernova77.中子星- Neutron Star78.脉冲星- Pulsar79.黑洞候选体- Black Hole Candidate80.高光度蓝变星- High-luminosity Blue Variable Star81.超巨星- Supergiant Star82.红巨星- Red Giant Star83.黄矮星- Yellow Dwarf Star84.白矮星- White Dwarf Star85.恒星演化模型- Stellar Evolution Model86.星际物质分布- Interstellar Matter Distribution87.分子光谱学- Molecular Spectroscopy88.高能天体物理学- High-energy Astrophysics89.天体化学- Astrochemistry90.宇宙射线物理学- Cosmic Ray Physics。
天文学家发现另一颗像塔比星那样闪烁的恒星
2019.02/中国科技教育／65本栏目文字与图片由 《科学新闻》版权所有，授权我刊使用，不得以任何形式转载、摘编，特此声明。
天文学家发现另一颗像塔比星那样闪烁的恒星Lisa Grossman到目前为止，天文学家发现银河系中还有另外一颗奇异闪烁的恒星。
天文学家使用位于智利的望远镜发现了一颗明暗变化奇异的恒星，这让人想起了塔比星——一颗曾经被认为拥有外星超级结构体的恒星。
超级结构体的想法首先在2015年提出，不久之后被撤销，主要是因为有数据显示这种亮度的衰减有可能是尘粒遮掩住恒星光线所致。
新近发现的这颗恒星的行为也可能不是外星生命所为。
但是它实在令人困惑，来自于巴西圣卡塔琳娜州联邦大学的天文学家Roberto Saito 说道。
他和他的同事于2018年11月6日在 上就这颗恒星奇异的闪烁作了报告。
“我们不知道那个物体是什么。
”他说道，“那实在太有意思了。
”这颗恒星或可拥有一些绕行的残骸，这些残骸会定期地挡住星光，但是Saito 和他的同事们表示他们需要更多的观测确定那是否可能，或者这种奇异的闪烁是由其他原因所导致的。
当研究团队从VISTA 望远镜（位于智利北部的阿塔卡马沙漠）的数据中锁定这个目标时，研究人员一直在搜寻那些随着爆发而突然增亮的超新星和恒星。
这些数据只是针对银河中心大规模探查数据的一部分，它们被称为银河VISTA 变量，或者VVV。
与增亮恰恰相反，这颗恒星突然变暗。
研究团队将它称为VVV-WIT-07，这到底是什么呢？从2010年到2018年，这颗恒星亮度的增加与减少从没有固定模式。
这种亮度模式的缺乏与塔比星十分相像，除了VVV-WIT-07的亮度可下降达80%，而塔比星的亮度只会下降20%。
此外还有一颗被称为J1407的闪烁恒星，它可能更为匹配。
这颗恒星周期性变暗程度可达95%，来自于美国纽约罗切斯特大学的天文学家Eric Mamajek 和他的同事在2012年对此作过报告。
天文学家认为J1407的一颗绕轨运行的行星具有庞大的星环系统，它能够周期性地遮掩恒星。
星体的消亡【英文】
Planetary Nebula IC 418 (Spirograph Nebula)
The Eskimo Nebula
White Dwarfs
Degenerate stellar remnant (C,O core) Extremely dense: 1 teaspoon of WD material: mass ≈ 16 tons!!! Chunk of WD material the size of a beach ball would outweigh an ocean liner!
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:
Subrahmanyan Chandrasekhar,
(1910-1995, Indian-born American):
In 1983 won Nobel Prize in Physics for his theoretical studies of the physical processes of importance to the structure and evolution of the stars. The Chandra X-Ray Space Telescope is named in his honor.
The Famous Supernova of 1987: SN 1987A
Before At maximum
Unusual type II Supernova in the Large Magellanic Cloud in Feb. 1987
银河英文作文素材高中
银河英文作文素材高中The Milky Way, also known as the Galaxy, is a barred spiral galaxy that is home to our solar system, along with billions of other stars and their planetary systems. It is a vast and awe-inspiring expanse of space that has captured the imagination of humans for centuries.The Milky Way is estimated to be about 100,000 light-years in diameter, and it is thought to contain between 100 billion and 400 billion stars. The exact number isdifficult to pin down, as many stars are too faint to be observed directly. This immense number of stars gives the Milky Way its characteristic appearance as a band of light stretching across the night sky.One of the most fascinating aspects of the Milky Way is the presence of dark matter. This mysterious substance is thought to make up about 85% of the total mass of the galaxy, yet it does not emit or reflect any electromagnetic radiation, making it invisible to telescopes. Its presenceis inferred from its gravitational effects on visible matter.The Milky Way is also home to a variety of celestial objects, including nebulae, star clusters, and supernova remnants. These objects provide valuable insights into the processes of star formation and evolution, and they are the focus of much research and observation by astronomers.The study of the Milky Way is ongoing, and new discoveries are constantly being made. From the structure and dynamics of the galaxy to the search for exoplanets and signs of extraterrestrial life, there is always something new and exciting to learn about our cosmic home.。
50年来最亮超新星爆炸 英国境内可用望远镜观看(英语学习).doc
50年来最亮超新星爆炸英国境内可用望远镜观看（英语学习）50年来最亮超新星爆炸英国境内可用望远镜观看There will be an once-in-a-lifetime event in the night sky over the next few days – as a star exploding 21 million light years away becomes so bright it will be visible through binoculars across Britain。
The supernova is predicted to reach its brightest between September 9 and 12, and will be the brightest since 1954, visible all over Britain, weather permitting. A team of scientists at Oxford University are tracking it using the Hubble Space Telescope。
Dr Mark Sullivan, the astrophysicist leading the Oxford team examining the supernova, said: “This is accessible to anyone with a decent pair of binoculars. For many it could be a once in a lifetime chance to see a supernova blossom and then fade before their eyes. We may not see another like it for over 100 years.”It will appear bluish-white, just above and to the left of the last two stars in the Big Dipper. Watchers are advised to stay away from street lights for maximum visibility.The matter from the explosion will eventually form new stars and planets. Such events, which include one in five supernovae, provide scientists with essential information on how the universe expands。
The effect of supernova heating on cluster properties and constraints on galaxy formation m
a r X i v :a s t r o -p h /9810008v 1 1 O c t 1998Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 1February 2008(MN L A T E X style file v1.4)The effect of supernova heating on cluster properties andconstraints on galaxy formation modelsK.K.S.Wu,1,3A.C.Fabian 1and P.E.J.Nulsen 21Institute of Astronomy,Madingley Road,Cambridge CB30HA2Department of Physics,University of Wollongong,Wollongong NSW 2522,Australia 3kwu@ABSTRACTModels of galaxy formation should be able to predict the properties of clusters of galaxies,in particular their gas fractions,metallicities,X-ray luminosity-temperature relation,temperature function and mass-deposition-rate function.Fitting these prop-erties places important constaints on galaxy formation on all scales.By following gas processes in detail,our semi-analytic model (based on that of Nulsen &Fabian 1997)is the only such model able to predict all of the above cluster properties.We use realistic gas fractions and gas density profiles,and as required by observations we break the self-similarity of cluster structure by including supernova heating of intracluster gas,the amount of which is indicated by the observed metallicities.We also highlight the importance of the mass-deposition-rate function as an independent and very sensitive probe of cluster structure.Key words:galaxies:clusters:general –galaxies:formation –galaxies:evolution –cooling flows –X-rays:galaxies1INTRODUCTIONOur understanding of galaxy formation through the hierar-chical clustering of gas and dark matter (DM)has improved greatly over the past decade.The aim of models of galaxy formation is to account for the properties of all structure,from the first dwarf galaxy to the rich clusters of galax-ies that are virialising now.The collapse of the dominant dark matter is relatively well understood,so that the ma-jor current problem is to model the complex gas processes that take place within collapsed and collapsing DM halos.Despite their success in accounting for some properties of galaxies,many semi-analytical models do not predict cor-rectly the properties of groups and clusters of galaxies.In particular,these models should predict gas fractions,metal-licities,the X-ray luminosity-temperature (L X −T )relation,the temperature function and the mass-deposition-rate (˙M)function of clusters.One problem is that the gas fraction in clusters,which is observed to be in the range 10–20per cent (White et al.1993b;White &Fabian 1995;David,Jones &Forman 1995;White,Jones &Forman 1997;Evrard 1997),is under-estimated by those models that have low baryon fractions (e.g.,most of the values considered by Kauffmann,White &Guiderdoni (1993),Cole et al.(1994),Heyl et al.(1995),Kauffmann &Charlot (1998)and Baugh et al.(1998)).In this paper we show that additional heat input tothe intracluster gas,which in our fiducial model we take tobe due to supernovae,can consistently account for the ma-jor X-ray properties of groups and clusters of galaxies.This has a similar effect to ‘preheating’as invoked by other au-thors (Kaiser 1991;Evrard &Henry 1991;Metzler &Evrard 1994;Navarro,Frenk &White 1995;Bower 1997;Jones et al.1998).A well-known problem addressed by preheating is the slope of the L X −T relation.Models and simulations which do not involve preheating (and in general those which inves-tigate galaxy properties do not)are generally ‘self-similar’and give L X ∝T 2(Kaiser 1986),whereas clusters are ob-served to follow L X ∝T 3(David et al.1993).Models which preheat the gas in clusters generally break the self-similarity.For example,a constant excess specific energy can have a large effect in the shallow potential wells of groups,while having little effect on the largest clusters.The excess energy raises the temperature as well as the potential energy of the gas by pushing it outwards,thereby flattening the gas den-sity profile.This lowers L X and steepens the relationship between L X and T .During galaxy formation gas is heated and possibly ejected from galaxies by supernovae.It retains most of this ‘excess energy’as thermal and gravitational potential energy (and possibly kinetic energy)as it passes through the col-lapse hierarchy,eventually becoming part of the intergalactic medium in groups and clusters.Gas that is ejected from a galaxy is expected to recollapse with the next ‘major merger’c0000RAS2K.K.S.Wu et al.(which in our model is the doubling,at least,of the mass of the halo that the galaxy resides in).This is reasonable since ejected gas would encounter the inter-galactic medium which subsequently forms part of a larger halo.In ourfidu-cial model the only source of heating and metal enrichment is Type II supernovae(SNe II)associated with star formation (Nulsen&Fabian1995,1997;hereafter NF95and NF97). There is some evidence that most of the metals in intraclus-ter gas came from SNe II rather than SNe Ia(Mushotzky et al.1996;Nagataki&Sato1998),but a further reason for our assumption is because while both types inject about the same amount of energy,SNe Ia inject about10times more iron than SNe II.Hence for the iron abundance mea-sured in intracluster gas,the associated energy injection is maximised by using only SNe II.We assume an energy in-jection of4×1050erg per supernova(Spitzer1978)which is not radiated locally.The mean mass of iron produced per supernova is0.07M⊙,which leads to3.7keV/particle ex-cess specific energy in gas with solar iron abundance.By choosing the initial metallicity in groups when they arefirst formed to be a suitable value,the iron abundance of clusters in our model is Z≈0.3Z⊙which corresponds to about1.1 keV/particle of excess energy.The semi-analytical model we use is based on that de-scribed in NF97,with an improved cosmological model and a more accurate form for dark matter halos.The model pays particular attention to gas processes,explicitly including the effects of coolingflows in its treatment of hot gas.When hot gas has had sufficient time to radiate its thermal energy it is assumed to preferentially form low mass stars,effectively baryonic dark matter(BDM),as observed in coolingflows in clusters.We assume that dark matter halos follow the NFW profile(Navarro,Frenk&White1997;hereafter NFW97). Gas in the resulting potential wells is assumed to be isother-mal and in hydrostatic equilibrium.The model clusters turn out to have gas density profiles closely resembling those in observed clusters.In this paper we use an open cosmology withΩ0=0.3, H0=50km s−1Mpc−1and a cosmological constant of zero. Densityfluctuations are obtained from a CDM model with primordial spectral index of n=1,normalised to makeσ8= 0.7.This normalisation,which is slightly lower than some estimates based on cluster numbers,is discussed in section3. We note that our results would be largely unchanged in a flat cosmology with the sameΩ0,since the mass function of clusters today would be the same.Likewise,our conclusions do not depend on when the excess energies were injected or the exact history of the clusters and their progenitors.We do however assume that the supernovae injected their energy into virialised gas,as opposed to the uncollapsed IGM.2DESCRIPTION OF THE MODELThe two main changes from the model described in NF97are the use of an open cosmology and the improvement of the DM and gas profiles.The mass of a halo is defined as that inside the virial radius,r200,and the mean density inside r200 is required to be200times the background density of anΩ= 1universe of the same age.(This is marginally different from NFW97,but follows the spherical collapse model strictly.) We use the NFW profile(NFW97)which takes the form ρ(r)=ρsx+1kTφ(r) ,(3) whereµm H is the mean mass per particle in the gas,T is its temperature and k is Boltzmann’s constant.Inserting the expression for the potential givesρg(r)=A(1+x)η/x(4) where A is a constant andη=µm Hα/(kT).The above pro-file,which we shall refer to as the NFW-gas profile,was shown by Makino et al.(1997)to closely approximate the conventionalβ-model(withβ=η/15).It tends to Aeηin the centre and to A for large x.Thus A is,in practice,very small and the plateau at large x is not noticeable.The pa-rameterαhas the same units as velocity dispersion squared, thus it is apparent thatηis closely related to the widely-used parameterβ,the ratio of the DM kinetic energy to the thermal energy of the gas when both are isothermal.The NFW-gas profile has beenfitted to the surface brightness profiles of observed clusters and it models most clusters very well(Ettori&Fabian1998).Values ofηin the largest clusters which have coolingflows(suggesting they are in a relaxed state,in contrast to non-coolingflows;Buote& Tsai1996)average about10.5,with a standard deviation of about1.0(Ettori,private communication).Direct compar-ison shows that the gas profile forη=10.5closely follows the NFW profile from x=0.4to3.The profiles differ in-side x=0.4due to theflat core of the NFW-gas profile, which implies that the gas fraction increases as a function of radius,as observed in real clusters(e.g.White,Jones& Forman1997).This last effect becomes more pronounced and spreads to larger radii for smaller values ofη,the major cause of which will be heating by supernovae.Sinceηgives both the gas temperature and the slope of the gas density profile,it is the structural parameter through which supernova heating exerts its influence on cluster prop-erties.The procedure for settingηis as follows.We postulate that the total specific energy of the gas(thermal plus gravi-c 0000RAS,MNRAS000,000–000Supernova heating3 tational)is proportional to the specific gravitational energyof the DM,and that any excess specific energy from super-nova heating is added to the above gas energy,as its nameimplies.i.e.,3kTM gas=K 1M DM+E excess,(5)whereρDM is the DM density,which follows the NFW pro-file,M gas and M DM are the total gas and DM masses,andE excess is the excess specific energy.The volumes of integra-tion are spheres of radius r200.Given the constant K,it iseasy to show thatηis only a function of c and E excess.Theconstant of proportionality K is calibrated so thatηis closeto the observed value of10.5for the largest clusters,whenE excess=0.We use the value K=1.2.(Note thatηvariesby around0.5depending on collapse redshift,through itsdependence on c.)The reason for matching to the largest clusters is that if supernova heating does occur,we expectit to have least effect on the largest clusters.As c varieslittle over cluster masses,this method ensures that clusters are self-similar when there is no excess energy(i.e.,c andηare roughly constant).The trends for c andηare to increaseslightly with decreasing mass,over all masses in our model (see below).The mass deposition rates of clusters are estimated byfinding the radius r cool at which the cooling time is equal to the time∆t to the next major merger(see below)or thepresent,and dividing the gas mass enclosed by∆t to give ˙M.For clusters with coolingflows,i.e.,those with significant˙M,the hot gas which cools does not form stars but BDM.The Cole&Kaiser(1988)block model is used to simu-late the merging history of dark matter halos.The smallest masses in the hierarchy are1.5×1010M⊙and there are20 levels of hierarchy so that the total mass in one collapse tree is7.9×1015M⊙.When a‘block’in the hierarchy virialises, it merges into one halo both older halos and previously un-collapsed material.The new average metallicity and excess energy of the gas can therefore be calculated.Since blocks double in mass up the hierarchy,each collapse of a block roughly corresponds to a major merger.As already men-tioned,we set the metallicities in groups to be high without considering the implications of this for star formation.Halos with masses in the range15–120×1012M⊙are given initial iron abundances of Z=0.5Z⊙˙(This implies that the gas in some of the smaller halos is unbound.)As a result the av-erage metallicities(for a given mass)range from0.3Z⊙for clusters of mass250×1012M⊙to0.25Z⊙for the largest clus-ters.The range of scatter in metallicities is≈0.1Z⊙.These are in good agreement with the recent ASCA measurements by Fukazawa et al.(1998)of iron abundances in40nearby clusters and the measurements of Allen&Fabian(1998).The gas fraction of the clusters in our model lie within one per cent of14per cent.3RESULTS AND DISCUSSIONTo illustratethe effect of heating from supernovae,we dis-play in Fig.1the L X-T distributions before and after the inclusion of supernova heating.We superimpose on the dis-tributions the power lawfit obtained by David et al.(1993), for bolometric luminosities.The excess energies bring the Figure 1.Contour plots of the luminosity-temperature distri-bution,without heating by supernovae(dotted lines)and with supernova heating(solid lines).The contours are spaced at equal logarithmic intervals.The long straight line is the bestfit(for bolometric luminosities)taken from David et al.(1993).The dis-tribution obtained without heating is roughly parallel to the short line segment which follows L X∝T2.In this case the smallest clusters are overluminous by an order of magnitude.The excess energies bring the smaller clusters into agreement with data. smaller clusters into agreement with the observed correla-tion,by increasing their temperature,flattening their den-sity profiles and thereby decreasing their luminosities.For clusters of mass2.5×1014M⊙,ηdecreases to around9.The spread in the L X-T distributions are significant and arise naturally in our simulation from the different formation his-tories of the clusters.For comparison with Fig.1,if we halve the excess en-ergies injected,the average luminosity of a2×107K cluster rises to5×1043erg s−1.Doubling the excess energies causes most of the clusters with T<3×107K to be unbound,which clearly disagrees with data,and roughly halves the luminos-ity of3×107K clusters.In future work we will investigate whether restricting the heating to the core of clusters can de-crease the excess energies required(preliminary results sug-gest that this could reduce the total energy requirements by about a third).In Figs.2and3we show the X-ray luminosity function (XLF)and temperature function respectively.The curves plotted for comparison are the bestfit Schechter function to the ROSAT Brightest Cluster Sample(BCS)bolometric luminosity function,obtained by Ebeling et al.(1997),and the best power lawfit to the temperature function obtained by Edge et al.(1990).The errors in the BCS XLF are very small,while the temperature function is currently uncertain by factors of around2or3.A problem which follows from an incorrect slope of the L X-T relation is that if the temper-ature functionfits the data reasonably well,then the XLF is too steep compared to data(e.g.Kitayama and Suto1996). Correcting the L X-T relation thus improves the slope of the XLF significantly,though it is still slightly steeper than ob-served.Estimates ofσ8from cluster abundances in general use a theoretically derived mass function and assume some mass-c 0000RAS,MNRAS000,000–0004K.K.S.Wu etal.Figure 2.The X-ray luminosity function (XLF)from the model with supernova heating.The curve is the best fit Schechter func-tion to the ROSAT Brightest Cluster Sample (BCS)bolometric luminosity function (Ebeling et al.1997).Figure 3.The temperature function from the model with su-pernova heating.The power law fit to the temperature function obtained by Edge et al.(1990)is plotted.temperature (M −T )relation in order to compare with an observed temperature function.The calibration of the M −T relation is thus crucial to the results,especially as the tem-perature function has a very steep slope.We find that with zero excess energy our model clusters obey the simple esti-mate (appropriate for isothermal r −2gas and DM density profiles)of GM 200µm H(6)to within a few per cent,where M 200is the total mass within r 200.Supernova heating raises the temperature slightly for small clusters.For a cluster of mass 4.9×1014M ⊙collapsing at z =0the temperature increases from 3.5×107K to 3.8×107K in the model described,close to 10per cent higher.The resulting temperatures in our model are anecessaryFigure 4.The smoother curve is the ˙Mcumulative function from our model with supernova heating,and is compared to the function taken from Peres et al.(1997)but with the age of clusters changed to 6Gyr,as explained in the text.We have also excluded clusters with T <2×107K;when all clusters are allowed to contribute,the function increases below 50M ⊙yr −1,rising to 6×10−5Mpc −3at 10M ⊙yr −1,but such clusters would not be included in the observed sample.consequence of fitting the L X −T relation.In a recent paper,Eke et al.(1998)used a more elaborate form of Equation 6and included scatter in the M-T relation,which brought down the predicted σ8.With our CDM shape parameter of Γ=Ω0h exp(−Ωb (1+1/Ω0))=0.12their Fig.7predicts a value of σ8≈0.75.Since preheating was not included,our value of σ8=0.7appears consistent with their results.Turning to the mass deposition rates,we display the ˙Mcumulative space density in Fig.4.We have excluded clus-ters with temperatures less than 2×107K since such objects would be too faint in the 2–10keV band to be included in the sample used by the two papers below.Our result agreesvery well with the ˙Mcumulative function obtained by Edge,Stewart &Fabian (1992)and lies slightly lower than that shown in Peres et al.(1997).The systematic uncertaintiesin measurements of ˙Min clusters are at present around a factor of 2.In particular the age of a cluster since its last major merger is unknown and in determining r cool the age of the universe is generally used.Lowering this age in the analysis of Peres et al.(1997)from 13Gyr to 6Gyr,which is the typical age of a 5keV cluster in our model,lowers r cooland more than halves the values of ˙Min several clusters (Peres,private communication).In Fig.4we show the cu-mulative function from Peres et al.(1997)recalculated with this change in the age of clusters.There is very good agree-ment for all but small values of ˙M,which is not a serious concern since the clusters and their measurements are both sensitive to small perturbations in this range.The mass deposition rate of a cluster is a highly sensi-tive probe of the gas density inside a radius of ∼0.1Mpc (the typical r cool observed in cooling flows).On the other hand,the luminosity in all but the most massive cooling flows comes from inside a radius ∼r s which is larger thanthe cooling flow region.Therefore L X and ˙Mare indepen-dent probes of the gas density profile at different radii,and due to their sensitivity they are efficient at eliminating mod-c0000RAS,MNRAS 000,000–000Supernova heating5els.For example,while we can adjust the overall density inside∼r s by changing the temperature,the ratio of the densities inside the two radii described above have to be cor-rect in order to match both the˙M function and the XLF. We found that models which used gas density profiles of the form r−2β(see NF97)overpredicted the˙M function by an order of magnitude or more.The agreement with the avail-able data suggests that the NFW-gas profile is much closer to the right shape.As a further example of the ability of˙M to discrimi-nate between models,without supernova heating wefind an average value of˙M≈100M⊙yr−1for coolingflow clusters with L X=6×1043erg s−1which is too high when compared with Fig.2of Peres et al.(1997).However,heating lowers the value to˙M≈30M⊙yr−1,which then agrees with their data. On the other hand,large clusters with L X=1045erg s−1 have the correct˙M with and without ing a hy-drodynamic and N-body simulation,Katz&White(1993) modelled a Virgo-like cluster with cooling of gas included, and obtained an excessively high value of˙M∼400M⊙yr−1. Our results suggest that non-gravitational heating could si-multaneously help solve such a problem.The above results argue forflatter gas density profiles in small clusters,in-dependently of the L X−T relation.We consider it very promising that by correctlyfitting the L X−T relation,the predictions pertaining to˙M naturally agree with the data. 4CONCLUSIONSWe have presented a galaxy formation model in which the X-ray properties of clusters agree well with what is observed. The model is based on that described by Nulsen&Fabian (1997),and uses observed gas fractions and metallicities.Re-alistic gas density profiles were used,which sit in potentials given by the NFW profile.In particular,we obtained good fits to the L X−T relation,the X-ray luminosity function, the temperature function and the˙M function,which wefind to be a very sensitive diagnostic of cluster structure in the core.To resolve a number of problems,including getting the correct slope for the L X−T relation and avoiding exces-sive mass deposition rates for low luminosity clusters,self-similarity of clusters has to be broken.In our model this is achieved byflattening the gas density profiles of the smaller clusters,which occurs naturally when we include heating of intracluster gas due to the retention of energy from super-novae in all previous collapse stages.Wefind that the energy required agrees well with the supernova energy released in producing the observed metallicities if most of this energy is retained in the intracluster gas.The result is that the above problems are simultaneously resolved once supernova heating is included.We have highlighted the importance of the mass de-position rate and the˙M function as diagnostics of cluster structure.The value of˙M probes the gas density profile at smaller radii than L X and hence is able to give us indepen-dent information.Due to the sensitivity of quantities such as L X and˙M to the structure and density of the hot gas, and the steep slopes of the three distribution functions we consider,detailed gas processes can be as important as cos-mological considerations in determining what we observe.ACKNOWLEDGEMENTSWe thank Stefano Ettori for the results of surface brightness profilefits,Clovis Peres for the new calculation of the˙M function,and Vince Eke,Stefano,Clovis and Martin Rees for very helpful discussions.KKSW is grateful to the Croucher Foundation forfinancial support.ACF thanks the Royal So-ciety for support.PEJN gratefully acknowledges the hospi-tality of the Institute of Astronomy during part of this work. 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