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Core Collapse SNe

Core Collapse SNe. Inma Domínguez Marco Limongi. Evolution of Massive Stars Hydrostatic Nucleosynthesis Explosion Mechanism Explosive Nucleosynthesis Contribution to the Chemical Evolution. INTERPRETATION OF THE SOLAR SYSTEM ABUNDANCES.

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Core Collapse SNe

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  1. Core Collapse SNe Inma Domínguez Marco Limongi

  2. Evolution of Massive Stars • Hydrostatic Nucleosynthesis • Explosion Mechanism • Explosive Nucleosynthesis • Contribution to the Chemical Evolution

  3. INTERPRETATION OF THE SOLAR SYSTEM ABUNDANCES BB = Big Bang; CR = Cosmic Rays;neut. = n induced reactions in SNII; IMS = Intermediate Mass Stars; SNII = Core collapse supernovae; SNIa = Termonuclear supernovae; s-r = slow-rapid neutron captures Type II SNe Chemical Evolution of the Galaxy Type II SNe 16 < A < 50 and 60 < A < 90 16O 49Ti 60Ni 90Zr

  4. Evolutionary Properties of Massive Stars: Progenitors of CCSNe • M > 12 M CCSNe Ignition of ALL Exothermic Nuclear Reactions • Central Conditions (T,) • The stars is never in degenerate conditions along its evolution

  5. STELLAR EVOLUTION EQUATIONS 1 Dimension Lagrangian Hydrostatic Mixing-length theory

  6. STELLAR EVOLUTION EQUATIONS + Chemical Evolution Production + Destruction For each time step 1000 (zones) systems of 4+N(isotopes) equations High Computational Time

  7. HYDROGEN BURNING - PP 4H  He Proton-Proton Chain 1H + 1H 2H + e+ + n 2H + 1H  3He + g 3He + 4He 7Be + g PPI 3He + 3He  4He + 2 1H PPII PPIII 7Be + e- 7Li + n 7Li + 1H 2 4He 7Be + 1H  8B + g 8B  8Be + e+ + n 8Be  2 4He Depending on T the different branchings become active. In all cases the result is 4 1H1 4He

  8. HYDROGEN BURNING CNO Cycle When C and/or N and/or O are present  CNO 12C + 1H 13N + g 13N  13C + e+ + n 13C + 1H 14N + g 14N + 1H 15O + g 15O  15N + e+ + n 15N + 1H 12C + 4He(99%) 16O + g (1%) CN T  3 107 K 16O + 1H 17F + g 17F  17O + e+ + n 17O + 1H 14N + 4He NO During the conversion of H into He through the CNO cycle C and O are burnt and N is produced Products of CNO C  N  O 

  9. HYDROGEN BURNING – ENERGY GENERATION The CNO cycle is more efficient than he PP chain over a certain Tcritica CNO PP From Hydrostatic Equilibrium Eq: Central Temperatura scales with Total Mass Massive stars H-burning CNO cycle

  10. HYDROGEN BURNING - CONVECTIVE CORE The Energy generated by the CNO-cycle depends strongly on T High Energy Flux  Increases Radiative Gradient  A Convective core Develops Masssive stars burn H within a Convective core At high T the main contribution to the Opacity comes from the Thomson Scattering When the H decreases, the Opacity decreases and the Convective Core receeds and finally, at H-exhaustion, disappears

  11. HYDROGEN BURNING – Ne-Na, Mg-Al Cycles If during the central convective H-burning T are high enoughlog T=7.5-7.8  Active Ne-Na e Mg-Al cycles Ne-Na Cycle Mg-Al Cycle 20Ne + 1H 21Na + g 21Na  21Ne + e+ + n 21Ne + 1H 22Na + g 22Na  22Ne + e+ + n 22Ne + 1H 23Na + g 23Na + 1H 20Ne + 4He 24Mg + 1H 25Al + g 25Al  25Mg + e+ + n 25Mg + 1H 26Al + g 26Al  26Mg + e+ + n 26Mg + 1H 27Al + g 27Al + 1H 24Mg + 4He Final results of the operation of these cycles Na-Na e Mg-Al • 21Na & 25Mg practically burnt • 22Ne is reduced by a factor 2 • 23Na & 26Mg increase by a factor 6 & 2, respectively • 26Al produced (~10-7) • 20Ne, 24Mg & 27Al do not change

  12. STRUCTURE AT CENTRAL H-EXHAUSTION He core H envelope The He-core is much more dense than the H-envelope because the mean molecular weight for 4He is greater than for 1H  Matter within the He-core is more compact The synthesis of heavier isotopes increases the mean molecular weight and the structure becomes more compact

  13. HYDROGEN SHELL BURNING Start Conv. Env. H exhaustion Convective envelope H burn.shell dup He core He H conv. core He conv. core CO core He burn. shell • At central H-exhaustion  H-burning sets in a Shell outside the He-core. • HR diagram: the star moves to the red • A convective envelope forms, the inner border of this envelope reachs zones chemically modified by he central H-burning. • The 1st dredge-up occurs: material processed by nuclear reactions is transported to the surface

  14. HELIUM BURNING – 3 At central H-exhaustion, the He core is mainly composed by 4He (98%) & 14N (1%) Withouth Nuclear Energy generation within the core, it contracts and Tc increases When Tc ~ 1.5 108 K  Efficient He-burning At the beginning 4He 8Be and 8Be rapidly decays to 4He 4He + 4He  8Be + g 8Be  4He + 4He Later, at higher T and  the equilibrium abundance of 8Beincreases and so increases the probability of the reaction 8Be + 4He producing 12C 4He + 4He  8Be + g 8Be  4He + 4He 8Be + 4He  12C + g 3 4He  12C + g

  15. HELIUM BURNING – REACTIONS Initially: 4He in 12C But when 12C abundance is significant and 4He abundance is reduced, it is more likely that 4He is captured by 12C than by 4He: 3 4He  12C + g 12C + 4He  12O + g 16O + 4He  20Ne + g 20Ne + 4He  24Mg + g The first 2 reactions are more efficient 3 4He Nuclear Cross Section depends markedly on T Like H-burning (CNO cycle) He-burning occurs within a convective core

  16. HELIUM BURNING: s-process 14N produced by the CNO cycle 14N + 4He  18F + g 18F  18O + e+ + n 18O + 4He  22Ne + g 22Ne + 4He  25Mg + n 78Rb 79Rb 80Rb 81Rb 82Rb 83Rb 84Rb 85Rb 86Kr 87Kr 88Kr 77Kr 78Kr 79Kr 80Kr 81Kr 82Kr 83Kr 84Kr 85Br 86Br 87Br b- 76Br 77Br 78Br 79Br 80Br 81Br 82Br 83Br 84Se 85Se 86Se b- 78Se 79Se 80Se 81Se 82Se 75Se 76Se 77Se 83As 84As 85As b- 74As 75As 76As 77As 78As 79As 80As 81As b 73Ge 74Ge 75Ge 76Ge 77Ge 79Ge 80Ge 78Ge n,g 72Ga 73Ga 74Ga 75Ga 76Ga 77Ga 78Ga 79Ga In Massive  during central He-burning, elements heavier than Fe are synthesized by the s-process. s-process depends on free neutrons and the neutron abundance depends on Z  The final s-element abundances scale with initial metallicity

  17. HELIUM EXHAUSTION 12C 26Mg 16O 22Ne 20Ne 25Mg H sh. ex He c.c. Conv. Envelope. Core di CO The most abundant isotopes at central He-exhaustion: 12C 16O 20Ne 25Mg 26Mg The first three are produced by: 3 4He  12C + g 12C + 4He  12O + g 16O + 4He  20Ne + g 25Mg & 26Mg come from the 14N-chain 14N + 4He  18F + g 18F  18O + e+ + n 18O + 4He  22Ne + g 22Ne + 4He  25Mg + n 22Ne + 4He  26Mg + g 12C, 16O, 20Ne, 25Mg & 26Mg are the most abundant isotopes and are produced by He-burning with the surface abundance 12C/16O ratio depends on the12C + 4He  12O + gnuclear cross section that it is still NOT well known at the energies of the He burning. This ratio has a strong influence on the subsequent evolution

  18. HELIUM EXHAUSTION: s-process elements 70Ge 80Kr 74Se H sh. Conv. Envelope. ex He c.c. Core di CO The most abundant elements are: 70Ge 74Se and 80Kr Heavier nuclei, like 87Rb, 88Sr, 89Y, 90Zr are not expected to be produced

  19. HELIUM SHELL BURNING – CONVECTIVE SHELL Convective envelope H burn.shell He conv.shell dup He core He H conv. core He conv. core CO core He burn. shell At central He exhaustion, He burning moves to a shell just outside the CO core The following evolution is characterized by the development of a convective He-burning shelllimited by the CO core and by the H-burning shell. The chemical composition of this shell, that will be active till the collapse, tends to get frozen because the evolution of the star is more and more rapid at the advanced phases.

  20. STRUCTURE at He-exhaustion CO core He core H envelope At central H-exhaustion, the  is composed by a CO core, a He-shell and a rich H envelope The two density gradients correspond to the border of the He core (~ 9 M) and to the border of the CO core (~ 6 M ) This density profile is important for the explosion properties

  21. ADVANCED EVOLUTIONARY PHASES: NEUTRINO DOMINATED Now the CO core, produced by the central He-burning, contracts During the contraction the  and T within the core favours the production of thermal neutrinos produced by pair anhilation. At T>109 K high energy photons produce e+e- pairs That suddenly recombine to produce a photon. BUT once over 1019 times, e+e- produces a neutrino-antineutrino pair This energy sink increases along the subsequent phases up to the pre-collapse phase Advanced evolutionary phases of massive stars are called “neutrino dominated”

  22. ADVANCED EVOLUTIONARY PHASES: NEUTRINO LUMINOSITY Nuclear Neutrino Photon From now on the energy losses: Photons from the surface Neutrinos from the center 108 Up to C central ignition the main energy losses are due to photons and after are due to neutrinos. As the nuclear energy gives the star what is lossing, it follows first the luminosity of photons, and after, the neutrino luminosity

  23. EVOLUTIONARY TIMES Enucis the energy per gram coming from nuclear reactions, If this is the only energy source in a star of mass M: Nuclear time scale: H burning: 4 1H  4He DM = 4 x 1.0078 – 4.0026 = 0.0287 AMU = 0.0287/4 AMU/nucleon = 0.007 AMU/nucleon Enuc = 0.007 x 931.1 x 1.602 10-6x 6.022 1023 = 6.44 1018 erg/g 1 AMU = 931.1 MeV : 1 MeV= 1.602 10-6 erg : NA = 6.022 1023 nucleon/g He burning: 4 4He  16O DM = 4 x 4.0026 – 15.9949= 0.0115 AMU = 0.0115/16 AMU/nucleon = 0.0009 AMU/nucleon Enuc = 0.0009 x 931.1 x 1.602 10-6x 6.022 1023= 8.70 1017 erg/g O burning: 2 16O  32S DM = 2 x 15.9949 – 31.9720= 0.0177 AMU = 0.0177/32 AMU/nucleon = 0.0005 AMU/nucleon Enuc = 0.0005 x 931.1 x 1.602 10-6x 6.022 1023= 4.98 1017 erg/g For fix mass, Luminosity and amount of fuel ! From models: The luminosity increases drastically due to neutrino losses  The evolutionary times are drastically reduced

  24. n g g n n g g n n g g n n n g g Advanced burning stages Neutrino losses play a dominant role in the evolution of a massive star beyond core He burning At high temperature (T>109 K) neutrino emission from pair production start to become very efficient Evolutionary times reduce dramatically

  25. CARBON BURNING Central C combustion stars ~104 years after central He-exhaustion Tc ~ 7 108 K e c ~ 1 105 g/cm3 C-burning depends on the 12C/16O ratio left after central He burning, 12C(a,g)16O on the amount of fuel The formation of a Convective Core depends on the existence of a positive energy flux A Convective Core develops enuc > en 12C abundances determines the nuclear energy generation rate NO Convective Core enuc < en In general, for a fix 12C(,)16O reaction rate and mixing technics 12C abundance decreases for higher initial masses In the 25M central carbon combustion occurs in radiative conditions

  26. Synthesis of Heavy Elements At high temperatures a larger number of nuclear reactions are activated Heavy nuclei start to be produced C-burning Ne-burning

  27. Synthesis of Heavy Elements O-burning

  28. At Si ignition (panel a + panel b) A=45 56Fe A=44 28Si Eq. Clusters Synthesis of Heavy Elements Balance between forward and reverse reactions for increasing number of processes At Oxygen exhaustion c + d a + b At Oxygen exhaustion At Si ignition Sc Si Equilibrium Equilibrium Partial Eq. Out of Eq. Out of Equilibrium 56,57,58Fe, 52,53,54Cr, 55Mn, 59Co, 62Ni

  29. MATTER PROPERTIES AT HIGH TEMPERATURE :NSE The chemical composition of matter in NSE is a function of T  Ye When the neutronization changes The nuclei with that neutron excess are favoured (with higher binding energies) =0.000,Ye=0.5000, 56Ni =0.038,Ye=0.481, 54Fe =0.072,Ye=0.464, 56Fe =0.104,Ye=0.448, 58Fe

  30. PRE-SUPERNOVA MODEL: CHEMICAL COMPOSITION H Centrale He Shell C conv. Shell He Centrale H Shell O conv. Shell Si burning(Cent.+Sehll) 4He 16O 1H 28Si “Fe” 20Ne 12C Studying the different isotope abundances in detail is possible to know from which burning phase they come from or the interior region of the star where they were produced

  31. PRE-SUPERNOVA MODEL: Fe-CORE STRUCTURE Fe/Si Si/O CO/He He/H 16O “Fe” 28Si 20Ne 12C

  32. EXPLOSION The gravitational collapse of a stars with M  12 Mcould liberate an energy of Most of this energy increases the electron energy and, after electron captures, is converted in neutrino energy Just a small fraction is used to eject (kinetic energy) the envelope So, the key question is to find a mechanism able to transform a small fraction of the binding energy left during the collapse in kinetic energy of the envelope with the observed velocities ( 104 km/s)

  33. 4He H Shell He Shell H Central 16O 1H He Central C conv. Shell O conv. Shell Si burning Piston 28Si “Fe” 20Ne 12C Explosive Nucleosynthesis and Chemical Yields Explosion Mechanism Still Uncertain The explosion can be simulated by means of a piston of initial velocity v0, located near the edge of the iron core • Explosion: 1D PPM Lagrangian Hydrocode (Collella & Woodward 1984) • Explosive Nucleosynthesis: same nuclear network adopted in the hydrostatic evolutions v0 is tuned in order to have a given amount of 56Ni ejected and/or a corresponding final kinetic energy Ekin

  34. EXPLOSIVE NUCLEOSYNTHESIS Passing through the envelope the Shock Wave increases the density and temperature and nuclear reactions occur We may define the burning time-scales for the available fuels : Si, O, Ne, C, He and H These time scales are determined by the corresponding destructive reactions Assuming the explosion time ~1s Burning products are similar to those obtained in hydrostatic burning He-explosive burning is not efficient in SNII

  35. EXPLOSIVE NUCLEOSYNTHESIS 56Fe A=45 A=44 28Si Clusters di equilibrio Analyzing the most eficient processes: Still out of NSE: Products are similar to those from hydrostatic burning EXPLOSIVE CARBON BURNING: Products: 20Ne, 23Na, 24Mg,25Mg, 26Mg EXPLOSIVE NEON BURNING: Products: 16O, 24Mg + 27Al, 29Si, 30Si, 31P, 35Cl, 37Cl Starting NSE (direct and inverse process) EXPLOSIVE OXYGEN BURNING: 2 clusters at quasi-NSE separated by A44. No connection between the 2 clusters Products: 28Si, 32S, 36Ar, 40Ca + 34S, 38Ar

  36. EXPLOSIVE NUCLEOSYNTHESIS 56Fe A=45 A=44 28Si Clusters di equilibrio Full NSE EXPLOSIVE INCOMPLETE SILICON BURNING: At this T the 2 clusters connect at A44. Most of the matter A<44  just part of 28Si reachs the upper cluster Products:36Ar, 40Ca + 56Ni(56Fe), 54Fe, 52Fe(52Cr),51Cr(51V), 55Co(55Mn), 57Ni(57Fe), 58Ni EXPLOSIVE COMPLETE SILICON BURNING: At this high temperature: NSE !!!!!! All 28Si is burnt to Fe-peak elements. Abundances depend on neutronization !! For NZ56Ni is the most abundant nuclei Products: Iron Peak Nuclei

  37. EXPLOSIVE NUCLEOSYNTHESIS Changes in T and r following expansion are crucial for the nucleosynthesis During the explosion Temperatures are very high It could be assumed that matter behind the shock is radiation dominated = Location and T of the shock The shock propagates in all directions (sphere) Each radial coordinate in the presupernova model will reach a maximum temperature

  38. EXPLOSIVE NUCLEOSYNTHESIS Complete Si burning Incomplete Si burning Explosive Oxygen Explosive Neon Explosive Carbon NSE QSE 1cluster QSE 2cluster Untouched Zone Sc,Ti,Fe,Co,Ni Cr,V,Mn,Fe Si,S,Ar,K,Ca Mg,Al, P, Cl Ne,Na,Mg 6400 11750 3700 5000 13400 For Eexpl=1051 erg we could infer in the presupernova model which regions (volumes) experience each burning

  39. EXPLOSIVE NUCLEOSYNTHESIS: PROGENITOR Influence of the Progenitor: 1) M-R RELATION (= density profile): Fix the mass inside a certain volume 2) Ye (neutronization): In those zones that reach NSE or QSE determines the rate between protons and neutrons T=5 109 K, r= 108 g/cm3, Ye=0.50  56Ni=0.63 – 55Co=0.11 – 52Fe=0.07 – 57Ni=0.06 – 54Fe=0.05 T=5 109 K, r= 108 g/cm3, Ye=0.49  54Fe=0.28 – 56Ni=0.24 – 55Co=0.16 – 58Ni=0.11 – 57Ni=0.08 3) Chemical Composition : For those zones that experience normal burnings (ie. Explosive Carbon e Neon burnings) fix the amount of fuel available.

  40. MASS CUT Mass Cut The Mass Cut depends on the piston initial velocity During the explosion internal zones fall back. At some point part of the matter is Expanding and some Collapsing Depending on v compare to vesc The mass coordinate at the bifurcation is defined as the Mass Cut In general, for greater initial velocities Smaller Mass Cut Greater kinetic Energies 1.110 1.144 1.170 1.220 1.250 1.263 The lack of a explosion model makes the MASS CUT and the KINETIC ENERGY quantities that depend on parameters (initial energy or piston initial velocity and place at which the explosion is started)

  41. EXPLOSION PROPERTIES: CHANGES IN CHEMESTRY Si-i Ox Cx Untouched Pre = Dotted Post = Solid Nex Si-c 4He 16O 28Si FallBack 20Ne 1H 12C Ekin=1.14 foe v0=1.5550 109 cm/s Mcut=1.89 M Taken: Mass Cut • The changes in composition due to the explosion occur only at the most internal ~3.1 M • Outside the chemical composition remains untouched. It is that from the hydrostatic burning • The complete explosive Si burning and part ot the incomplete explosive Si burning fall back to the compact remant

  42. MASS CUT CALIBRATION: LIGHT CURVES Total 56Ni 56Co 56Ni=0.15 M 56Ni=0.07 M 56Ni=0.01 M From the LC we obtain information for the Mcut After an initial phase, different for the different types of SNe, the LC is powered by the photons produced by the radioactive decay 8.8 111 Based on the Bolometric LCs and on the distance, we can deduce the amount of 56Ni produced during the explosion 56Ni is produced in the most internal zone depends critically on the Mass Cut  The Mass Cut may be choose to reproduce a certain amount of 56Ni in agreement with the observations. The theoretical kinetic energy must be compatible with the observed

  43. MASS CUT CALIBRATION vs INITIAL MASS From the observed initial mass of the progenitor we may obtain an empirical relaction between this mass and the 56Ni produced (or Mcut) Hamuy et al. 2003 PROBLEMS !!!! • Few estimations of the progenitor initial mass from the observations • Similar masses give very different 56Ni masses

  44. CHOOSING A MASS CUT 1)FLAT Case: All masses produce the same 56Ni mass = 0.05 M For each model a different mass cut is chosen in order to reproduce this amount of Ni 2) TREND Case: We adopt a relation between Initial Mass and 56Ni Mass:

  45. PRODUCTION FACTORS To compare with Solar Abundances we introduce the Production Factor Two isotopes with the same Production Factor Same Rate as in the Sun Oxygen is produced only by Type II SNe and is the most abundant element produced by SNII  Oxygen Production Factor is a Good Metallicity indicator It is useful to normalize all PF to that of Oxygen to show wich isotopes follow Oxygen (Z)

  46. INTEGRATED YIELDS (Elements) Dots: 13 – 15 – 20 – 25 – 30 – 35M Solid line: Salpeter Mass Function Flat 56Ni => 0.05 M Yields from 13-35 M + Salpeter Mass Function It is assumed that all masses produce the same amount of 56Ni (FLAT) We consider “Solar Scaled” with respect to O all elements with a PF within a factor 2 of the O PF The yields produced by a generation of massive stars integrated by a Salpeter IMF depend mainly on the yields coming from a 20-25 M star

  47. Contribution of Type Ia SNe Production of Fe  the percentage of SNIa, relative to SNII, has been fixed by requiring that PFFe=PFO Open circles = No SNIa Filled circles = 12% SNIa • SNIa contribute only to the Solar System abundances of nuclei in the range Ti-Ni • The inclusion of SNIa brings 50Ti and 54Cr into the band of compatibility  50Ti and 54Cr become scaled solar compared to O 3) 14N and lot of heavy elements come from AGB stars

  48. CONCLUSIONS with mass loss: 11 -120 M • Massive Stars are responsible for producing elements from 12C (Z=6) up to 90Zr (Z=40) + r-elements • Assuming a Salpeted IMF the efficiency of enriching the ISM with heavy elements is: For each solar mass of gas returned to the ISM H: decreased by f=0.64 He: increased by f=1.47 Metals: increased by f=6.84 Pre/Post SN models and explosive yields available athttp://www.mporzio.astro.it/~limongi Alessandro Chieffi & Marco Limongi (ApJ 1998-2007)

  49. Uncertainties in the computation PreSN Models • Extension of the Convective Core (Overshooting, Semiconvection) • Mass Loss Uncertainties in the computation of the Explosion Models • Explosion itself Piston: • Mass-cut - Mini • 56Ni (LC) • Energy (vexp)

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