Evolution of globular cluster systems in elliptical galaxies. II. Power-law initial mass fu

合集下载

【英语单词记忆】天文术语 D F

【英语单词记忆】天文术语 D F 【英语单词记忆】天文术语d-fdabundance氘丰度dactyl艾卫darkhalo暗晕dataacquisition数据采集declinephase下降阶段deep-fieldobservation浅天区观测densityarm密度臂densityprofile密度轮廓dereddening红化改正desdemona天卫十destabiliizingeffect去稳效应dewshield露罩diagonalmirror对角镜diagnosticdiagram确诊图differentialreddening较差红化diffusedensityEnergetic密度diffusedwarf弥漫矮星系diffusex-ray弥漫着x射线diffusionapproximation扩散近似digitalopticalskysurvey数字光学巡天digitalskysurvey数字巡天disappearance掩始cisconnectionevent断尾事件dish碟形天线diskglobularcluster盘族球状星团dispersionmeasure频散量度dissector析象管distanceestimator估距关系distributionparameter分布参数disturbedgalaxy告以星系disturbinggalaxy扰动星系dobsonianmounting多布森装置dobsonianreflector多布森反射望远镜dobsoniantelescope多布森望远镜dominantgalaxy主星系double-modecepheid双锻铁父变星double-modepulsator双模脉动星double-moderrlyraestar双模天琴rr型星 double-ringgalaxy双环星系dqherculisstar武仙dq型星dredge-up上翻driftscanning飘移读取drivingsystem驱动系统dumbbellradiogalaxy哑铃状射电星系duponttelescope杜邦望远镜dustring尘环dwarfcarbonstar碳矮星dwarfspheroidal狼球状星系dwarfspheroidalgalaxy矮球状星系 dwarfspiral狼旋涡星系dwarfspiralgalaxy矮旋涡星系dynamicalage动力学年龄dynamicalastronomy动力天文dynamicalevolution动力学进化eaglenebula(m16)鹰状星云eartycluster晚型星系团earlyearth早期地球。

Do Globular Clusters Harbor Black Holes?

Do Globular Clusters Harbor Black Holes？佚名【期刊名称】《天文和天体物理学研究》【年(卷),期】2001(001)004【摘要】It has been firmly established that there exists a tight correlation be-tween the mass of the central black hole and velocity dispersion (or luminosity) in elliptical galaxies, "pseudobulges" and bulges of galaxies, although the nature of this correlation still remains unclear. We explore the possibility of extrapolating such a correlation to less massive, spherical systems like globular clusters. In par-ticular, motivated by the apparent success in the globular cluster M15, we present an estimate of the central black hole mass for a number of globular clusters with available velocity dispersion data.【总页数】5页(P291-295)【正文语种】中文【中图分类】P14【相关文献】1.The Quantization of Black Holes, Lower Mass Limit, Temperature, and Lifetime of Black Holes in a Simple Way [J], Sirus Arya Enejad2.Black Hole Clusters: The Dark Matter [J], Kenneth Dalton3.Has LIGO detected primordial black hole dark matter?——tidaldisruption in binary black hole formation [J], Yuan Gao;Xiao-Jia Zhang;Meng Su4.How a Laser Physics Induced Kerr-Newman Black Hole Can Release Gravitational Waves without Igniting the Black Hole Bomb (Explosion of a Mini Black Hole in a Laboratory) [J], Andrew Walcott Beckwith5.Looking at Quantization Conditions, for a Wormhole Wavefunction, While Considering Differences between Magnetic Black Holes, Versus Standard Black Holes as Generating Signals from a Wormhole Mouth [J], Andrew Beckwith因版权原因，仅展示原文概要，查看原文内容请购买。

proper 造句

proper 造句1、Resize the fields to proper size.将字段的大小重新调整为适当的大小。

2、He gave us a proper example.他给我们举了一个恰当的例子。

3、When it is only right to speak proper Mandarin什么时候应该说正确华语4、I held my ground as they explained proper grammatical execution to me.编辑向我解释正确的语法应用，但我坚持自己的风格。

5、Gratifyingly, people are interested in physics and this is a proper story.令人欣慰的是，大众对物理感兴趣，而这是一个合适的故事。

6、Posts inventory to proper General Ledger accounts.被用来记入存货到正确的总账账目。

7、I don't have proper equipment to fully test this alternator.我没有适当的设备，以充分测试此发电机。

8、Choose protectors of proper size.选购适当大小的护具。

9、A PROPER MOTION STUDY OF THE GLOBULAR CLUSTER M10 (NGC 6254)球状星团M10(NGC6254)的自行研究10、Sanctity flows out of proper use of the divinely ordained covenantsigns and seals.成圣乃出于正当地执行了神命定的圣约记号和标记。

绘制球状星团的郝罗图

先在wiki了解关于M系列的球状星团的基本资料，注意到最基本的参数ra,dec, 星等，直径。查看M2的链接资料
正好有我需要的星团年龄，还有可能会用到的外部链接
文字很多，但不需要全部看完，只看有链接的蓝色字体，找关键字
非常详细的链接资料，都是关于globular clusters
参数很详尽，至此知道所需球状星团的参数资料。
/edr/en/sdss/skyserver/
我用这个第一次下载数据画的图不正常，重复试验两次都不行也没再检查其他可能出错的步骤
对网站布局不熟先看看help，找到了最重要的
/dr7/en/proj/advanced/hr/globularcluster.asp
2.球状星团查询
/cluster_4.php?ggc=NGC+5272
3.Mathematica免费正版
/products/special/chinastudent/
复制第一个计算出来的g-r值，从最后一行，即第1316行往上选中 D列，即可得到所有行的g-r值。注意，不要用点击最顶上的D来选中整个列，这样会选中从1到 65536行，如右图，excel会用0 自动填充其余行，后面导入数据到matlab时这些属于无用数据。
保存时提示，选择“否”，不改变原来下载的用txt格式保存的数据。另存为工作簿格式，如右图。
绘制球状星团的赫罗图
数据的形式(参数)？球状星团数据到哪里找数据？星表（catalogue of globular clusters）大型天文数据库SDSS
如何处理所需数据？
/wiki/Globular_cluster
/wiki/List_of_globular_clusters

GRE阅读高频机经原文：蓝脱序星的两种形成过程

GRE阅读高频机经原文：蓝脱序星的两种形成过程gre阅读是许多考生难以攻克的大山，下面先来看看GRE阅读高频机经原文：蓝脱序星的两种形成过程，一起来学习吧！GRE阅读高频机经原文：蓝脱序星的两种形成过程蓝脱序星blue straggler的两种形成过程Vampires and collisions rejuvenate starsUsing the NASA/ESA Hubble Space Telescope, astronomers have uncovered two distinct kinds of "rejuvenated" stars in the globular cluster Messier 30. A new study shows that both stellar collisions and a process sometimes called vampirism are behind this cosmic "face lift". The scientists also uncover evidence that both sorts of blue stragglers were produced during a critical dynamical event (known as "core collapse") that occurred in Messier 30 a few billion years ago.Stars in globular clusters [1] are generally extremely old, with ages of 12-13 billion years. However, a small fraction of them appear to be significantly younger than the average population and, because they seem to have been left behind by the stars that followed the normal path of stellar evolution and became red giants, have been dubbed blue stragglers [2]. Blue stragglers appear to regress from "old age" back to a hotter and brighter "youth", gaining a new lease on life in the process. A team of astronomers used Hubble to study the blue straggler star content in Messier 30, which formed 13 billion years ago and was discovered in 1764 by Charles Messier. Located about 28 000 light-years away from Earth, this globular cluster — a swarm of several hundred thousand stars — is about 90 light-years across.Although blue stragglers have been known since the early 1950s, their formation process is still an unsolved puzzle in astrophysics. "It’s like seeing a few kids in the group picture of arest-home for retired people. It is natural to wonder why they are there," says Francesco Ferraro from the University of Bologna in Italy, lead author of the study that will be published this week in Nature [3]. Researchers have been studying these stars for many years and knew that bluestragglers are indeed old. They were thought to have arisen in a tight binary system [4]. In such a pair, the less massive star acts as a "vampire", siphoning fresh hydrogen from its more massive companion star. The new fuel supply allows the smaller star to heat up, growing bluer and hotter — behaving like a star at an earlier stage in its evolution.The new study shows that some of the blue stragglers have instead been rejuvenated by a sort of "cosmic facelift", courtesy of cosmic collisions. These stellar encounters are nearlyhead-on collisions in which the stars might actually merge, mixing their nuclear fuel andre-stoking the fires of nuclear fusion. Merged stars and binary systems would both be about twice the typical mass of individual stars in the cluster."Our observations demonstrate that blue stragglers formed by collisions have slightly different properties from those formed by vampirism. This provides a direct demonstration that the two formation scenarios are valid and that they are both operating simultaneously in this cluster," says team member Giacomo Beccari from ESA.Using data from the now-retired Wide Field Planetary Camera 2 (WFPC2) aboard Hubble, astronomers found that these "straggling" stars are much more concentrated towards the centre of the cluster than the average star. "This indicates that blue stragglers are more massive than the average star in this cluster," says Ferraro. "More massive stars tend to sink deep into the cluster the way a billiard ball would sink in a bucket of honey."The central regions of high density globular clusters are crowded neighbourhoods where interactions between stars are nearly inevitable. Researchers conjecture that one or two billion years ago, Messier 30 underwent a major "core collapse" that started to throw stars towards the centre of the cluster, leading to a rapid increase in the density of stars. This event significantly increased the number of collisions among stars, and favoured the formation of one of the families of blue stragglers. On the other hand, the increase of stellar crowding due to the collapse of the core also perturbed the twin systems, encouraging the vampirism phenomenon and thus forming the other family of blue stragglers. "Almost ten percent of galactic globular clusters have experienced core collapse, but this is the first time that we see the effect of the core collapse imprinted on a stellar population," says Barbara Lanzoni, University of Bologna."The two distinct populations of blue stragglers discovered in Messier 30 are the relics of the collapse of the core that occurred two billion years ago. In a broad context our discovery is direct evidence of the impact of star cluster dynamics on stellar evolution. We should now try to see if other globular clusters present this double population of blue stragglers," concludes Ferraro.GRE阅读词汇精选之渗透douse v.把…浸入水中，用水泼drenched adj.湿透的soak v.浸泡，渗透soaked adj.湿透的sodden adj.浸透了的soggy adj.湿透的，濡湿的souse v.浸在水中，使湿透steep v.浸泡，浸透logged adj笨重的，湿透的immerse v.浸入，沉浸于immersion n.沉入，浸入macerate v.浸软，消瘦GRE阅读表示选择的逻辑词汇总逻辑词条词性例句选择otherwiseadv.You need to work hard. Otherwise, you will fail.选择or (else)conj.You need to work hard, or (else) you will fail.选择lestconj.You need to work hard, lest you fail the exam.选择in caseconj.You need to work hard, in case the exam is hard. GRE阅读表示转折的逻辑词汇总逻辑词条词性例句转折butconj.I worked hard, but I failed.转折howeveradv.I worked hard. However, I failed.转折neverthelessadv.I worked hard. Nevertheless, I failed.转折stilladv.I worked hard. Still, I failed.转折nonethelessadv.I worked hard. Nonetheless, I failed.转折thoughadv.I worked hard. I failed, though.。

Compact binaries in globular clusters

a r X i v :a s t r o -p h /0402537v 2 23 F eb 2004Revista Mexicana de Astronom´ıa y Astrof´ısica ,00,??–??(2004)COMPACT BINARIES IN GLOBULAR CLUSTERSNatalia Ivanova and Frederic A.RasioNorthwestern University,USAReceived ;acceptedRESUMENEl resumen ser´a traducido al espa˜n ol por los editores.In dense stellarsystems the frequent dynamical interactions between stars play a crucial role in the formation and evolution of compact binaries.We study these processes using a novel approach combining a state-of-the-art binary population synthesis code with a simple treatment of dynamical interactions in dense star cluster cores.Here we focus on the dynamical and evolutionary processes leading to the formation of compact binaries containing white dwarfs in dense globular clusters.We demonstrate that dynamics can increase by factors ∼2−100the production rates of interesting binaries such as cataclysmic variables,“nonﬂickerers”(He white dwarfs with a heavier dark companion),merging white dwarf binaries with total masses above the Chandrasekhar limit,and white dwarf binaries emitting gravitational waves in the LISA band.ABSTRACTIn dense stellar systems the frequent dynamical interactions between stars play a crucial role in the formation and evolution of compact binaries.We study these processes using a novel approach combining a state-of-the-art binary popu-lation synthesis code with a simple treatment of dynamical interactions in dense star cluster cores.Here we focus on the dynamical and evolutionary processes lead-ing to the formation of compact binaries containing white dwarfs in dense globular clusters.We demonstrate that dynamics can increase by factors ∼2−100the pro-duction rates of interesting binaries such as cataclysmic variables,“nonﬂickerers”(He white dwarfs with a heavier dark companion),merging white dwarf binaries with total masses above the Chandrasekhar limit,and white dwarf binaries emitting gravitational waves in the LISA band.Key Words:GLOBULAR CLUSTERS:GENERAL—BINARIES:CLOSE —WHITE DW ARFS 1.INTRODUCTIONFrom the earliest observations of X-ray binaries in globular clusters it has always been clear that they must be very eﬃcient factories for the production of compact binary systems (Clark 1975).The over-abundance of compact binaries in clusters,as com-pared to the ﬁeld,must be a result of close stellar encounters.The key processes that aﬀect the binary population in dense cluster environments include the destruction of wide binaries,hardening of close bina-ries (following “Heggie’s law”(Heggie 1975)),and exchange interactions,through which low-mass com-panions tend to be replaced by a more massive par-ticipant in the encounter.As a result of these pro-cesses,in the dense cores of globular clusters,bi-naries are strongly depleted and their period distri-bution is very diﬀerent from that of a ﬁeld popu-lation (Ivanova et al.2004).These processes also lead to an interesting and complex interplay between dynamics and binary evolution.For example,ex-change interactions involving compact objects often produce systems that will evolve through a common-envelope (CE)phase and form very short-period bi-naries,which are much less common in ﬁeld popula-tions (Rasio,Pfahl,&Rappaport 2000).There are two possible approaches to the study of binary evolution and dynamics in glob-ular clusters.One can start from N -body sim-12IVANOVA AND RASIOulations and introduce various simpliﬁed treat-ments of binary star evolution.This hasbeen the traditional approach for many years (for recent examples see Shara &Hurley 2002;Portegies Zwart,McMillan,Hut,&Makino 2001).Alternatively,one can start from a binary popula-tion synthesis code and add a treatment of dynam-ical interactions.This approach was pioneered by Portegies Zwart et al.(1997)and has been adopted in our recent work.It has the great advantage that it is computationally much less expensive than N -body simulations,so that more exploration of the (enor-mous)parameter space is possible,and more realistic simulations,using suﬃciently large numbers of stars and binaries,are possible today.In contrast,even when using special-purpose GRAPE computers,N -body simulations are still limited to smaller systems like open clusters with limited coverage of parameter space and with unrealistically small numbers of bina-ries (see Ivanova et al.2004;Wilkinson et al.2003).In our code we combined StarTrack ,a state-of-the-art binary population synthesis code (Belczynski et al.2002)and FewBody ,a small-N -body integrator that we use to compute 3-body and 4-body interactions (Fregeau et al.2004;Fregeau &Rappaport 2004).Currently we adopt a simple two-zone model,in which the clus-ter is partitioned into an inner core and an outer halo,with all interactions assumed to take place in the core.This background cluster model remains unchanged throughout the evolution (Hut,McMillan,&Romani 1992).In particular,the core density is assumed constant.However,our ul-timate aim is to incorporate full dynamical Monte Carlo models (Fregeau et al.2003).In a typical simulation we start with N ∼105stars,with be-tween 50%and 100%binaries.This high primor-dial binary fraction (much higher than assumed in all previous studies)is needed in order to match the observed binary fractions in globular cluster cores today (Ivanova et al.2004).PACT BINARIES AND MERGERS Consider the evolution of a typical dense cluster with central velocity dispersion σ=10km s −1and core density n c =105pc −3.Dynamical interactions lead to greatly enhanced numbers of compact bina-ries containing white dwarf (WD)and neutron star (NS)components,and,in particular,to much larger numbers of heavier compact binaries (Fig.1).Here we focus in particular on the fate of WDs involved in CE events leading to compact binary formation or mergers of WDs driven by gravitational wave emis-sion.Our simulations conﬁrm that the formationFig.1.Mergers and dynamical formation of compact binaries containing white dwarfs (WD)or neutron stars (NS).The horizontal axis gives the cluster age when the event occurred and the vertical axis gives the total mass of the binary.The top panel shows a population evolved without dynamical interactions,while the bottom panel shows the same initial population evolved in a dense clus-ter with core density n c =105pc −3.The size of each symbol indicates the types of stars involved,while the shape indicates the type of event:binary merger (round dots;usually driven by gravitational radiation or spiral-in during a common envelope phase),compact binary formation following a common envelope phase (stars),or merger following a physical collision (triangles).It is clear that dynamics increases both the total number of events and the typical mass of mergers and compact binaries.GLOBULAR CLUSTERS3rate of compact binaries containing a Helium WD with a heavier companion via CE events is increased signiﬁcantly in dense clusters.The brighter Helium WDs in these binaries could be detectable as “non-ﬂickerers.”These wereobserved for the ﬁrst time in the core of NGC 6397(Cool et al.1998)and are indeed thought to be double WD binaries containing a young Helium WD with an older and heavier WD companion (Hansen,Kalogera,&Rasio 2003).We can also examine the rate of double WD mergers,and,in particular,those for which the to-tal mass is ≥M Ch ≃1.4M ⊙).These so-called supra-Chandrasekhar mergers could lead either to a Type Ia supernova,or to a “merger-induced”col-lapse of the remnant to form a NS (and perhaps a millisecond radio pulsar).It is possible that the NS in this case is formed without a signiﬁcant kick (see the article by Podsiadlowski in this volume).An increased rate of Type Ia supernovae from star cluster dynamics would likely be redshift-dependent (as more stars are formed in starburst environments —which favor star cluster formation —at higher redshifts)and this has important potential conse-quences for their use in cosmology (for a review see Leibundgut 2001).Alternatively,merger-induced collapse could lead to the formation of neutron stars and millisecond pulsars in clusters,thereby alleviat-ing or perhaps eliminating the NS “retention prob-lem”(the ejection of most NS from the shallow clus-ter potentials if they are born with the natal kicks expected from asymmetric supernova explosions;see,e.g.,Chen &Leonard 1993;Pfahl,Rappaport,&Podsiadlowski 2002)The enhanced production rate of double WD mergers in dense stellar clusters was ﬁrst discussed in detail by Shara &Hurley (2002).They estimated that,for stars born in open clusters (which can be simulated directly using their N -body code),the supra-Chandrasekhar WD merger rate can be in-creased by an order of magnitude.The results of Shara &Hurley (2002)are based on N -body simu-lations for a typical open cluster containing ∼104stars with 10%primordial binary fraction,and with σ=2km s −1and n c =103pc −3.Our simula-tions are for much denser and massive star clusters with a primordial binary fraction of 100%.Not sur-prisingly,we ﬁnd an even larger number of supra-Chandrasekhar WD mergers,with an enhancement factor (compared to a ﬁeld population)closer to ∼100for a typical dense globular cluster.In con-trast,the total number of double WD mergers (of all types)is typically increased by a factor of a few only.The majority of these mergers are driven ul-Fig.2.All LISA-detectable binaries during the last Gyr of evolution for a typical dense cluster model with core density n c =106pc −3.Each source is shown only once,at a randomly chosen moment in its evolution across the LISA band.Here P is the binary orbital period and M chirp =(M 1M 2)3/5/(M 1+M 2)1/5is the chirp mass.The diﬀerent symbols indicate binaries with diﬀerent types of components.We again compare a ﬁeld pop-ulation (top)to our cluster model including dynamical interactions (bottom).4IVANOVA AND RASIOtimately by gravitational radiation,although a few come from physical collisions of WDs during hard binary encounters (Fregeau et al.2004).3.LISA SOURCESOur results show that compact double WD bina-ries are mainly formed dynamically and have typi-cally experienced multiple hardening encounters be-fore merging.Prior to merger,these systems may be detectable as gravitational wave sources by LISA,when their orbital period becomes smaller than about 2000s (Benacquista,Portegies Zwart &Rasio,2001).This limit on the orbital period is imposed by the background noise from Galactic binaries.At the same time,the positional accuracy of LISA is much greater for binaries with these shorter periods,so that the sources can then be associated with speciﬁc globular clusters in our Galaxy.Figure 2shows all LISA-detectable sources (chirp masses and periods)that appeared during the last Gyr of our simulation for a typical dense cluster.For this model,where the total cluster mass today is about 2×105M ⊙,at least one LISA source is present at any given time.On average,there are ∼5LISA sources at any given moment,about twice the number predicted for a ﬁeld population.In addition to this rise in the number of sources,we also note changes in their typical properties:in particular,the number of sources with chirp mass above 0.4M ⊙is increased signiﬁcantly in the cluster model.We also ﬁnd that NS-WD binaries represent about 20%of all LISA sources.Therefore,the number of LISA-detectable NS-WD binaries in all Galactic globular clusters (M tot ∼107.5M ⊙)could be as high as ∼>100,while the total number of detectable WD-WD binaries could be ∼>500.However,since the cluster models we have used so far in our simulations are denser than average,these numbers should be taken as upper bounds.4.MASS TRANSFER SYSTEMSAs they spiral in and evolve across the LISA band,WD-WD and NS-WD binaries will eventually come into contact around a period P ∼100s.At ﬁrst the binary orbit shrinks as it looses angular mo-mentum to gravitational radiation.However,during stable mass transfer,the orbit will evolve towards a larger period.During this mass transfer phase theNatalia Ivanova:Dept of Physics and Astronomy,Northwestern University,2145Sheridan Rd,Evanston,IL 60208,USA (nata@ ).Frederic A.Rasio:Dept of Physics and Astronomy,Northwestern University,2145Sheridan Rd,Evanston,IL 60208,USA (rasio@ ).binary can also appear as an ultracompact X-ray bi-nary (NS-WD)or an AM CVn type cataclysmic vari-able (WD-WD).As expected,we ﬁnd that the popu-lation of these mass transfer binaries is also increased signiﬁcantly by dynamical interactions.For exam-ple,for our typical cluster model with n c =105pc −3,we predict about 50AM CVn binaries,roughly twice the number obtained without dynamics.This work was supported by NASA ATP Grant NAG5-12044and a Chandra Theory grant. F.A.R.thanks the organizers of IAU Colloquium 194for support and acknowledges the hospitality of the Kavli Institute for Theoretical Physics.REFERENCESBelczynski,K.,Kalogera,V.,&Bulik,T.2002,ApJ,572,407Benacquista,M.J.,Portegies Zwart,S.,and Rasio,F.A.2001,Class.Quantum Grav.,18,4025Chen,K.,&Leonard,P.J.T.1993,ApJ,411,L75Clark,G.W.1975,ApJ,199,L143Cool,A.M.,Grindlay,J.E.,Cohn,H.N.,Lugger,P.M.,&Bailyn,C.D.1998,ApJ,508,L75Fregeau,J.M.,G¨u rkan,M.A.,Joshi,K.J.,&Rasio,F.A.2003,ApJ,593,772Fregeau,J.M.,&Rappaport,S.A.2004,in preparation Fregeau,J.M.,Cheung,P.,Portegies Zwart,S.F.,&Rasio, F.A.2004,submitted to MNRAS [astro-ph/0401004]Hansen,B.M.S.,Kalogera,V.,&Rasio,F.A.2003,ApJ,586,1364Heggie,D.C.1975,MNRAS,173,729Hut,P.,McMillan,S.,&Romani,R.W.1992,ApJ,389,527Ivanova,N.,Belczynski,K.,Fregeau,J.M.,&Rasio,F.A.2004,submitted to ApJ[astro-ph/0312497]Leibundgut,B.2001,ARA&A,39,67Pfahl,E.,Rappaport,S.,&Podsiadlowski,P.2002,ApJ,573,283Portegies Zwart,S.F.,Hut,P.,McMillan,S.L.W.,&Ver-bunt,F.1997,A&A,328,143Portegies Zwart,S.F.,McMillan,S.L.W.,Hut,P.,&Makino,J.2001,MNRAS,321,199Rasio,F.A.,Pfahl,E.D.,&Rappaport,S.2000,ApJ,532,L47Shara,M.M.&Hurley,J.R.2002,ApJ,571,830Wilkinson,M.I.,Hurley,J.R.,Mackey,A.D.,Gilmore,G.F.,&Tout,C.A.2003,MNRAS,343,1025。

第三章恒星的演化

2．较高质量 (M > ~2M⊙) 恒星的演化 (20.4, 21.221.3) (1) 与低质量恒星演化的主要区别恒星内部的H燃烧通过CNO循环进行，内部温度更高，辐射压对维持恒星的力学平衡起更大的作用，主序寿命更短。 He核不再是简并的，C和更重元素的燃烧可以进行。核心区核反应产生的能量主要以对流的方式向外传递。
第三章恒星的演化
§3.1 主序星的演化 §3.2 恒星主序后的演化 §3.3 恒星演化的观测证据 §3.4 密近双星的演化
§3.1 主序星的演化
(20.1)
1. 恒星演化的基本原理
恒星在一生的演化中总是试图处于稳定状态（流体静力学平衡和热平衡）。当恒星无法产生足够多的能量时，它们就无法维持热平衡和流体静力学平衡，于是开始演化。
L ~ M 2.5-4, R ~ M 0.5-1
主序星的演化
(1) 零龄主序 (zero age main-sequence star, ZAMS) 刚刚开始核心H燃烧的恒星，在H-R图上占据主序带的最左侧。 (2) 演化时标 ——核反应 (4 1H→4He +γ) 时标 tn＝η△Mc2/L ≈(1010 yr) (M/M⊙) (L/L⊙)-1 ≈(1010 yr) (M/M⊙)-2.5 for M > M⊙ or (1010 yr) (M/M⊙)-2 for M < M⊙
(4) 特大质量恒星的演化
星风引起的质量损失和恒星演化。高光度恒星通常有很强的星风～10-6-10-4 M⊙yr-1 如沃尔夫-拉叶(WR)星。演化过程 O型星→蓝超巨星→（红超巨星）→WR星→Ib/Ic型超新星 + 中子星/黑洞
小结：
不同质量恒星的演化结局
恒星初始质量 (M⊙) < 0.01 0.01 < M < 0.08 0.08 < M < 0.25 0.25 < M < 8 8 < M < 12 12 < M < 40 M > 40 演化结局行星褐矮星 He白矮星 CO白矮星? ONeMg白矮星? 超新星→中子星? 超新星→黑洞?

天文学专用词汇

Galactic aggregate 银河星集Galactic astronomy 银河系天文Galactic bar 银河系棒galactic bar 星系棒galactic cannibalism 星系吞食galactic content 星系成分galactic merge 星系并合galactic pericentre 近银心点Galactocentric distance 银心距galaxy cluster 星系团Galle ring 伽勒环Galilean transformation 伽利略变换Galileo 〈伽利略〉木星探测器gas-dust complex 气尘复合体Genesis rock 创世岩Gemini Telescope 大型双子望远镜Geoalert, Geophysical Alert Broadcast 地球物理警报广播giant granulation 巨米粒组织giant granule 巨米粒giant radio pulse 巨射电脉冲Ginga 〈星系〉X 射线天文卫星Giotto 〈乔托〉空间探测器glassceramic 微晶玻璃glitch activity 自转突变活动global change 全球变化global sensitivity 全局灵敏度GMC, giant molecular cloud 巨分子云g-mode g 模、重力模gold spot 金斑病GONG, Global Oscillation Network 太阳全球振荡监测网GroupGPS, global positioning system 全球定位系统Granat 〈石榴〉号天文卫星grand design spiral 宏象旋涡星系gravitational astronomy 引力天文gravitational lensing 引力透镜效应gravitational micro-lensing 微引力透镜效应great attractor 巨引源Great Dark Spot 大暗斑Great White Spot 大白斑grism 棱栅GRO, Gamma-Ray Observatory γ射线天文台guidscope 导星镜GW Virginis star 室女GW 型星habitable planet 可居住行星Hakucho 〈天鹅〉X 射线天文卫星Hale Telescope 海尔望远镜halo dwarf 晕族矮星halo globular cluster 晕族球状星团Hanle effect 汉勒效应hard X-ray source 硬X 射线源Hay spot 哈伊斑HEAO, High-Energy Astronomical 〈HEAO〉高能天文台Observatoryheavy-element star 重元素星heiligenschein 灵光Helene 土卫十二helicity 螺度heliocentric radial velocity 日心视向速度heliomagnetosphere 日球磁层helioseismology 日震学helium abundance 氦丰度helium main-sequence 氦主序helium-strong star 强氦线星helium white dwarf 氦白矮星Helix galaxy （NGC 2685 ）螺旋星系Herbig Ae star 赫比格Ae 型星Herbig Be star 赫比格Be 型星Herbig-Haro flow 赫比格-阿罗流Herbig-Haro shock wave 赫比格-阿罗激波hidden magnetic flux 隐磁流high-field pulsar 强磁场脉冲星highly polarized quasar （HPQ ）高偏振类星体high-mass X-ray binary 大质量X 射线双星high-metallicity cluster 高金属度星团;高金属度星系团high-resolution spectrograph 高分辨摄谱仪high-resolution spectroscopy 高分辨分光high - z 大红移Hinotori 〈火鸟〉太阳探测器Hipparcos, High Precision Parallax 〈依巴谷〉卫星Collecting SatelliteHipparcos and Tycho Catalogues 〈依巴谷〉和〈第谷〉星表holographic grating 全息光栅Hooker Telescope 胡克望远镜host galaxy 寄主星系hot R Coronae Borealis star 高温北冕R 型星HST, Hubble Space Telescope 哈勃空间望远镜Hubble age 哈勃年龄Hubble distance 哈勃距离Hubble parameter 哈勃参数Hubble velocity 哈勃速度hump cepheid 驼峰造父变星Hyad 毕团星hybrid-chromosphere star 混合色球星hybrid star 混合大气星hydrogen-deficient star 缺氢星hydrogenous atmosphere 氢型大气hypergiant 特超巨星Ida 艾达（小行星243号）IEH, International Extreme Ultraviolet 〈IEH〉国际极紫外飞行器HitchhikerIERS, International Earth Rotation 国际地球自转服务Serviceimage deconvolution 图象消旋image degradation 星象劣化image dissector 析象管image distoration 星象复原image photon counting system 成象光子计数系统image sharpening 星象增锐image spread 星象扩散度imaging polarimetry 成象偏振测量imaging spectrophotometry 成象分光光度测量immersed echelle 浸渍阶梯光栅impulsive solar flare 脉冲太阳耀斑infralateral arc 外侧晕弧infrared CCD 红外CCDinfrared corona 红外冕infrared helioseismology 红外日震学infrared index 红外infrared observatory 红外天文台infrared spectroscopy 红外分光initial earth 初始地球initial mass distribution 初始质量分布initial planet 初始行星initial star 初始恒星initial sun 初始太阳inner coma 内彗发inner halo cluster 内晕族星团integrability 可积性Integral Sign galaxy （UGC 3697 ）积分号星系integrated diode array （IDA ）集成二极管阵intensified CCD 增强CCDIntercosmos 〈国际宇宙〉天文卫星interline transfer 行间转移intermediate parent body 中间母体intermediate polar 中介偏振星international atomic time 国际原子时International Celestial Reference 国际天球参考系Frame （ICRF ）intraday variation 快速变化intranetwork element 网内元intrinsic dispersion 内廪弥散度ion spot 离子斑IPCS, Image Photon Counting System 图象光子计数器IRIS, Infrared Imager / Spectrograph 红外成象器/摄谱仪IRPS, Infrared Photometer / Spectro- 红外光度计/分光计meterirregular cluster 不规则星团; 不规则星系团IRTF, NASA Infrared Telescope 〈IRTF〉美国宇航局红外Facility 望远镜IRTS, Infrared Telescope in Space 〈IRTS〉空间红外望远镜ISO, Infrared Space Observatory 〈ISO〉红外空间天文台isochrone method 等龄线法IUE, International Ultraviolet 〈IUE〉国际紫外探测器ExplorerJewel Box （NGC 4755 ）宝盒星团Jovian magnetosphere 木星磁层Jovian ring 木星环Jovian ringlet 木星细环Jovian seismology 木震学jovicentric orbit 木心轨道J-type star J 型星Juliet 天卫十一Jupiter-crossing asteroid 越木小行星Kalman filter 卡尔曼滤波器KAO, Kuiper Air-borne Observatory 〈柯伊伯〉机载望远镜Keck ⅠTelescope 凯克Ⅰ望远镜Keck ⅡTelescope 凯克Ⅱ望远镜Kuiper belt 柯伊伯带Kuiper-belt object 柯伊伯带天体Kuiper disk 柯伊伯盘LAMOST, Large Multi-Object Fibre 大型多天体分光望远镜Spectroscopic TelescopeLaplacian plane 拉普拉斯平面late cluster 晚型星系团LBT, Large Binocular Telescope 〈LBT〉大型双筒望远镜lead oxide vidicon 氧化铅光导摄象管Leo Triplet 狮子三重星系LEST, Large Earth-based Solar 〈LEST〉大型地基太阳望远镜Telescopelevel-Ⅰcivilization Ⅰ级文明level-Ⅱcivilization Ⅱ级文明level-Ⅲcivilization Ⅲ级文明Leverrier ring 勒威耶环Liapunov characteristic number 李雅普诺夫特征数（LCN ）light crown 轻冕玻璃light echo 回光light-gathering aperture 聚光孔径light pollution 光污染light sensation 光感line image sensor 线成象敏感器line locking 线锁line-ratio method 谱线比法Liner, low ionization nuclear 低电离核区emission-line regionline spread function 线扩散函数LMT, Large Millimeter Telescope 〈LMT〉大型毫米波望远镜local galaxy 局域星系local inertial frame 局域惯性架local inertial system 局域惯性系local object 局域天体local star 局域恒星look-up table （LUT ）对照表low-mass X-ray binary 小质量X 射线双星low-metallicity cluster 低金属度星团;低金属度星系团low-resolution spectrograph 低分辨摄谱仪low-resolution spectroscopy 低分辨分光low - z 小红移luminosity mass 光度质量luminosity segregation 光度层化luminous blue variable 高光度蓝变星lunar atmosphere 月球大气lunar chiaroscuro 月相图Lunar Prospector 〈月球勘探者〉Ly-α forest 莱曼-α 森林MACHO （massive compact halo 晕族大质量致密天体object ）Magellan 〈麦哲伦〉金星探测器Magellan Telescope 〈麦哲伦〉望远镜magnetic canopy 磁蓬magnetic cataclysmic variable 磁激变变星magnetic curve 磁变曲线magnetic obliquity 磁夹角magnetic period 磁变周期magnetic phase 磁变相位magnitude range 星等范围main asteroid belt 主小行星带main-belt asteroid 主带小行星main resonance 主共振main-sequence band 主序带Mars-crossing asteroid 越火小行星Mars Pathfinder 火星探路者mass loss rate 质量损失率mass segregation 质量层化Mayall Telescope 梅奥尔望远镜Mclntosh classification 麦金托什分类McMullan camera 麦克马伦电子照相机mean motion resonance 平均运动共振membership of cluster of galaxies 星系团成员membership of star cluster 星团成员merge 并合merger 并合星系; 并合恒星merging galaxy 并合星系merging star 并合恒星mesogranulation 中米粒组织mesogranule 中米粒metallicity 金属度metallicity gradient 金属度梯度metal-poor cluster 贫金属星团metal-rich cluster 富金属星团MGS, Mars Global Surveyor 火星环球勘测者micro-arcsec astrometry 微角秒天体测量microchannel electron multiplier 微通道电子倍增管microflare 微耀斑microgravitational lens 微引力透镜microgravitational lensing 微引力透镜效应microturbulent velocity 微湍速度millimeter-wave astronomy 毫米波天文millisecond pulsar 毫秒脉冲星minimum mass 质量下限minimum variance 最小方差mixed-polarity magnetic field 极性混合磁场MMT, Multiple-Mirror Telescope 多镜面望远镜moderate-resolution spectrograph 中分辨摄谱仪moderate-resolution spectroscopy 中分辨分光modified isochrone method 改进等龄线法molecular outflow 外向分子流molecular shock 分子激波monolithic-mirror telescope 单镜面望远镜moom 行星环卫星moon-crossing asteroid 越月小行星morphological astronomy 形态天文morphology segregation 形态层化MSSSO, Mount Stromlo and Siding 斯特朗洛山和赛丁泉天文台Spring Observatorymultichannel astrometric photometer 多通道天测光度计（MAP ）multi-object spectroscopy 多天体分光multiple-arc method 复弧法multiple redshift 多重红移multiple system 多重星系multi-wavelength astronomy 多波段天文multi-wavelength astrophysics 多波段天体物。

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a r X i v :a s t r o -p h /0010111v 1 5 O c t 2000Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 1February 2008(MN L A T E X style ﬁle v1.4)Evolution of globular cluster systems in elliptical galaxies.II:power-law initial mass functionE.Vesperini ⋆Department of Astronomy,University of Massachusetts,Amherst,MA,01003,USA 1February 2008ABSTRACTWe have studied the evolution of globular cluster systems (GCS)in elliptical galaxies with a power-law initial GCS mass function (GCMF)(f (M )∝M −α)similar to that predicted by some theoretical studies of globular clusters formation and to that of young cluster systems observed in merging galaxies.We have carried out a survey over a large number of diﬀerent host galaxies and we have considered diﬀerent values for the index,α,of the initial power-law GCMF (α=1.5,1.8,2.0);we show the dependence of the main GCS ﬁnal properties (mean mass and dispersion of the ﬁnal GCMF,fraction of surviving clusters,radial gradient of the GCMF parameters)on the structure of the host galaxy and on the slope of the initial GCMF.For a subsample of host galaxies with values of eﬀective masses and radii equal to those determined using observational data for a number of giant,normal and dwarf galaxies our results show that the relation between the ﬁnal GCMF properties and those of the host galaxies as well as the dependence of the ﬁnal GCMF parame-ters on the galactocentric distance within individual galaxies diﬀer from those ob-served in old GCS:the values of the ﬁnal GCS mean mass are in general smaller(4.2<∼log M f is larger than that reported by observational analyses.The results are compared with those of a companion paper in which we investigated the evolution of GCS with a log-normal initial GCMF and in which the ﬁnal GCS properties were perfectly consistent with observations.Key words:globular clusters:general –celestial mechanics,stellar dynamics –galax-ies:star clusters1INTRODUCTIONIn a recent paper (Vesperini 2000)we have investigated the evolution of the main properties of globular clusters systems (hereafter GCS)in elliptical galaxies starting with a log-normal GCS initial mass function.The choice of such a functional form for the initial mass function was motivated by the fact that all the globular cluster system mass functions (hereafter GCMF;we will indicate a globular cluster system luminosity function by GCLF)observed so far are well ﬁtted by a log-normal distribution;in particular,a log-normal GCMF ﬁts well the observed GCMF of clusters located in the external regions of galaxies where evolutionary processes are unlikely to have signiﬁcantly altered the initial properties of clusters.In Vesperini (2000)it was shown that the main ﬁnal GCS properties resulting from the evolution of GCS with a log-normal initial GCMF and the relations between GCS properties and those of the host galaxies are in very good agreement with those reported by a number of observational analyses.In this paper we study the evolution of GCS starting with a power-law initial GCMF.The motivation for considering this functional form for the initial GCMF comes both from some theoretical investigations of globular clusters formation (see e.g.Elmegreen &Efremov 1997,Harris &Pudritz 1994)which predict this shape for the initial GCMF and from several⋆E-mail:vesperin@ c0000RAS2 E.Vesperini−0.50.00.51.01.52.02.5logM el o g R eFigure 1.Set of values of the eﬀective mass,M e (M ⊙),and of the eﬀective radius,R e (kpc),of the host galaxies considered in the paper.observational studies of young cluster systems in interacting and merging galaxies (see e.g.Schweizer et al.1996,Miller et al.1997,Johnson et al.1999,Zepf et al.1999;see also Whitmore 1999for a review and references therein)showing that these systems are characterized by a power-law luminosity function.In fact,whether the observed power-law luminosity function indeed corresponds to an underlying power-law mass function or it results from the age spread of clusters with a log-normal mass function is matter of debate (Fritze-von Alvensleben 1998,1999,Carlson et al.1999,Zhang &Fall 1999);moreover a recent analysis of the GCLF of young clusters in the Antennae system seems to show a turnover in the LF which would be therefore better ﬁtted by a two-index power-law (Whitmore et al.1999).Most observational analyses,on the basis of the high luminosities and compact sizes observed,support the idea that the young clusters found in interacting galaxies are globular clusters which will eventually evolve into systems similar to old globular clusters (see e.g.the results of Ho &Filippenko 1996a,1996b which strongly suggest that at least the brightest clusters must indeed be globular clusters;see also Carlson et al.1998,1999)but this point has been questioned too:van den Bergh (1995),on the basis of the shape of the GCLF,has claimed that these objects would be more properly classiﬁed as young open clusters rather than as young globular clusters.Several theoretical investigations have shown that evolutionary processes can lead to the disruption of a signiﬁcant number of clusters and alter the parameters and shape of the initial GCMF (Fall &Rees 1977,Fall &Malkan 1978,Caputo &Castellani 1984,Chernoﬀ,Kochanek &Shapiro 1986,Chernoﬀ&Shapiro 1987,Aguilar,Hut &Ostriker 1988,Vesperini,1994,1997,1998,Okazaki &Tosa 1995,Capuzzo Dolcetta &Tesseri 1997,Gnedin &Ostriker 1997,Murali &Weinberg 1997a,1997b,Ostriker &Gnedin 1997,Baumgardt 1998);in particular a power-law initial GCMF can be turned by evolutionary processes into a log-normal GCMF (or in general into a bell shaped GCMF).On the other hand it is not clear whether evolutionary processes,acting with diﬀerent eﬃciency in galaxies with diﬀerent structures,can turn an initial power-law into a log-normal GCMF with approximately universal parameters and with a weak radial variation of the GCMF parameters within individual galaxies as found in most current observational studies.In Vesperini (2000)it has been shown that,for a log-normal initial GCMF,the galaxy-to-galaxy variation of the GCMF parameters resulting from theoretical calculations is perfectly consistent with the observed trends and that a considerable disruption of clusters does not necessarily give rise to a radial gradient of the mean mass of clusters inconsistent with observations.The goal of this paper is that of determining if the same conclusions hold for the case of GCS with a power-law initial GCMF.The layout of the paper is the following.In §2we brieﬂy sketch the method used for the investigation and the initialc0000RAS,MNRAS 000,000–000Evolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function3 conditions adopted;in§3we describe the general results while in§4we discuss in detail the implications of our results for galaxies for which observational data are available.We summarize our conclusions in§5.2METHOD AND INITIAL CONDITIONSThe method adopted to follow the evolution of the masses of individual globular clusters is the same used in Vesperini(2000; see also Vesperini1998)and we refer to that paper for further details.The evolutionary processes included are mass loss due to stellar evolution,two-body relaxation,the presence of the tidalﬁeld of the host galaxy and dynamical friction;the eﬀects of the time-variation of the tidalﬁeld for clusters on non-circular orbits(see e.g.Weinberg1994a,1994b,1994c,Gnedin, Hernquist&Ostriker1999)were not included in the N-body simulations by Vesperini&Heggie(1997)and are not considered here.The analytical expression used to determine the mass of a cluster located at distance R g from the center of its host galaxy at time t is based on the N-body simulations carried out by Vesperini&Heggie(1997)and is given byM(t)M i −0.828M iis the mass loss due to stellar evolution(see eq.10in Vesperini&Heggie1997);F CW is aparameter introduced by Chernoﬀ&Weinberg(1990),which is proportional to the initial relaxation time of the cluster and is deﬁned asF CW=M ikpc1v c,(2)where N is the total initial number of stars in the cluster and v c is the circular velocity around the host galaxy.For the host galaxy we will adopt a simple isothermal model with constant circular velocity.The eﬀects of dynamical friction at any time t are included by removing,at that time,all clusters with time-scales of orbital decay(see e.g.Binney&Tremaine1987) smaller than t.The values of the eﬀective masses,M e,and eﬀective radii,R e,of the host galaxies considered are the same studied in Vesperini(2000)and they are plotted in Fig.1.Each GCS investigated initially contains20000clusters with a GCMF given bydN(M)=AM−αdM for104M⊙<M<107M⊙;(3) the values ofαconsidered areα=1.5,1.8,2.0which are close to those determined from observation of the GCLF of young cluster systems in merging and interacting galaxies.Clusters are initially distributed inside the host galaxy between R g=0.16R e and R g=5R e with a number of clusters per cubic kpc proportional to R−3.5gwhich is similar to that observed for Galactic halo clusters(see also Murali&Weinberg1997a where a similar slope for the initial radial distribution is derived for the M87GCS).The evolution of each GCS is followed for15Gyr.3GENERAL RESULTSFig.2shows the contour plots of theﬁnal mean mass and dispersion of the GCMF,log M f is for a given model of the host galaxy. We will discuss below in section4the implications of our results for host galaxies with values of M e and R e equal to those determined by observations but we note here that the range of values spanned bylog M(see Vesperini1998),are more prone to the formation of c 0000RAS,MNRAS000,000–0004 E.VesperinilogM e l o g R e89101112−0.50.00.51.01.52.02.5α=1.54.24.44.4 4.65.05.5logM e l o g R e89101112−0.50.00.51.01.52.02.5α=1.84.14.24.2 4.55.05.5logM el o g R e89101112−0.50.00.51.01.52.02.5α=24.14.04.1 4.55.05.5logM e l o g R e89101112−0.50.00.51.01.52.02.5α=1.50.60.70.8logM e l o g R e89101112−0.50.00.51.01.52.02.5α=1.80.60.70.8logM el o g R e89101112−0.50.00.51.01.52.02.5α=20.60.70.8Figure 2.Contour plots ofEvolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function 5logM e l o g R e891011120.00.51.01.52.02.5−0.20.00.20.50.00.20.40.60.8 1.0−1.5−1.0−0.50.00.5N f N il o g M i n n −o u tFigure 4.(Left panel)Contour plot of the diﬀerence between the ﬁnal mean mass of inner (R g <R e )and outer (R g >R e )clusters,∆log M inn −out versus the fraction of surviving clusters after 15Gyr,N f /N i .Both panels refer to systems with an initial power-law GCMF with α=1.8.stronger radial gradients oflog M inn −out does not necessarily imply a negligible disruption of clusters;the diﬀerence in the range ofvalues of ∆log M f already shown in Fig.2and discussed in §3with the points corresponding tothe observational values of log M e and log R e superimposed.Figs 6a-c showlog M f ≃5.16;the galaxy-to-galaxyrms dispersion of log M f(4.2<log M f to increase as M e decreases.The inconsistency between the observational result of Harris (2000)and the ﬁnal properties of GCS starting with an initial power-law with α=1.8is further illustrated by Fig.7:this ﬁgure shows the distribution of theoretical values oflog M f for low-(log M e <9.5),intermediate-(9.5<log M e <10.5)and high-mass (log M e >10.5)ellipticals at t =2,5,10,15Gyr;the values of log R e and log M e considered for these plotsc0000RAS,MNRAS 000,000–0006 E.VesperinilogM el o g R e89101112−0.50.00.51.01.52.02.5Figure 5.Contour plot oflog M f =4.99with a galaxy-to-galaxy dispersion equal to 0.24).It is clear from Fig.9that,adopting a power-law initialGCMF,the ﬁnal values oflog M f for diﬀerent classes of galaxies,and the diﬀerence between the distribution oflog M f for diﬀerent classes of galaxies,shown in Fig.9,is a consequence of the strongdependence of the evolution of the GCMF on the structure of the host galaxy when a power-law initial GCMF is adopted.4.2Radial dependence of the GCMFFor four ﬁducial systems with values of log R e and log M e shown as ﬁlled dots in Fig.8we have studied in larger detail the radial variation oflog M f and N f /N i vs R g /R e .For all the four host galaxies considered,the fraction of disrupted clustersis large also beyond R e ;only for the most massive galaxy there is no disruption beyond R g =2R e while for all the others disruption is signiﬁcant at any galactocentric distance.As shown in the upper panel of Fig.10,log M f with R g depends on the structure of the host galaxy and it is notnecessarily monotonic.For the two most massive host galaxies considered,the mean mass of the innermost clusters and that of the outermost clusters diﬀer by approximately one order of magnitude or slightly less.Since in external galaxies only projected distances can be determined,to ease the comparison with observations,the upper panel of Fig.10shows also the variation oflog M f is too large to be consistent with that reported by observational studies.It is interesting to note the contrast between the results shown in Fig.10and those obtained in Vesperini (2000)for GCS with a log-normal initial GCMF (see Figs 12a and 12b in Vesperini 2000):with a log-normal initial GCMF,although a signiﬁcant fraction of clusters is disrupted,the radial gradient ofEvolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function 7logM el o g M flogM eN f N ilogM eM G C S f M G C S Figure 6.(a)8 E.Vesperini251N154.2 4.4 4.6 4.85.0logM fFigure7.Distribution ofEvolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function 94.0 4.2 4.4 4.6 4.85.0 5.251015logM1N t o t d N d l o g M t=2 Gyr4.04.2 4.4 4.6 4.85.0 5.2123456logM1N t o t d N d l o g M t=5 Gyr4.0 4.2 4.4 4.6 4.85.0 5.21234logM1N t o t d Nd l o g M t=10 Gyr4.04.2 4.4 4.6 4.85.0 5.20.00.51.01.52.0logM1N t o t d N d l o g M t=15 GyrFigure 9.Evolution of the distribution oflog M f for high-mass host galaxies have been found to be smaller than those observedand the galaxy-to-galaxy dispersion much larger than that observed.Although values of αtoo diﬀerent from that adopted above have not received any support either by theoretical studies of clusters formation or by observational analyses of young cluster systems,it is interesting to study the dependence of our results on αand explore the evolution of GCS with initial values of αoutside the range considered in the previous sections.We focus our attention on high-mass galaxies with log M e >10.5and consider the following values of (log M e ,log R e ):(12,1.4),(11.75,1.18),(11.5,1),(11.25,0.8),(11.0,0.64),(10.75,0.52),(10.5,0.4);these values span the entire strip of the log M e −log R e plane covered by real galaxies with log M e >10.5.Figs 11a-c showlog M f .Values of10 E.Vesperini4.04.24.44.64.85.05.2R g R el o g M f (R g)0.00.20.40.60.81.0R g R eN f N i (R g )Figure 10.log M f versus the projected galactocentric distance (normalized by the eﬀective radius of the host galaxy).those determined observationally from the GCLF of young cluster systems)of the index of the initial power-law GCMF have been explored (α=1.5,1.8,2.0).While evolutionary processes can easily turn a GCMF with an initial power-law shape into a GCMF with a log-normal shape like that observed in old cluster systems,our investigation reveals several inconsistencies between the observed properties of old GCS in elliptical galaxies and the theoretical results obtained adopting a power-law initial GCMF.In particular,studying the evolution of GCS in a sample of giant,normal and dwarf elliptical galaxies with eﬀective radii and eﬀective masses equal to those determined observationally,we have shown that:•the theoretical values oflog M f is signiﬁcantly larger than that reported by observational studies;in particular,for galaxieswith log M e >10.5,we have shown that starting with a power-law initial GCMF with α=1.8,log M f (Evolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function 111.0 1.2 1.41.6 1.82.04.04.55.05.56.0αl o g M f (a)1.0 1.2 1.41.6 1.82.00.00.20.40.60.81.0αN f N i (b)1.0 1.2 1.41.6 1.82.00.00.20.40.60.81.0αM G C S f M G C S(c)Figure 11.(a)log M f varies signiﬁcantly with the eﬀective mass of the host galaxy;speciﬁcallylog M f is approximately constant and larger thanlog M f on the galactocentric distance is produced bythe eﬀects of evolutionary processes;this is in contrast with several observational studies which fail to ﬁnd a signiﬁcant radial gradient of12 E.Vesperini•Starting with an initial power-law GCMF,values ofEvolution of globular cluster systems in elliptical galaxies.II:power-law initial mass function13 Vesperini E.,Heggie D.C.,1997,MNRAS,289,898Weinberg M.D.,1994a,AJ,108,1398Weinberg M.D.,1994b,AJ,108,1403Weinberg M.D.,1994c,AJ,108,1414Whitmore B.C.,1999,in Galaxy interactions at low and high redshift,IAU Symp.186,Barnes J.E.&Sanders D.B.editors, Kluwer Academic Publishers,p.251Whitmore B.C.,1997,in The Extragalactic distance scale,M.Livio,M.Donahue,N.Panagia editors,Cambridge University PressWhitmore B.C.,Zhang Q.,Leitherer C.,Fall S.M.,Schweizer F.,Miller B.W.,1999,AJ,118,1551Zepf S.E.,Ashman K.M.,English J.,Freeman K.C.,Sharples R.M.,1999,AJ,118,752Zhang Q.,Fall S.M.,1999,ApJ,527,L81c 0000RAS,MNRAS000,000–000。