2015恒星结构与演化2020

1、恒星结构与演化(2020.2-2020.6)第2部分 恒星物理罗新炼仙林校区天文楼521房间： xlluo89685982状态方程辐射传能第2部分 恒星物理对流传能核过程恒星内部核过程参见 Kippenhahns book page 146-1723恒星内部的中微子过程恒星内部主要的核反应电荷效应对核反应的影响热核反应率核反应截面预备知识在天体物理的环境中,参与核反应的原子核几乎是完全电离的(等离子体)。除了核子之间的库仑排斥外,如果所处环境的密度很高,周围电子气体的分布,会使得反应的核子间库仑排斥有所降低.从而使得相对 核的反应,核反应率将有所提高.电子ECoulomb potential效

2、应.V (r) =+Ecoul Z1Z2 (MeV)Ekin kT(keV)核的库仑势(排斥)通常人们引入电荷势0(吸引) ?因子fjk.rr0nuclear well 30 MeVShielding potential4v ×s (v)= fv ×s (v)screenedjkbaretunneleffectUe (r)Z Z e2 12rElectron Shielding (or Electron screening)留意前面略过的计算了除电荷自身以外系统内部其它所有电荷在它所在位置处产生的电势。1. 高温, 低密情况(Weak Screening)kTn <&

3、lt; ()3离子间库仑能<< 热运动能量的氢燃烧。要求满足条件zZ 2e2典型的天体环境: 如恒星5具体考查了两种极限情况。 1. 高温低密情况2. 零温电离气体实际电离气体(EOS)课后完成 6课后完成 polarized by the charge of the ion通常引入ö1/ 2E / keV æT» 2000ç7÷rD / rc0è z × r / g cm-3Z Zøjk来其中电荷效应的强弱.r= Z Z e2 Ec0jk0带入正常恒星中心的参数,发现rD / rc0>>1

4、,效应很弱E效应使得核子间库仑相Coulomb potential互作用降低，相对核而言，Ecoul Z1Z2 (MeV)等效于的核子热运动能量增Ekin kT(keV)tunnel effect加ETo first order0Dr0Shielding potentialE = E + (V-V) » E +rccbarnuclear well 30 MeV代入7describe a corrected Coulomb barrierfor the astrophysical environment.¥v ×s (v) = ò0 v ×s (

5、E) f (E)dEZ Z e2 rjkD课后完成效应的因子(screening factor), fjk可得电荷，ED / k T << 1。This case applies to stellar densities适用条件，弱< 104 g cm3.， ED / k T1对于强e 为电子的平均量。-1m = éå X A / Z ùêiii úeë iû整体趋势：低温高密度时，效应越来越重要。8Eéù æ r / g cm-3 ö1/ 3D» 0.02

6、05 (Z + Z )5 / 3 - Z 5/3 - Z 5/3T -1kTêëjkjkúû çm÷7èeøEZ Z e21/ 2 D =jk= 5.92´10-3 Z Z (z × r / g cm-3 ) T -3/2kTr ´ kTjk7Df jk = exp(ED / kT )z = å Zi (Zi +1) XAiii课后完成pycnonuclear reactions密度敏感温度敏感Thermal nuclear reactionsThe shielding fa

7、ctor for two protons as a function of temperatureFor sufficiently large densities and low temperatures, 9考虑电荷效应后的产能率<sv >screened = f jk引入幂率关系<sv >bare其中n = t - 2 - EDl = 1+ 1 ED3 kTlg T9.033kTt = 19.721×W×T-1/ 31/ 3Thermal nuclear7mjmkW = m=2 Z 22 Z 2ZZjkjkm + mjk8.5jkED()1/ 2

8、= 5.92´ Z Zz × r / g cm-3/ 23Tjk7kT致密物质核反应在极晚期演化中起作用.0510lg10A line of constant energy generation rate for 12C +12C burning.请推导.e = e rlTn0v ×s (v)µt 2e-t baref jk = exp(ED / kT )e= rjk ×r X × X× v ×s (v)jkrjk1+ dm mjkscreenedjkjk天文中常用到的形式留意11Density and tempe

9、rature exponents12重要的辅助方程恒星内部核过程参见 Kippenhahns13恒星内部的中微子恒星内部主要的核反应到此也差不多够了电荷效应对核反应的影响e = e rlTn0热核反应率核反应截面选做习题:类似电荷效应讨论,给出共振反应的产能率表达式.预备知识1415系恒星主要形成于旋臂上巨大的、冷的致密星际云。的坍缩造成恒星成群形成。恒星形成基本过程：、加热 原恒星 主序星坍缩、按照virial定理当天体自引力收缩时,自引力做功,自引力能的一部分增加系统的内能（升温），另一部分则辐射出去了.16恒星内部主要的核反应若时间在各个演化阶段在穿插细致的核过程else碳燃烧氦燃烧氢燃

10、烧恒星内部主要的核反应main sequence (MS) phasethe longest phase of stellar evolution, spend 8590% of their nuclear life. (He-burning 1015%, the further stages up to the supernova only 103)Why longest?Produces more nuclear energy per nucleonLess luminous than in later phasesConvective cores, when present, are l

11、arger than in later phases, thus the nuclear reservoirs are larger.氢燃烧 (T > 8106 K)氢燃烧等效为4 1H 4He + EE(4mHmHe) c2(4×1.67×10-246.644×10-24) × c2 26.731 MeV = 4×10-5 erg燃烧效率 0.7 %26.73 Mev230%太阳内部每秒都有7750 万吨的氢在这种过程中转化为氦。氢燃烧 (T > 8106 K)21(2) 碳氮氧循环 (CNO cycle)分界1.1 (1.5)

12、M(1) 质子-质子链 (p-p chain)恒星内部氢燃烧的两种主要的方式如何估算？The three branches of the PP chain.名字由来Main branch PP-I of the proton proton chain.T > 1.4 ´ 107 kT > 2.3 ´ 107 k(1) 质子-质子链 (proton-proton chain)Weak interactionslowest reaction2%4%28%1016 sThe pp chains, with energies and timescales.23(1) 质

13、子-质子链 (proton-proton chain)2He is unstablep + p¾¾®2HeStep 1:Step 2:d + d ¾ ®4Hed abundance is too low3He + p¾ ®4Li3He + d ¾ ®4He + n4Li is unstableStep 3:243He+3He¾ ®4He + 2 pd + p¾ ®3Hep + p ¾ ® d + e+ + veppI原初核。d + d ¾

14、; ®4He25查对比由第一和第二步核反应来命名 1H + 1H 2H +e 2H + 1H 3He +decay,弱相互作用.反应率非常低.(bottle neck) 3He到4He可以由不同的方式来完成.26 Why not 2H + 2H 4He ? (2H abundanceis too low)p-p I Why not 1H + 1H 2He ? (2He is unstable)e+ Why does nature use a long complicated chain reaction process to fuse four protons into one he

15、lium nucleus?(1) 质子-质子链 (proton-proton chain) pp13He + 3He 4He + 21H3He + 4He 7Be +如果存在4He pp2 pp37Be + e- 7Li +7Li + 1H 4He + 4Hee7Be +1H 8B +8B 8Be +e+ +e8Be 4He + 4HeTemperature Range (107 K)1 2.33.0Energy release without neutrino26.2025.6719.20ProcessE(MeV)totpp1pp2 pp326.7426.7426.73 W

16、ith increasing T, pp2 and pp3 will dominate more andmore over pp127pp链氢燃烧的产能率1 / 3e= 2.38´106y fg r X T-2-2 / 333.80 /Te6pp1111H6g= 1+ 0.0123×T1/3 + 0.0109 ×T 2/3 + 0.0009 ×T11666其中f11为因子,表示, pp2 , pp3对产能率的修正.的数值在1到2之间,与化学成分,温度有关.28不必在意29pp neutrino<E> = 0.27 MeV14%2%CNO cy

17、cle84%7Be neutrino8BneutrinoE=0.39,0.86 MeV<E>=6.74 MeV1 eV =energy of an electron passing through one volt of potential.=1.602 ´ 10-19 J.30思考：如何计算分支比？太阳内部. 太阳中微子的谱Water7Be+e-à7Li+可研究太阳的物理性质.31CNO循环名字的由来，32(2) 碳氮氧循环 (CNO cycle)T = 2.5107 KslowestCoulomb barriers and S-factors33(2) 碳氮

18、氧循环 (CNO cycle)initially恒星内部氢燃烧的另一种主要方式. (24.97 MeV 扣除中微子后)T 2×10 7 K, M 1.1 M碳氮氧起到催化剂的作用?CN cycle 12C + 1H 13N + 13N 13C + e+e 13C + 1H 14N + 15O 15N + e+e 15N + 1H 12C + 4Hemain cycle 16O +Secondary cycle (10-4 )bottle neck343414N + 1H 15O +(2) 碳氮氧循环 (CNO cycle)cycle limited by b decay of 13N

19、 (t 10 min) and 15O (t 2 min) ？(e+n)(p,g)(p,g)(e+n)(p,a)The CN cycle in the atomic weightenergy plane.35(p,g)3637真实过程复杂得多恒星内部碳氮氧循环要比CN循环远远来得复杂.CN cycle (99.9%)O Extension 1 (0.1%)O Extension 2O Extension 3O(8)N(7)C(6)3456789NO cycle16O + 1H ® 17F + gneutron number17F ® 17O + e+ n17O + 1H &

20、#174; (18F) -® 14N+ 4He¯ ® 18F + g38请留意:novae, X-ray bursts(T > 8×10 7 K)环境中的高温碳氮氧循环反应.Ne(10)F(9)许多不同形式CNO循环的产能率1 / 3e= 8.67 ´1027 gr X2 / 3-152.28 /TXTe6CNO14,1CNOH6=1+ 0.0027×T1/3 - 0.00778×T 2/3 - 0.000149×Tg14,1666其中XCNO为碳氮氧三种核素的质量丰度之和.20 M starTypical

21、CNO abundance ratios (inmass fractions) overall rate of CNO-cycle determinedreaction apart from 4He, 14N is the major product of the CNO-cycleby the 14N(p, )15O39不必在意假想(conversion of all hydrogen to helium)0.9950.005 apart from4He, 14N is the major product of the CNO-cycle40宇宙中绝大部分14N产生于CNO循环质子-质子链与

22、碳氮氧循环核反应的比较恒星内部的核反应速率对温度十分敏感，因库仑位垒的关系CNO循环需要更高温。41ppX12T41.1(1.5) M T6 > 17CNOX1 X14 T18nthe log of the rates of nuclear energy as a function of T in different stars on the ZAMS and for the present Sun.the exponent as a function of T42选做习题: 选其中任何一种特殊天体环境中的氢燃烧过程做简单的调研报告. NeNa and MgAl Cycles, rp-p

23、rocess .43else碳燃烧氦燃烧氢燃烧恒星内部主要的核反应宇宙中主要的C，O来源To build elements heavier than 4He, it would seem normal to first consider proton or captures by helium nuclei; however the absence of stable nuclei of atomic mass A = 5 and 8 makes this kind of building problematic.Nothing was supposed to halt the collaps

24、e at the end of H burning until supernova explosion intervenes at T > 109 K氦燃烧(Helium Burning)Saha like equilibriumX (8Be) 1.4×108 at T = 108 KSalpeter:Saha equationsacapture12CHoyle showed that the triple- reaction would not be fast enough at T = 2×108 K to account for all the C, O and

25、 Ne observed in the Universe without a resonance of the reaction 8Be(, )12C, which was effectively found subsequently.共振MeV0.29 MeV45不必在意细节氦燃烧(Helium Burning) He燃烧 (3反应 the triple alpha reaction)T 10 8 K3 4He 12C + 4He + 4He 8Be(Q = - 92.1 keV) 8Be + 4He 12C* (- 286 keV) 12C +(Q = 7.66 MeV)Q = 7.27

26、MeV随着温度增加1) 4He + 4He 反应率增加Þ 8Be 丰度增加;2) 8Be + 4He 反应率增加Þ 12C丰度增加C12的某共振能级46 在高温高密度环境下8Be 再俘获一个a粒子形成12C. 8Be 的10-16 s 衰变时标仍然比其与 粒子的某种非共振方式散射时标高出5个量级. 8Be 是一个极不稳定的核素,在10-16 s 内衰变为两个a粒子.氦燃烧(Helium Burning) 问：为何原初核无3反应? builds up small equilibrium concentration of 8Bereaction rate is uncertai

27、n affects final C/O ratio becomes possible at T 108K due to a resonance in12C(predicted by Fred Hoyle in1954) net effect3 4He 12C + (Q = 7.275 MeV)(Q = 7.126 MeV)4712C + 16O + 氦燃烧阶段, 还得考虑其它a粒子俘获反应:3 a® ¹2 C + gscreening factorC + a ® 16O + g¹2efr X3-3-= 5.09´1011244.027 /TTe

28、83a3aa816O + a ® 20Ne + g2æö1+ 0.134 ×T2 / 3以及效率更低的20Ne + a ® 24Mg + g24Mg + a ® 28Si + g1 / 3e= 1.3´1027 fr XX T-2-69.20 /T8eç÷812,a12,a12a 81+ 0.01×T 2/3èø81/ 3e=fr XX 1.82´10 Te27-2 / 3 -85.65/T816,a16,a16a8+ 9.22´1019 T -3/ 2e

29、-103.59 /T8 8Y 为4He 质量丰度48产能率公式参见Kippenhahn书不必在意495051温度逐升到108 K，3-alpha反一旦应可以进行，恒星由红巨星进入另一个演化阶段.Helium flashhorizontal branch5253HR diagram showing the location of the carbon stars. These are stars inside which the s-process operates. The process responsible for the synthesis may also bring the fre

30、shly synthesized elements to the surface of the star, so that they can be observed. The s-process elements thus observed where not synthesized in a previous generation of stars氦燃烧场所？54细节暂不讨论具体参见：第五章AGB 演化55细节暂不讨论课后请阅读else碳燃烧氦燃烧氢燃烧恒星内部主要的核反应58M > 8 MM >12M59Evolution of the central T and r cond

31、itions60碳燃烧(Carbon Burning)T 6×10 8 K12C +12C 24Mg + 23Na + p 20Ne + 4He 23Mg + n 16O + 2 4He(Q = 13.931 MeV)(Q = 2.238 MeV) 50 % (Q = 4.616 MeV) 50 % (Q = -2.605 MeV)(Q = -0.114 MeV)61产能率公式参见Kippenhahn书dominates碳燃烧(Carbon Burning)T 5×108 K r 3×106 g cm3光之裂解20Ne + 16O + 4He(Q = -4.7 M

32、eV)产生的a粒子20Ne +4He 24Mg +(Q = 9. 3 MeV)62氖燃烧(Neon Burning)T 109 K16O + 16O 32S + 31P + p 28Si + 4He 31S + n 24Mg + 2 4He(Q = 16.541 MeV) (Q = 7.677 MeV) (Q = 9.593 MeV) (Q = 1.453 MeV) (Q = -0.393 MeV)6312C/16O BURNING12C ashes = Ne, Na, Mg16O ashes = Al, Simajor ash 28SiSUPER RED-GIANT STARS氧燃烧(Oxy

33、gen Burning)T 1.5×10 9 KT 2109 KT 1.5×10 9 K28Si + 28Si 56Ni +56Ni 56Fe + 2e+major ash = 56Fe+ 2e64硅燃烧(Silicon Burning)T 3109 K当恒星内部形成Fe后，由于Fe的聚变反应吸热而不是放热，恒星内部的热核反应至此停止。High ( > 812 M)Mass Starsonion模型Ne Photodisintegration66The onion skin structure of a massive star with 25 M67Structur

34、e and evolution of a 25M star of solar mlicity, as predicted by one-dimensional, spherically symmetric ms8平稳燃烧for T > 4109 K almost nuclear statistical equilibrium (NSE) may bereachedPre-SupernovaSuper Giant 3x104 yO, Ne Red Giant 3x108 yMain Sequence 1010 yCHeHfinal compositionmay be mostly56FeG

35、ravitational Contractionbecause p/n < 1 (due to -decays and e- captures)>photodisintegrations69补充The main parameters in the advancedevolution of a 15Mstar.Physics Formation and Evolution of Rotating Stars70photonsneutrino emission1. 宇宙元素丰度注意,在此提到的仅仅是重子物质,没有涉及暗物质,暗能量.71元素粒子数相对丰度（%）H（1个核子）90He（4

36、个核子）9Li族（7.1个核子）0.000001C族（12个核子）0.2Si族（23.8个核子）0.01Fe族（50.2个核子）0.01中等质量元素（63个核子）0.00000001重元素（>100个核子）0.000000001恒星演化与元素宇宙元素丰度宇宙中的各种元素是如何形成的？72在星际介质中高能宇宙射线一代又一代恒星演化、不断地累积的结果。原初核。2. 原初元素H, He和少量的Li, B, Be，形成于宇宙大爆炸初期。3. 恒星内部的核(nuclear synthesis)73问： 14N 在哪形成？燃烧过程产物温度(K)最小质量(M )H燃烧He2×1070.1He

37、燃烧C, O2×1081C燃烧O, Ne, Na,Mg8×1081.4Ne燃烧O, Mg1.5×1095O燃烧Mg-S2.0×10910Si燃烧Fe峰元素3.0×10920比Fe 峰元素更重元素的形成中子俘获反应(Z, A) + n (Z, A+1) +衰变：(Z, A+1) (Z+1, A+1) + e- +ne2) 快过程 (r-process)1) 慢过程(s-process)中子俘获过程比衰变快中子俘获过程比发生在恒星内部，衰变慢发生在超爆发，形成 251Cf（锎）元素。形成 209Bi（铋）元素。一代又一代恒星演化的结果。74讲义第1

38、2章内容.见彭75查ZN76重元素77Schematic representation (mass versus time) of a low- or intermediate-mass (M 9 M), thermally pulsing AGB star.7880Stellar sitesNuclear processesBig Bang (primordial nucleosynthesis)Reactions between the lightest elements p, d, He, Be, LiHydrogen burningproton-proton chain, CNO cy

39、cle,Ne-Na cycle, Mg-Al cycleMain sequence(ex. Sun)Helium burning3a-process, 12C(a,g)16OOther (a,g) and (a, n) reactionsRed giant stars, stars of the Asymptotic branchSuper giant stars, Wolf-Rayet stars and Pre-supernovaeAdvance burning stages Reactions of C, O, N, Ne, SiExplosive burning Hot CNO cyc

40、leRapid proton capture (rp process)Novae, supernovae,X-ray burstsAGB stars, supernovae II, Neutrons starsNucleosynthesis beyond iron Slow neutron capture (s-process) Rapid neutron capture (r-process)photodisintegration and proton capture (p-process)81Ø hot burning in massive AGB stars (> 4 M

41、)(T9 0.08)Ø nova explosions on accreting white dwarfs(T9 0.4)Ø X-ray bursts on accreting neutron stars(T9 2)Ø accretion disks around low mass black holesØ neutrino driven wind in core collapse supernovaeØ neutron star mergers请留意特殊天体环境下的氢燃烧过程.(温度,密度与通常恒星内部很不一样)A schematic dia

42、gram showing the principal products of the collision of a high energy proton with a nucleus.请留意特殊天体环境下的氢燃烧过程.(温度,密度与通常恒星内部很不一样)Schematic of the thermonuclear flashmof an X-ray burstTheoretical mof an X-ray burst and its evolution with time.87问题：形成的proton-rich 核素如何脱离中子星表面？88需要Nuclear data:Masses (pro

43、ton separation energies)-decay ratesReaction rates (p, n -capture and ,p)Nucleosynthesis is a gradual, still ongoing process:H, He, LiStar FormationBig Bangcontineous enrichment, increasingEjection of envelope into ISMLife of astarmlicityDeath of a star (Supernova, planetary nebula)Remnants(WD,NS,BH

44、)BH: Black Hole NS: Neutron StarWD: White Dwarf StarISM Interstellar Medium星系化学演化Nucleosynthesis !Nucleosynthesis !Illustration of the two principal stages of the formation of the elements showing how the first- generation stars contained only the light elements from the Big Bang, while second-gener

45、ation stars contain the heavier elements from the supernovae explosions.90 No CNO cycles working initially. Only the pp chains are present opacities are generally lower, which makes a larger outgoing luminosity and a smaller radius, lower mass and angular momentum losses. Without CO molecules to pro

46、vide cooling, the clouds that formed the first stars had to be considerably warmer than todays molecular clouds The first stars must therefore have been more massive than most of todays stars, for gravity to overcome pressureBIRTHgravitationalcontractionInterstellar gasStarsexplosionejectionDEATHmix

47、ing of interstellar gasthermonuclearreactionsabundance distribution energy production stability against collapse synthesis of “ms”9192Giant molecular cloudsHomework:(选做)请登陆, 任选其中一个核反应网络进行计算,分析计算结果并做出相关图形.93Homework:(选做)请登陆, 对星系化学演化进行试算,并大致说明星系化学演化以及这个程序编写的基本思路,如果你来做,会做哪些改进?2.7 Neutron capture reacti

48、ons949596恒星内部核过程参见 Kippenhahns book page 146-17297恒星内部的中微子过程恒星内部主要的核反应电荷效应对核反应的影响热核反应率核反应截面预备知识估算中微子的平均自由程 For “normal” stellar matter with r »1 g cm-3,ln » 1020cm » 100 pc » 1.4´109 R For r » 106 g cm-3, one hasln » 3000 R For r » 1014 g cm-3,one hasln »

49、 20 kmDuring the H- and He-burning phases, the energy goes out from the stars in the form of electromagnetic radiation. In later phases including supernova explosions, most of the energy goes out in the form of neutrinos and we also examine here these processes of energy losses.JPress, 1989-process

50、, WoosleyJ., Vol. 356, p. 272, 1990., Astrophys.99此节内容参见Kippenhahn的P169-172页内容。或 “Physics Formation and Evolution. N. Bahcall, Neutrino Astrophysics, Cambridge: Cambridge University恒星内部的中微子过程有的同学补充整理Star is transparent to neutrinosThe star, once driven by photon losses, is now driven by neutrino los

51、ses.The time scale of evolution shortensdramaticallyto becombefore thNeutrino luminosity and photonluminosity in a 15Mstar as asupernovfunction of the central temperature in 109 K. Above 0.5 × 109 K, the neutrino luminosity takes over and controls the evolution of the starexplosio100a few hourserg g-1s-1A comparison between the neutrino losses and various nuclear energygeneration reactions according to Hayashi. (1962).101Plasma NeutrinoPhotoneutrinoPair AnnihilationThe core cools fast, while the envelope, still dominated by photons, hardly notices what