Nuclear Astrophysics : an introduction

Transcription

1 Nuclear Astrophysics : an introduction Sailajananda Bhattacharya VECC, Kolkata.

2 Astronomy :: a natural science, is the study of celestial objects (i.e., stars, galaxies, planets, moons, asteroids, comets and nebulae) and processes (such as supernovae explosions, gamma ray bursts, and cosmic microwave background radiation), the physics, chemistry, and evolution of such objects and processes, Astrophysics :: the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the heavenly bodies, rather than their positions or motions in space. Nuclear Physics :: Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. scale Astro Nuclear Length :: Light yr (~ m) fm (10-15 m) variation ~O(10 30 ) Time ::: Gyr (~ s) ns (10-9 s) variation ~O(10 5 ) Nuclear Astrophysics :: Links MEGA-world to MICRO-world SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016

3 We owe our existence to Solar System Solar system is a part of Milky way galaxy Milky way is a part of Virgo supercluster About Universe Superclusters ~ 0 m Large galaxies ~ 350 b Stars ~ 30 b. t. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 3

4 BIG BANG :: THE COSMIC JOURNEY BEGINS SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 4

5 THE COSMIC EVOLUTION HOYLE CYCLE SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 5

6 Formation of stars, planets,. Formation of a Protostar from interstellar cloud Center contracts / heats up Protostar radiates more heat Formation of Solar System Shockwaves radiate outward releasing material Material coalesces into planets, moons or comets SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 6

7 Evolution of stars :: Hertzprung-Russell Diagram Sun : a main sequence star Brighter than 85% stars in Our galaxy (Milky Way) Age ~ 4.5 Gy : live for another ~4.8 Gy as MS star Radius ~ 109 Earth Mass ~ 333,000 Earth Core temp ~ 15 MK Core density ~ 160 g/cm 3 (~ 1 Earth) To understand the ORIGIN & EVOLUTION of STARS NUCLEAR ASTROPHYSICS M star ~9M M star ~9M SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 7

8 Nuclear Astrophysics :: branch of physics involving various subfields of nuclear physics and astrophysics aiming to understand the inner workings of stars. Two major Questions to be answered in Nuclear Astrophysics:: How the stellar bodies evolved? How energy is generated in stars? How different elements were formed in the universe / solar system? Often the two above are interlinked; Stellar evolution is linked with energy production, which in turn influences production of elements and elemental abundance. The cooking processes above are of pure nuclear physics origin. Other factors (gravitation, electron pressure, etc) provide optimum cooking pot for proper cooking which are also equally important for proper cooking..so, SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 8

9 In the rest of the talk, we try to sketch some of the major cosmic cooking processes : generally termed as Nucleosynthesis SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 9

10 Elemental abundances in Universe Facts : H, He most abundant in Universe (~75% H, ~5% He) Nearly 300 elements on earth Fe (~30%) contributed most to mass of earth Abundances of elements on earth Question : How they were formed? SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

11 Creation of Elements in the Universe : Hadron formation : between 10 6 sec and 1 sec after the Big Bang Bigbang Nucleosynthesis : lasted for few minutes ~ (3-0 Min ) only. Stellar Nucleosynthesis : after star formation (~ 500My) ; still continuing Explosive Nucleosynthesis : in massive stars (supernovae) : short duration (~day) Each stage produced different groups of elements SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

12 BIG BANG NUCLEOSYNTHESIS : Chronology Under thermodynamic equilibrium, the n/p transforms as n e p e ; n e n p e ( m p m )/ kt e ; n p e At equilibrium, n p (1.93)/ T ( MeV ) ~ e e Time (sec) T (MeV) T 9 (K) Elements produced (abundance) ~0.01 ~10 ~100 n,p (1:1) ~1 ~1 ~10 n,p (1:3) d-production (photo-unstable) ~10 ~0.3 ~3 n,p (1:7) d-production stable ~00 ~0.1 ~1 1 H, 4 He (1:1) (3:1 by mass) (synthesis of He ) ~000 ~0.0 ~0. 1H (~75%),4He (~5%) (BBN over) SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 1

13 BIG BANG NUCLEOSYNTHESIS BBN ended with H & He; Rest of the elements were produced later in stellar environments SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

14 Elements as on today :: Periodic Table of Nucleosynthesis All other elements (except Hydrogen & Helium-4) produced at later stages of stellar evolution SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

15 Stellar Nucleosynthesis first few steps: p-p chain :: for stars at temp > 4x 10 6 K End product 4He + 6 MeV Main process in Sun & all MS Stars Depletion of 1H Build up of 4He 3a process : route to A > 4 elements CNO Cycle : for stars > 1.3 M Occurs at higher temp > 15x 10 6 K SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

16 Stellar Nucleosynthesis next steps: H burning He burning C burning O, Ne, Mg.. Si burning Fe core? NOTE :: H burning for sun : ~10 10 yr :: In general, bigger the size, lesser the life Fusion stops at Fe :: NO MORE heavier elements!! All other heavier Elements are then produced by neutron (& proton) capture followed by b-decay (s, r, p,..) processes. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

17 Nucleosynthesis beyond Fe: s process slow neutron capture process : occurs at Helium burning phase of AGB stars : typical T ~ K ; neutron density ~ 10 8 n/cc Neutron sources : 13C(a,n)16O ; Na(a,n)5Mg Capture rate and b-decay rates comparable, so products close to b-stability line Problem : cannot explain multiple peaks in abundance curve r process rapid neutron capture process : occurs at supernova explosion : typical T ~ 3 GK ; neutron density ~ 10 0 n/cc Multiple n-capture before b-decay, so products close to n-drip line SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

18 Nucleosynthesis beyond Fe (contd.): At a point, n-capture and photodisintegration rates are in equilibrium (waiting point) As neutron flux vanishes, they decay back to populate n-rich nuclei. p process responsible for abundance of several neutron deficient stable nuclei of 74 < A < 196 (typically 74 Se, 113,115 Sn, 138 La, 180 Ta, 196 Hg) : occurs in supernova : typical T ~ K ; Needs seed s-, r- nuclei as starting point, then proceeds by (g,n), (g,p), (g,a) photodisintegration processes Typical p-process SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

19 Summary of nucleosynthesis processes and locations process main products Where H-burning 4 He main seq. He-burning 1 C, 16 O Red Giant C-O-Ne-Si 0 Ne, 8 Si, 3 Si, Supergiants burning up to 56 Fe s-process many elements Red Giants, Supergiants r-process many medium /heavy supernova p-process elements SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

20 Problems : (1) Large no. of nuclei, () many exotic species, (3) not enough experimental data existing, (3) theoretical modelling needed,. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 0

21 What nuclear physics inputs required? Almost everything!! cross sections, beta decay half-lives :: (for major burning stages, s-process,..) reaction rates, weak rates ( for extrapolation of reaction rates at astrophysical energies, modification of weak decay rates under stellar environment.. Measurement / Estimation of other nuclear properties ( ground state / excited state properties, such as deformation, level density, structure, optical model potential, fission barrier, EM decay strength functions, Equation of state. To meet the challenges of nuclear astrophysics SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 1

22 Challenges to face for measurements in astrophysical domain Extremely low cross-sections : special care needed Measurements to be carried out at deep sub-barrier energies. This requires special kind of accelerators, special laboratories, special techniques,.. Modification of decay rates under astrophysical environment Astrophysical environments are very different from lab. Environment. So, many decay rates, considered to be constant in lab condition undergo drastic modification Modification of other nuclear properties under astrophysical environment For example, EOS, Nuclear Level density, mass, deformation etc. may be very different for nuclei with extreme N/Z ratio, say drip-line nuclei, neutron star; These infos are crucial for neutron star evolution, drip line prediction, How to extract. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016

23 Nuclear cross sections of Astrophysical relevance Assume :: Astrophysical reactions occur under thermal equilibrium For any nuclear reactions (other than neutron induced), energy must be above coulomb barrier ; So, ) ( ) 3 ( 1 1 R e Z Z V kt v m coul H ) ( fm R Z Z T kr e Z Z T So, p-p reaction to occur, typical temp. needed is K; but in sun the core temp. is ~ 10 7 K. So, reaction can occur ONLY thru tunneling. For tunneling, the particles should be within one De-Broglie wavelength apart; So, e Z Z m h m h m p v m e Z Z H H H H 0.5) / ( , Z Z T k h m e Z Z k e Z Z T or H For p-p reaction, the temp (T 6 ) is close to sun core temp. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 3

24 Reaction rate : (Monoenergetic beam on static target) X-sec defined as dn dt n ( E) v( E) Reaction rate No. of reactions in a given volume of gas per unit time No. density of particle-1. flux of particle-. reaction x-sec dn reac dt n1n 1v SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 4

25 When both the reactants are gaseous and in thermal equilibrium.. Both the reactants follow the M-B distribution dn 1, n01, 1 E1, / kt E1, e 3 de ( kt) So, Flux of N as seen by N 1 N v Similarly, Flux of N 1 as seen by N N 1 v (Where, v is relative velocity v 1 -v ) So, the generalised reaction rate is dn reac dt n01n 1 n1n C ( kt) 3/ 0 1 v n01n ( E) E exp( E / kt) de ( ij to avoid double counting for identical reactants) 0 1 ( E) v( E) dn( E) de de SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 5

26 A. Reaction rate for neutron induced reaction Rate Coefficient For low energy neutrons, dn v ( E) v( E) de de 0 ( v ) 1/ v ( E) 1/ E So, C C 1/ v ( E) E exp( E / kt) de E exp( E / kt) de 3 / 3/ ( kt) ( kt) 0 0 (M-B distribution) So, reaction rate for low energy neutron induced reaction is determined by the corresponding M-B distribution SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 6

27 B. Reaction rate for photon induced reaction n1 ng c ( Eg ) n1 c ng ( Eg ) ( Eg ) deg 0 dn ( 1) reac / n1 c ng ( Eg ) ( Eg ) deg dt 0 dn reac dt g Photon energy distribution Planck s law When photons are in thermal equilibrium in stellar plasma : ((E g ) is photodisintegration x-sec.) Decay constant : : probability of decay per nucleus per second 3 8h 1 u( ) d d 3 h / kt c e 1 No of photons between E g and E g +de g n g ( E g ) de g u( E E g g ) de g 8 ( h c ) 3 Eg de exp( E / kt) 1 g g Substituting that, we get, the decay constant for photodisintegration reaction (1) g 8 3 h c E g ( Eg ) exp( Eg / kt) 1 0/ E th de NOTE : this decay constant does not depend on stellar density g For endothermic (Q g < 0) reaction, the lower limit of integration is E th (= Q g ) SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 7

28 C. Reaction rate for charged particle induced reaction : For non-resonant case, (l 1) At low energies, only l=0 contributes; So, More generally, it may be expressed as, Where, S(E) is a constant or weakly varying with E l Tl T T ( E) / ( E ) T ( E) S( E) / E E For astrophysical reactions involving charged particles, energies are always well below the Coulomb barrier. So, T 0 (E) is now the tunneling probability G(E) So, final expression for cross-section is, Where, Tunneling probability Z 1Ze G ~ exp( ) exp( v ( E ) G( E) S( E) / E ) exp[ ( E 4 Z1 Z e e Gamow energy is defined as : E G c ( Z1Z a ) ; a 1/ 137 c And, S(E) is called the astrophysical S-factor. G E ) 1/ ] SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 8

29 Coulomb Tunneling : Gamow Peak So, Rate Coefficient C v ( kt) C ( kt) 3/ 3/ 0 0 S( E)exp( v 0 dn j ( E) v( E) de de C ( E) E exp( E / kt) de ( kt) E G / E E kt ) de The integrand has a maximum at E=E 0, where, d E {exp( EG / E )} 0 de kt 3 4 1/ E0 EG ( kt / ) ; E0 ( E0 kt) 3 This maximum is known as Gammow peak 3/ 0 For thermally equilibrated system, C 1/ dn / de ~ E exp( E / kt) 3/ ( kt) G( E) S( E)exp( E / kt) de NOTE :: All astrophysically meaningful reactions take place within the shaded region under the Gammow peak SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 9

30 Reaction rate in presence of Resonances BW ( E) J Breit-Wigner resonance GG J i i f /[( E E (J 1) /( j 1)( j 1) ; G G f R ) ( G / ) i G f ] For a narrow resonance, A narrow resonance v 0 BW C ( kt) C 3 / BW ( E) E exp( E / kt) de E exp( E / kt) 3/ R R BW ( E) ( kt) 0 0 ( E) de GG /( G / ) GG / G So, the reaction rate at resonance is dn dt reac J i f C n01n0 exp( E / kt) 3/ Jg i f R ( kt) 1 ij At resonance, reaction rate depends on the resonance strength g J i f J g i f de SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

31 S-factor : utility Putting numerical factors, E 0 E 1.[ Z [ Z Z 1 Z T 6 T ] 5 6 1/3 ] 1/6 kev Typical Gammow peak values : T~ K System E 0 (KeV) E 0 (kev) 3He+3He p+1c a+1c O+16O As S-factor changes slowly against the fast falling x-secs, It is useful for extrapolation of measured x-secs to astrophysical energies (in nonresonant domain) SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

32 Evolution of Abundance with time Take simple reaction between nuclei 1 and : Rate of change of abundance of 1 due to due to reaction with = reaction rate dn dt 1 so, (1) n (1) n 1 n 1 1 / (1); X v M now, N dn dt 1 A 1 (1 v 1 ) r 1 n n 1 1 Molar reaction rate v Stellar density Mass fraction NOTE : The decay constant of a nucleus destructed by particle induced reaction depends explicitly on stellar density; on the other hand,, For photon induced decay, it does not depend on stellar density For a more general reaction ( destruction of 1 by several reactions) 1 (1) 1 (1 i i ) Important for quantitative understanding of nuclear burning stages SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 3

33 The generalised abundance evolution equation dn dt i [ j, k [ n n j n n n k n v i v jki ni o l b, li b, io n n i l p m g, mi g, i p n n i ] m ] Creation of eleement i Destruction of element i Forward and backward reaction rate : The cross-sections are connected through reciprocity theorem ( j ( j 3 1 1)( j 1)( j 4 1) 1) p p 34 1 (1 ( ) ( j ) ( j 3 1 1)( j 1)( j So, the ratio of forward-to-backward reaction rates 4 1) 1) m m 34 1 E E 34 1 (1 ( ) ) N N A A v v where, E 34 E E1/ kt E1 134e de1 1/ 0 Q134/ kt ( m34 m1) ~ e E34/ kt E34 341e de Q 134 SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

34 Example 1: Evolution of 5Al in stellar plasma Simplified example taking only processes : determination of the preferred one Q. In stars, 5Al may be destroyed in ways; (1) capture reaction 5Al(p,g)6Si and/or () b + -decay (t 1/ ~ 7. s) take : Molar reacn. Rate ~ cm 3 mol -1 s -1 ; density ~ 10 4 g/cm 3, X H ~ 0.7 Ans : for b + -decay : t b (5Al) = t 1/ / ln ~ 10.4 s X 1 For p-capture, t p (5Al) = ( N A 1v ) 0. 08s M So, p-capture is dominant destruction mode However, at lower density, the two processes may compete : so, not only nuclear, but other physical parameters also play important role. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

35 Example : Estimation of reaction parameters for s-, r- processes Q. Estimate neutron density required for s-, r- processes. For transformation of a nucleus A A+1 by n-capture v 1/ n n g n A For low energy neutrons, we know that ~1/v or v ~ const. Let us take, ~ 1 b. and v ~ 10 7 cm/s ;; so, n = 1/v ~ s neutrons/cm 3 For a reaction with capture time A ~ 10 yr ( ~ 3x10 8 s) Typical neutron density required is ~ 3x10 8 neutrons / cm 3 (s process) For r-process, however, the captures need to be very fast : let A ~ 1 ms Typical neutron density required is ~ 10 0 neutrons / cm 3 (supernova) SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

36 Example 3 : Equilibrium D/H ratio in pp1 chain Simplified example taking only processes : a. creation of D : p(p, e + ) H b. Destruction of D : H(p,g) 3 H Problem : To find equilibrium D/H Ratio : lifetimes : pp d : y :: pd 3He : y (at T ~ 15T 6 (sun) pp1 chain p(p,e + )d d(p,g) 3 He 3 He( 3 He,p)a dd dt r pp (1 dp ) r dp H At equilibrium, dd/dt = 0, v (1 pp ) so, pp (1 ( D dp H) HD v ) (1 ) eq dp dp v v pp H dp dp v pp pp HD v dp NOTE : (D/H) eq is much less than the primordial concentration of D, (D/H) BBN ~ 10-5 ; this concentration is sufficient to initiate first H-burning thru d(p,g)3he reaction at lower temperatures (~MK) before actual H-burning is triggered (at T~10MK). This is the source of first thermonuclear energy in some stars (M star ~0.08M ). SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

37 Example-3 (contd) : Equilibration time for D/H ratio Soln: then, From lifetime consideration, d abundance changes much faster than H abundance. So, H abundance may be assumed to remain constant till D/H equilibrium occurs d( D / H) H D so, v H( ) v dy / dx dt a bx y, y b dt y dt where, y pp x ( D / H ) ; a H H v bt bt 0 e : ( assume y y0 at t 0) x ( x0e ) :: x0 ( D / H ) 0 pp ; a b dp b H v t so, ( D / H) t ( D / H) e (( D / H) e ( D / H) 0)exp( ) ( d) a b p dp a / b ( D / H ) D/H equilibrium ratio - very small, ~ , is reached very fast, ~ p (d) ~ few sec. e NOTE: Since D is burnt out very fast and there are no other stellar sites for D production in good amount, so the observed D-abundance in the universe is lower limit of the D produced during primordial nucleosynthesis which may be an important test for BBN model. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

38 Modification of beta decay lifetime in stellar environment A. Effect of Ionisation New weak processes show up in stars due to its plasma environment In Lab : (a) b, (b) b, (c) orbital e - capture In stellar plasma: (d, e) continuum e - / e + captures, (f) bound state b decay At star temperature, av. Energy (~ 1/10 KeV for T~ MK) is enough to ionise the atoms completely bound electron capture is very small; On the other hand, due to the presence of free electrons, probability of continuum captures become significant. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

39 Modification of beta decay lifetime in stellar environment (contd.) B. Effect of Excited States Let us take the decay of 6Al 6Mg IMPORTANT TO NOTE :: Detection of 6Al in interstellar medium through gamma ray (1809 KeV) mapping confirmed that nucleosynthesis is still now active Consider the ground and 1 st excited (8 KeV) states of 6Al. Ist excited state is an isomer (6Al m ) ( M5 tran.) Both 6Al g, 6Al m undergo b-decay to 6Mg T 1/ (6Al m ) ~ 6.3 s ; T 1/ (6Al g ) ~ y 6Al g b-decay feeds 1 st excited state of 6Mg, which then emits 1809 kev line. On the contrary, 6Al m b-decay feeds directly ground state of 6Mg (no g-ray emission) SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

40 B. Effect of Excited States (contd.) Stellar environment (hot plasma) is different from Lab. as substantial part of the nuclei may remain in excited state. P ( j 1) e E / kt ( j 1) e E / kt In Lab. There is ground state b-decay only. In stellar plasma There is both ground and excited state b-decays So, effective b-decay width is the weighted sum of all b-decay transition rates eff b Pi i j ij SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

41 B. Effect of Excited States (contd.) So, for the decay of 6Al, eff b P gs gs P m m P gs ln T gs 1/ P m ln T m 1/ For 6Al, 8 kev state cannot be directly excited from gs due to M5 transition, so equilibrium is achieved via nd (417 Kev) or higher excited states Above ~0.4Gk, both gs and 1 st excited state are in equilibrium and lifetime changes drastically as we see in fig. above SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

42 Summing Up. Discussed about various nucleosynthesis stages and importance of nuclear physics inputs Discussed how reaction rates for astrophysical processes may be estimated quantitatively Discussed about the concepts of astrophysical S-factor, its evaluation and significance Discussed about the effects of stellar environment on various decay rates SNP016 Orientation programme : SINP S. Bhattacharya Dec 04, 016 4

43 Challenges for future. n-capture data comparison Better and precision data (reduced errors) with better theoretical predictions Reduced uncertainty in abundances Estimation of the effect of astronomical environment e.g. screening enhancing x-secs for charged particle reactions; excited state population, ionisation etc. affecting decay life-times, A few important reactions for astrophysics Reaction significance Gamow energy (kev),3 H(a,g) 6,7 Li BBN ,18 O(p,g) 18,19 F Stellar Nucl C(a,g) 16 O Stell N (C/O ratio) C(a,n) 16 O Stll N (n-source for s- process) Ne(a,n) 5 Mg Stll N ((n-source for s- process) Al(p,g) 6 Si Stel. N (prod. Of 6Al in Nova).. And there are many more... Enough to keep you busy for many more years. SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,

44 Acknowledgements In preparation of this lecture, many books, journals, lecture notes have been consulted, and many figures, graphs, numerical results have been directly taken from different sources. Major references are given below, though it may not be complete and omissions (if any) are regretted. 1. K. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle, Rev. Mod. Phys. 9 (1957) A.G.W. Cameron, Chalk River Report CRL - 41 (1957). 3. M. Arnould, EAS Publications series, (008). 4. C. Iliadis, Nuclear Physics of Stars, (Wiley-007). 5. C. Rolfs and W. Rodney, Cauldrons in the Cosmos, (University of Chicago Press ). 6. K. E. Rehm, Nuclear Astrophysics talk (011). 7. K. Langanke, Nuclear Astrophysics talk (011). 8. Wikipedia Thank you SNP016 Orientation programme : SINP S. Bhattacharya Dec 04,