2015恒星結構與演化2020

1、恒星結構與演化(2020.2-2020.6)第2部分 恒星物理羅新煉仙林校區(qū)天文樓521房間： xlluo89685982狀態(tài)方程輻射傳能第2部分 恒星物理對流傳能核過程恒星內部核過程參見 Kippenhahns book page 146-1723恒星內部的中微子過程恒星內部主要的核反應電荷效應對核反應的影響熱核反應率核反應截面預備知識在天體物理的環(huán)境中,參與核反應的原子核幾乎是完全電離的(等離子體)。除了核子之間的庫侖排斥外,如果所處環(huán)境的密度很高,周圍電子氣體的分布,會使得反應的核子間庫侖排斥有所降低.從而使得相對 核的反應,核反應率將有所提高.電子ECoulomb potential效

2、應.V (r) =+Ecoul Z1Z2 (MeV)Ekin kT(keV)核的庫侖勢(排斥)通常人們引入電荷勢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)留意前面略過的計算了除電荷自身以外系統(tǒng)內部其它所有電荷在它所在位置處產生的電勢。1. 高溫, 低密情況(Weak Screening)kTn <&

3、lt; ()3離子間庫侖能<< 熱運動能量的氫燃燒。要求滿足條件zZ 2e2典型的天體環(huán)境: 如恒星5具體考查了兩種極限情況。 1. 高溫低密情況2. 零溫電離氣體實際電離氣體(EOS)課后完成 6課后完成 polarized by the charge of the ion通常引入ö1/ 2E / keV æT» 2000ç7÷rD / rc0è z × r / g cm-3Z Zøjk來其中電荷效應的強弱.r= Z Z e2 Ec0jk0帶入正常恒星中心的參數(shù),發(fā)現(xiàn)rD / rc0>>1

4、,效應很弱E效應使得核子間庫侖相Coulomb potential互作用降低，相對核而言，Ecoul Z1Z2 (MeV)等效于的核子熱運動能量增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課后完成效應的因子(screening factor), fjk可得電荷，ED / k T << 1。This case applies to stellar densities適用條件，弱< 104 g cm3.， ED / k T1對于強e 為電子的平均量。-1m = éå X A / Z ùêiii úeë iû整體趨勢：低溫高密度時，效應越來越重要。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課后完成pycnonuclear reactions密度敏感溫度敏感Thermal nuclear reactionsThe shielding fa

7、ctor for two protons as a function of temperatureFor sufficiently large densities and low temperatures, 9考慮電荷效應后的產能率<sv >screened = f jk引入冪率關系<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致密物質核反應在極晚期演化中起作用.0510lg10A line of constant energy generation rate for 12C +12C burning.請推導.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重要的輔助方程恒星內部核過程參見 Kippenhahns13恒星內部的中微子恒星內部主要的核反應到此也差不多夠了電荷效應對核反應的影響e = e rlTn0熱核反應率核反應截面選做習題:類似電荷效應討論,給出共振反應的產能率表達式.預備知識1415系恒星主要形成于旋臂上巨大的、冷的致密星際云。的坍縮造成恒星成群形成。恒星形成基本過程：、加熱 原恒星 主序星坍縮、按照virial定理當天體自引力收縮時,自引力做功,自引力能的一部分增加系統(tǒng)的內能（升溫），另一部分則輻射出去了.16恒星內部主要的核反應若時間在各個演化階段在穿插細致的核過程else碳燃燒氦燃燒氫燃

10、燒恒星內部主要的核反應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.氫燃燒 (T > 8106 K)氫燃燒等效為4 1H 4He + EE(4mHmHe) c2(4×1.67×10-246.644×10-24) × c2 26.731 MeV = 4×10-5 erg燃燒效率 0.7 %26.73 Mev230%太陽內部每秒都有7750 萬噸的氫在這種過程中轉化為氦。氫燃燒 (T > 8106 K)21(2) 碳氮氧循環(huán) (CNO cycle)分界1.1 (1.5)

12、M(1) 質子-質子鏈 (p-p chain)恒星內部氫燃燒的兩種主要的方式如何估算？The three branches of the PP chain.名字由來Main branch PP-I of the proton proton chain.T > 1.4 ´ 107 kT > 2.3 ´ 107 k(1) 質子-質子鏈 (proton-proton chain)Weak interactionslowest reaction2%4%28%1016 sThe pp chains, with energies and timescales.23(1) 質

13、子-質子鏈 (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查對比由第一和第二步核反應來命名 1H + 1H 2H +e 2H + 1H 3He +decay,弱相互作用.反應率非常低.(bottle neck) 3He到4He可以由不同的方式來完成.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) 質子-質子鏈 (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鏈氫燃燒的產能率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為因子,表示, pp2 , pp3對產能率的修正.的數(shù)值在1到2之間,與化學成分,溫度有關.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：如何計算分支比？太陽內部. 太陽中微子的譜Water7Be+e-à7Li+可研究太陽的物理性質.31CNO循環(huán)名字的由來，32(2) 碳氮氧循環(huán) (CNO cycle)T = 2.5107 KslowestCoulomb barriers and S-factors33(2) 碳氮

18、氧循環(huán) (CNO cycle)initially恒星內部氫燃燒的另一種主要方式. (24.97 MeV 扣除中微子后)T 2×10 7 K, M 1.1 M碳氮氧起到催化劑的作用?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) 碳氮氧循環(huán) (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真實過程復雜得多恒星內部碳氮氧循環(huán)要比CN循環(huán)遠遠來得復雜.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請留意:novae, X-ray bursts(T > 8×10 7 K)環(huán)境中的高溫碳氮氧循環(huán)反應.Ne(10)F(9)許多不同形式CNO循環(huán)的產能率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為碳氮氧三種核素的質量豐度之和.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宇宙中絕大部分14N產生于CNO循環(huán)質子-質子鏈與

22、碳氮氧循環(huán)核反應的比較恒星內部的核反應速率對溫度十分敏感，因庫侖位壘的關系CNO循環(huán)需要更高溫。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選做習題: 選其中任何一種特殊天體環(huán)境中的氫燃燒過程做簡單的調研報告. NeNa and MgAl Cycles, rp-p

23、rocess .43else碳燃燒氦燃燒氫燃燒恒星內部主要的核反應宇宙中主要的C，O來源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氦燃燒(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不必在意細節(jié)氦燃燒(Helium Burning) He燃燒 (3反應 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隨著溫度增加1) 4He + 4He 反應率增加Þ 8Be 豐度增加;2) 8Be + 4He 反應率增加Þ 12C豐度增加C12的某共振能級46 在高溫高密度環(huán)境下8Be 再俘獲一個a粒子形成12C. 8Be 的10-16 s 衰變時標仍然比其與 粒子的某種非共振方式散射時標高出5個量級. 8Be 是一個極不穩(wěn)定的核素,在10-16 s 內衰變?yōu)閮蓚€a粒子.氦燃燒(Helium Burning) 問：為何原初核無3反應? 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 + 氦燃燒階段, 還得考慮其它a粒子俘獲反應: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 為4He 質量豐度48產能率公式參見Kippenhahn書不必在意495051溫度逐升到108 K，3-alpha反一旦應可以進行，恒星由紅巨星進入另一個演化階段.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氦燃燒場所？54細節(jié)暫不討論具體參見：第五章AGB 演化55細節(jié)暫不討論課后請閱讀else碳燃燒氦燃燒氫燃燒恒星內部主要的核反應58M > 8 MM >12M59Evolution of the central T and r cond

31、itions60碳燃燒(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產能率公式參見Kippenhahn書dominates碳燃燒(Carbon Burning)T 5×108 K r 3×106 g cm3光之裂解20Ne + 16O + 4He(Q = -4.7 M

32、eV)產生的a粒子20Ne +4He 24Mg +(Q = 9. 3 MeV)62氖燃燒(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氧燃燒(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硅燃燒(Silicon Burning)T 3109 K當恒星內部形成Fe后，由于Fe的聚變反應吸熱而不是放熱，恒星內部的熱核反應至此停止。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平穩(wěn)燃燒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補充The main parameters in the advancedevolution of a 15Mstar.Physics Formation and Evolution of Rotating Stars70photonsneutrino emission1. 宇宙元素豐度注意,在此提到的僅僅是重子物質,沒有涉及暗物質,暗能量.71元素粒子數(shù)相對豐度（%）H（1個核子）90He（4

36、個核子）9Li族（7.1個核子）0.000001C族（12個核子）0.2Si族（23.8個核子）0.01Fe族（50.2個核子）0.01中等質量元素（63個核子）0.00000001重元素（>100個核子）0.000000001恒星演化與元素宇宙元素豐度宇宙中的各種元素是如何形成的？72在星際介質中高能宇宙射線一代又一代恒星演化、不斷地累積的結果。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. 恒星內部的核(nuclear synthesis)73問： 14N 在哪形成？燃燒過程產物溫度(K)最小質量(M )H燃燒He2×1070.1He

37、燃燒C, O2×1081C燃燒O, Ne, Na,Mg8×1081.4Ne燃燒O, Mg1.5×1095O燃燒Mg-S2.0×10910Si燃燒Fe峰元素3.0×10920比Fe 峰元素更重元素的形成中子俘獲反應(Z, A) + n (Z, A+1) +衰變：(Z, A+1) (Z+1, A+1) + e- +ne2) 快過程 (r-process)1) 慢過程(s-process)中子俘獲過程比衰變快中子俘獲過程比發(fā)生在恒星內部，衰變慢發(fā)生在超爆發(fā)，形成 251Cf（锎）元素。形成 209Bi（鉍）元素。一代又一代恒星演化的結果。74講義第1

38、2章內容.見彭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請留意特殊天體環(huán)境下的氫燃燒過程.(溫度,密度與通常恒星內部很不一樣)A schematic dia

42、gram showing the principal products of the collision of a high energy proton with a nucleus.請留意特殊天體環(huán)境下的氫燃燒過程.(溫度,密度與通常恒星內部很不一樣)Schematic of the thermonuclear flashmof an X-ray burstTheoretical mof an X-ray burst and its evolution with time.87問題：形成的proton-rich 核素如何脫離中子星表面？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星系化學演化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:(選做)請登陸, 任選其中一個核反應網絡進行計算,分析計算結果并做出相關圖形.93Homework:(選做)請登陸, 對星系化學演化進行試算,并大致說明星系化學演化以及這個程序編寫的基本思路,如果你來做,會做哪些改進?2.7 Neutron capture reacti

48、ons949596恒星內部核過程參見 Kippenhahns book page 146-17297恒星內部的中微子過程恒星內部主要的核反應電荷效應對核反應的影響熱核反應率核反應截面預備知識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此節(jié)內容參見Kippenhahn的P169-172頁內容。或 “Physics Formation and Evolution. N. Bahcall, Neutrino Astrophysics, Cambridge: Cambridge University恒星內部的中微子過程有的同學補充整理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