DOCSLIB.ORG

Nuclear Statistical Equilibrium and the Iron Peak

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Nuclear Statistical Equilibrium and the Iron Peak RICE UNIVERSITY NUCLEAR STATISTICAL EQUILIBRIUM AND THE IRON PEAK by Kem Hainebach A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE Thesis Director's signature: Houston, Texas ABSTRACT NUCLEAR STATISTICAL EQUILIBRIUM AND THE IRON PEAK Kem Lawrence Hainebach The equations governing the abundance distribution of the nuclear species (atomic nuclei) under conditions of statistical equilibrium of the strong nuclear interaction are rederived and discussed. An algorithm for their solu¬ tion on a computer is presented, giving abundance distribu¬ tions as a function of temperature, density and overall neutron-proton ratio. A computer search of nuclear species abundance dis¬ tributions and mixtures of two distributions is carried out in an attempt to match equilibrium distributions, after weak interaction decay, of certain "iron peak" species to their observed solar system distributions. A mixture is found which reproduces the solar system abundance distribution 54 56 of Fe ' '57,58> Ninety-nine percent of the Fe~*^ is produced in nuclear statistical equilibrium as Ni 5 6 , lending hope to the proposed observation by gamma ray astronomy of the decay of Ni 56 to Fe 56 following a super¬ nova event. 266 C5llm, SBuubcvfi bu bid) atfcufaftC OB bcr fommcnbctt (9cfcf;id)lcn: 2)aC ©c[c(3 beC Scltenaflc ftomiten voir ?mei itid)t bcrnicBten. ©Wjt«. 9?cmicn foil i$, fagt i()v, tncitte knight im SiebcrreicBl Khoren, bie il)r feib, id) hunt ©te am hjcnigficti t>ott end). gragt mid) nad) ber Shtgcn garBe, Rragt mid) uad) ber ©tintmc £ott, ftragt itad) <$attg imb $£att} unb Raiding, 21$, unb maG meift i$ bafcon. 3ft bte ©onne nid)t bie DttcITe Me8 2eBcnC, atlcC SicBt'e! Unb mac miffett fcott berfelBefc 3$ unb mtb atfe? — nic^ts. gttbrlegiidj. 5Dit meiftt cC too^l, id) BlciB’ biv fent Unb matty' biv feitten Summer, Gin £rauiitBilb aBer jog' id) gent 2ftand)mat burd) bcinen ©glummer. Gin latter SBinb Bemegt baC $)iol)r, Unb BlaftBlau BliiBt ber glicbcr, 3d) fiiffe bir auf 2ttunb unb Dfyr 2)aC fd^iJnftc tnciner 2icber. 2)tt fpricbft mit ntir 311111 erflcitmal, 2D?eiit Gott, nic^t fo gcfcBnrittbe, ©0 jaud)$t ber 23ad) I;iuaB itiC ©0 rauftyi eC in ber £itibe. SCBir merbett bieC oBtt’ Uttterlaft 3m £i»tmcl cittntal BaBcn, SBcrbriefjlid) i(l baBci tiur, bag .©ie fritter unc BegraBett. TABLE OF CONTENTS Page I. INTRODUCTION 1 II. THE EQUATIONS OF NUCLEAR STATISTICAL EQUILIBRIUM 3 Existence and Uniqueness of Solutions 14 Numerical Method 16 Application of the Method to the Problem.... 18 III. NUCLEAR STATISTICAL EQUILIBRIUM AND THE IRON PEAK NUCLEI 20 Fitting of Abundance Ratios: A Norm 22 NSE as an Approximation to Freeze Out 25 One and Two Zone Models: Mixing 27 Results 39 IV. CONCLUSIONS 55 ACKNOWLEDGEMENTS 66 REFERENCES 67 LIST OF TABLES Page 1. 1964 Atomic Mass Table 32 2. Table of Two Zone Mixture of NSE Distributions 7 3 at Tg = 3, p = 10 g/cm , = 0.0837, = 0.0037, a = 0.013 40 6 3 3. NSE Distribution at Tg = 3.8, p = 3.1 x 10 g/cm , r\ = 0.069 45 4. NSE Distribution at T = 3.0, p = 3.1 x 10^ a/cm3, T) = 0.0 69 50 LIST OF FIGURES Page 1. (none) 2. Graph of Two Zone Mixture of NSE Distributions 7 3 at Tg = 3, p = 10 g/cm , nx = 0.0837, T|2 = 0.0037, a = 0.013 40 6 3 3. NSE Distribution at Tg = 3.8, p = 3.1 x 10 g/cm , T) = 0.069 45 6 3 4. NSE Distribution at Tg = 3.0, p = 3.1 x 10 g/cm , Ti = 0.069 50 NSE Abundances (Mass Fractions) vs. T), for 7 Tg = 3, p = 10 ; Stable Isotopes of the Elements: 5. Titanium (Ti) . 56 6. Vanadium (V) 56 7. Chromium (Cr) 56 8. Manganese (Mn) and Cobalt (Co) 56 9. Iron (Fe) 56 10. Nickel (Ni) 56 11. Copper (Cu) 56 12. Zinc (Zn) 56 I. INTRODUCTION This study of nuclear statistical equilibrium extends the work of many previous investigators, one of the more recent studies being the work of Clifford and Tayler (1965) The present study uses the experimental values for nuclear binding energies given in the 1964 Atomic Mass Table by Mattauch, Thiele and Wapstra (1965) whereas Clifford and Tayler used the 1960 Nuclear Mass Table by Everling, Koenig Mattauch and Wapstra (1960). We have developed a computer code which solves the equations of nuclear statistical equilibrium, giving nuclei abundance distributions as a function of the three indepen¬ dent parameters: temperature, nucleon density, and neutron excess. The code is also part of another code which was developed to search for linear combinations of equilibrium distributions which approximate the solar system distribu¬ tion of certain nuclei in the iron peak, specifically in' the range of elements between titanium and zinc (atomic numbers 22 to 30). This search was undertaken as the next reasonable step following the failure of any single equi¬ librium distribution to produce a good fit to the solar system iron peak distribution. 2 Attempts are made to fit the solar abundances of the four stable iron isotopes with linear combinations of NSE abundance distributions. The possible consequences for gamma ray astronomy are discussed. 3 II. THE EQUATIONS OF NUCLEAR STATISTICAL EQUILIBRIUM We repeat, with slight change in notation, the sketch of the basic equations given by Clifford and Tayler (1965). In nuclear statistical equilibrium (NSE), the number density of any species is governed by the equation ( (Eir“Mi)//kT Vn. E (1) 1 r where the particles are contained in volume V, n^ is the number density of the particles of the i kind. The sum is over all (relativistic) energy states E^r, internal and kinetic, of species i, and includes the 2j + 1 spin states of any-internal energy level (J = spin). Mi is the chemical potential of species i, defined by Mi = (Hr) S-V'N <2> where E is the average relativistic internal energy of all particles in volume V; Ni = Vni ; the subscripts S,V,N denote entropy, volume and numbers of all other species held constant. The plus and minus signs refer to Fermi- Dirac and Bose-Einstein particles, respectively. 4 If species A^ react to form species (and vice versa) as E a.A. E 8 .B . (3a) 1 1 1 j 3 D then, from the definition of chemical equilibrium (see e.g., Reif, Ch. 8), their chemical potentials obey the relation 2 aiMi = 2 (3b) At the temperature and densities of interest in this study, the nuclear particles are non-degenerate and non- relativistic. This results in several simplifications. One can write. E. =“e. +m.c 2 ;e. = pT/2 2m. + lr lr I ' lr *1' 1 internal energy terms where ITU is the mass of a nucleus of species i. 2 M. N, , ( ) denotes 1 3N. (< >) 1 energy average 2 “ aST [< sNj(^7 + mjc )>] = < + m. c 2m^ 1 5 The term ) can l>e looked on as a non-relativistic 1 2 chemical potential. Denote it by U. Then M. = u. + m.c . l ill Then equation (3b) becomes 2 2 S or. u. + £ a.m.c = £ p.|i. + £ p.m.c i 1 1 i 1 1 3 3 3 3 3 3 or S = £ P-U. - Q (4) i j J J where 2 2 Q £ or.m.c - £ p.m.c (5) i 3 3 3 Another simplification is that equation (1) goes over to the Maxwell distribution 1 ^n. = £ exp[-(Eir-M.)AT] = £ exp^e^-u^AT] = expAT^ £ exp^-eirAT) . (6) The sums of kinetic and internal energies can be separated and the sum over kinetic energies converted to an integral by allowing one state per volume h in phase space. Then 6 U.AT e T Vn. e 1 S (2J +l) - int,lA 1 r -p2/2m.kT 4nV 2 3 p e dp (7) h where p = momentum and we have multiplied by the density of states in phase space and integrated over all of phase space contained in the volume V. The integral in equation (7) can be done, giving li.-AT t ^ \3/2 n^ = e (ju^[2TimJcT/n j (8) where e " iintnt rr^ a)± = S (2Jr+l) e ' y (9) r tTi Jr = spin of the r excited state. In the present study, temperatures are encountered at which the excited states of some nuclei become impor¬ tant, and these states are included in the statistical weights UK . The temperature dependent partition func¬ tions (partition function = statistical weight) of N. Bahcall and W. Fowler (1970) were used, viz. the approximate curve fittings of the form (in their notation) 7 GL = g? + K± exp(-a±/T9) , (10) r where , g? is the ground state partition function, and a^ are fitting constants. (See Table 1.) Equations (4), (5) and (8) relate the abundances of all species to the abundances of free neutrons and free protons, or, through these, to the abundances of any two chosen species. From equation (4) one has Vp + Niun = ui - Qi (ID Qi " (Zimp + Nimn - mi) °2 (12) and Z^ = atomic number of species i, ISL = neutron number, m = proton mass, m = neutron mass, and equation (12) Jr ** defines Q^, the binding energy of species i. Exponentiating equation (11), one obtains z.|i AT N.U AT U.AT -Q.AT e 1 p e 1 n = e 1 e 1 (13) From equation (8) one obtains expressions for the U±AT e , which when substituted in equation (13) yields 8 N. n z.
Load more

Recommended publications
  • R-Process Elements from Magnetorotational Hypernovae
    r-Process elements from magnetorotational hypernovae D. Yong1,2*, C. Kobayashi3,2, G. S. Da Costa1,2, M. S. Bessell1, A. Chiti4, A. Frebel4, K. Lind5, A. D. Mackey1,2, T. Nordlander1,2, M. Asplund6, A. R. Casey7,2, A. F. Marino8, S. J. Murphy9,1 & B. P. Schmidt1 1Research School of Astronomy & Astrophysics, Australian National University, Canberra, ACT 2611, Australia 2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia 3Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, AL10 9AB, UK 4Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 5Department of Astronomy, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden 6Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany 7School of Physics and Astronomy, Monash University, VIC 3800, Australia 8Istituto NaZionale di Astrofisica - Osservatorio Astronomico di Arcetri, Largo Enrico Fermi, 5, 50125, Firenze, Italy 9School of Science, The University of New South Wales, Canberra, ACT 2600, Australia Neutron-star mergers were recently confirmed as sites of rapid-neutron-capture (r-process) nucleosynthesis1–3. However, in Galactic chemical evolution models, neutron-star mergers alone cannot reproduce the observed element abundance patterns of extremely metal-poor stars, which indicates the existence of other sites of r-process nucleosynthesis4–6. These sites may be investigated by studying the element abundance patterns of chemically primitive stars in the halo of the Milky Way, because these objects retain the nucleosynthetic signatures of the earliest generation of stars7–13.
    [Show full text]
  • Concrete Analysis by Neutron-Capture Gamma Rays Using Californium 252
    CONCRETE ANALYSIS BY NEUTRON-CAPTURE GAMMA RAYS USING CALIFORNIUM 252 Dick Duffey, College of Engineering, University of Maryland; Peter F. Wiggins, Naval Systems Engineering Department, U.S. Naval Academy; Frank E. Senftle, U.S. Geological Survey; and A. A. El Kady, United Arab Republic Atomic Energy Establishment, Cairo The feasibility of analyzing concrete and cement by a measurement of the neutron-capture or prompt gamma rays was investigated; a 100-ug californium-252 source was used to supply the neutrons. A lithium drifted germanium crystal detected the capture gamma rays emitted. The capture gamma rays from cement, sand, and 3 coarse aggregates-quartzite gravel, limestone, and diabase--:were studied. Concrete blocks made from these materials were then tested. The capture gamma ray response of the calcium, silicon, and iron in the concrete blocks was in accord with the elements identified in the mix materials. The principal spectral lines used were the 6.42 MeV line of calcium, the 4.93 MeV line of silicon, and the doublet of iron at about 7 .64 MeV. The aluminum line at 7. 72 MeV was ob­ served in some cases but at a lower intensity with the limited electronic equipment available. This nuclear spectroscopic technique offers a possi­ ble method of determining the components of sizable concrete samples in a nondestructive, in situ manner. In addition, the neutron-capture gamma ray technique might find application in control of the concrete and cement processes and furnish needed information on production operations and inventories. • FROM THE point of view of the geochemical analyst, concrete may be considered as rock relocated and reformed at the convenience of the engineer.
    [Show full text]
  • Nuclear Astrophysics: the Unfinished Quest for the Origin of the Elements
    Nuclear astrophysics: the unfinished quest for the origin of the elements Jordi Jos´e Departament de F´ısica i Enginyeria Nuclear, EUETIB, Universitat Polit`ecnica de Catalunya, E-08036 Barcelona, Spain; Institut d’Estudis Espacials de Catalunya, E-08034 Barcelona, Spain E-mail: [email protected] Christian Iliadis Department of Physics & Astronomy, University of North Carolina, Chapel Hill, North Carolina, 27599, USA; Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA E-mail: [email protected] Abstract. Half a century has passed since the foundation of nuclear astrophysics. Since then, this discipline has reached its maturity. Today, nuclear astrophysics constitutes a multidisciplinary crucible of knowledge that combines the achievements in theoretical astrophysics, observational astronomy, cosmochemistry and nuclear physics. New tools and developments have revolutionized our understanding of the origin of the elements: supercomputers have provided astrophysicists with the required computational capabilities to study the evolution of stars in a multidimensional framework; the emergence of high-energy astrophysics with space-borne observatories has opened new windows to observe the Universe, from a novel panchromatic perspective; cosmochemists have isolated tiny pieces of stardust embedded in primitive meteorites, giving clues on the processes operating in stars as well as on the way matter condenses to form solids; and nuclear physicists have measured reactions near stellar energies, through the combined efforts using stable and radioactive ion beam facilities. This review provides comprehensive insight into the nuclear history of the Universe arXiv:1107.2234v1 [astro-ph.SR] 12 Jul 2011 and related topics: starting from the Big Bang, when the ashes from the primordial explosion were transformed to hydrogen, helium, and few trace elements, to the rich variety of nucleosynthesis mechanisms and sites in the Universe.
    [Show full text]
  • Iron Isotope Cosmochemistry Kun Wang Washington University in St
    Washington University in St. Louis Washington University Open Scholarship All Theses and Dissertations (ETDs) 12-2-2013 Iron Isotope Cosmochemistry Kun Wang Washington University in St. Louis Follow this and additional works at: https://openscholarship.wustl.edu/etd Part of the Earth Sciences Commons Recommended Citation Wang, Kun, "Iron Isotope Cosmochemistry" (2013). All Theses and Dissertations (ETDs). 1189. https://openscholarship.wustl.edu/etd/1189 This Dissertation is brought to you for free and open access by Washington University Open Scholarship. It has been accepted for inclusion in All Theses and Dissertations (ETDs) by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. WASHINGTON UNIVERSITY IN ST. LOUIS Department of Earth and Planetary Sciences Dissertation Examination Committee: Frédéric Moynier, Chair Thomas J. Bernatowicz Robert E. Criss Bruce Fegley, Jr. Christine Floss Bradley L. Jolliff Iron Isotope Cosmochemistry by Kun Wang A dissertation presented to the Graduate School of Arts and Sciences of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy December 2013 St. Louis, Missouri Copyright © 2013, Kun Wang All rights reserved. Table of Contents LIST OF FIGURES ....................................................................................................................... vi LIST OF TABLES ........................................................................................................................
    [Show full text]
  • Alpha Process
    Alpha process The alpha process, also known as the alpha ladder, is one of two classes of nuclear fusion reactions by which stars convert helium into heavier elements, the other being the triple-alpha process.[1] The triple-alpha process consumes only helium, and produces carbon. After enough carbon has accumulated, the reactions below take place, all consuming only helium and the product of the previous reaction. E is the energy produced by the reaction, released primarily as gamma rays (γ). It is a common misconception that the above sequence ends at (or , which is a decay product of [2]) because it is the most stable nuclide - i.e., it has the highest nuclear binding energy per nucleon, and production of heavier nuclei requires energy (is endothermic) instead of releasing it (exothermic). (Nickel-62) is actually the most stable nuclide.[3] However, the sequence ends at because conditions in the stellar interior cause the competition between photodisintegration and the alpha process to favor photodisintegration around iron,[2][4] leading to more being produced than . All these reactions have a very low rate at the temperatures and densities in stars and therefore do not contribute significantly to a star's energy production; with elements heavier than neon (atomic number > 10), they occur even less easily due to the increasing Coulomb barrier. Alpha process elements (or alpha elements) are so-called since their most abundant isotopes are integer multiples of four, the mass of the helium nucleus (the alpha particle); these isotopes are known as alpha nuclides. Stable alpha elements are: C, O, Ne, Mg, Si, and S; Ar and Ca are observationally stable.
    [Show full text]
  • Arxiv:1710.04254V5 [Astro-Ph.SR] 25 Jun 2019 Hr Xssawd Iest Nsei Se
    Accepted for publication in Astrophysical Journal Supplement, submitted on 19 September 2017, revised on 16 April 2018 Typeset using LATEX twocolumn style in AASTeX62 Explosive Nucleosynthesis in Near-Chandrasekhar Mass White Dwarf Models for Type Ia supernovae: Dependence on Model Parameters Shing-Chi Leung, Ken’ichi Nomoto1 1Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study The University of Tokyo, Kashiwa, Chiba 277-8583, Japan ABSTRACT We present two-dimensional hydrodynamics simulations of near-Chandrasekhar mass white dwarf (WD) models for Type Ia supernovae (SNe Ia) using the turbulent deflagration model with deflagration- detonation transition (DDT). We perform a parameter survey for 41 models to study the effects of the initial central density (i.e., WD mass), metallicity, flame shape, DDT criteria, and turbulent flame formula for a much wider parameter space than earlier studies. The final isotopic abundances of 11C to 91Tc in these simulations are obtained by post-process nucleosynthesis calculations. The survey includes SNe Ia models with the central density from 5 108 g cm−3 to 5 109 g cm−3 (WD masses × × of 1.30 - 1.38 M⊙), metallicity from 0 to 5 Z⊙, C/O mass ratio from 0.3 - 1.0 and ignition kernels including centered and off-centered ignition kernels. We present the yield tables of stable isotopes from 12C to 70Zn as well as the major radioactive isotopes for 33 models. Observational abundances of 55Mn, 56Fe, 57Fe and 58Ni obtained from the solar composition, well-observed SNe Ia and SN Ia remnants are used to constrain the explosion models and the supernova progenitor.
    [Show full text]
  • Abundance Gradients in the Milky Way for Α Elements, Iron Peak Elements, Barium, Lanthanum, and Europium
    A&A 462, 943–951 (2007) Astronomy DOI: 10.1051/0004-6361:20065403 & c ESO 2007 Astrophysics Abundance gradients in the Milky Way for α elements, iron peak elements, barium, lanthanum, and europium G. Cescutti1,F.Matteucci1,2,P.François3,4, and C. Chiappini2 1 Dipartimento di Astronomia, Universitá di Trieste, via G.B. Tiepolo 11, 34131 Trieste, Italy e-mail: [email protected] 2 I.N.A.F. Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, Italy 3 Observatoire de Paris/Meudon, GEPI, 61 avenue de l’Observatoire, 75014 Paris, France 4 European Southern Observatory, Casilla 19001, Santiago 19, Chile Received 10 April 2006 / Accepted 25 September 2006 ABSTRACT We model the abundance gradients in the disk of the Milky Way for several chemical elements (O, Mg, Si, S, Ca, Sc, Ti, Co, V, Fe, Ni, Zn, Cu, Mn, Cr, Ba, La and Eu), and compare our results with the most recent and homogeneous observational data. We adopt a chemical evolution model able to well reproduce the main properties of the solar vicinity. The model assumes that the disk formed inside-out with a timescale for the formation of the thin disk of 7 Gyr in the solar vicinity, whereas the halo formed on a timescale of 0.8 Gyr. We adopt new empirical stellar yields derived to best fit the abundances and the abundance ratios in the solar vicinity. We compute, for the first time, the abundance gradients for all the mentioned elements in the galactocentric distance range 4–22 kpc. Comparison with the observed data on Cepheids in the galactocentric distance range 5–17 kpc gives a very good agreement for many of the studied elements.
    [Show full text]
  • Cobalt and Copper Abundances in 56 Galactic Bulge Red Giants ? H
    Astronomy & Astrophysics manuscript no. 37869corr c ESO 2020 July 2, 2020 Cobalt and copper abundances in 56 Galactic bulge red giants ? H. Ernandes1; 2; 3, B. Barbuy1, A. Friaça1, V. Hill4, M. Zoccali5; 6, D. Minniti6; 7; 8, A. Renzini9, and S. Ortolani10; 11 1 Universidade de São Paulo, IAG, Rua do Matão 1226, Cidade Universitária, São Paulo 05508-900, Brazil 2 UK Astronomy Technology Centre, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK 3 IfA, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK 4 Université de Sophia-Antipolis, Observatoire de la Côte d’Azur, CNRS UMR 6202, BP4229, 06304 Nice Cedex 4, France 5 Universidad Catolica de Chile, Departamento de Astronomia y Astrofisica, Casilla 306, Santiago 22, Chile 6 Millennium Institute of Astrophysics, Av. Vicuna Mackenna 4860, 782-0436, Santiago, Chile 7 Departamento de Ciencias Fisicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Av. Fernandez Concha 700, Las Condes, Santiago, Chile 8 Vatican Observatory, V00120 Vatican City State, Italy 9 Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 10 Università di Padova, Dipartimento di Fisica e Astronomia, Vicolo dell’Osservatorio 2, I-35122 Padova, Italy 11 INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy ABSTRACT Context. The Milky Way bulge is an important tracer of the early formation and chemical enrichment of the Galaxy. The abundances of different iron-peak elements in field bulge stars can give information on the nucleosynthesis processes that took place in the earliest supernovae. Cobalt (Z=27) and copper (Z=29) are particularly interesting.
    [Show full text]
  • 56Ni, Explosive Nucleosynthesis, and Sne Ia Diversity
    56Ni, Explosive Nucleosynthesis, and SNe Ia Diversity James W Truran1,2, Ami S Glasner3, and Yeunjin Kim1 1Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA 2Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA 3Racah Institute of Physics, The Hebrew University, Jerusalem 91904, ISRAEL E-mail: [email protected] Abstract. The origin of the iron-group elements titanium to zinc in nature is understood to occur under explosive burning conditions in both Type Ia (thermonuclear) and Type II (core collapse) supernovae. In these dynamic environments, the most abundant product is found to be 56Ni ((τ = 8.5 days) that decays through 56Co (τ = 111.5 days) to 56Fe. For the case of SNe Ia, the peak luminosities are proportional to the mass ejected in the form of 56Ni. It follows that the diversity of SNe Ia reflected in the range of peak luminosity provides a direct measure of the mass of 56Ni ejected. In this contribution, we identify and briefly discuss the factors that can influence the 56Ni mass and use both observations and theory to quantify their impact. We address specifically the variations in different stellar populations and possible distinctions with respect to SNe Ia progenitors. 1. Introduction Dating back to the early work by Hoyle and Fowler [1], the ‘standard’ model for a Type Ia supernova has been assumed to involve the explosion of a carbon-oxygen (CO) white dwarf, with iron peak nuclei being a major product. The history of our understanding of supernova iron production began with Hoyle’s [2] identification of the nucleosynthesis mechanism with a “nuclear statistical equilibrium” process occurring at high temperatures and densities in stellar cores.
    [Show full text]
  • By Massive Stars
    The Alchemists or How the stars made the periodic table L. Sbordone And so it began Defines α-process, p- capture, s- and r- neutron capture, statistical equilibrium nucleosynthesis. 62 years later we are largely still there. Burbidge, Burbidge, Fowler & Hoyle 1957, a.k.a. “B2FH” And so it began Defines α-process, p- capture, s- and r- neutron capture, statistical equilibrium nucleosynthesis. 62 years later we are largely still there. Margaret Burbidge Burbidge, Burbidge, Fowler & turned 100 this year! Hoyle 1957, a.k.a. “B2FH” C,N, H He Li C,N, C,N,O α, Fe-peak, r-process H He Li C,N, C,N,O α, Fe-peak, r-process H He Li C,N, C,N,O α, Fe-peak, r-process C,N,O, light-odd, α, Fe- peak, r- process H He Li C,N, C,N,O α, Fe-peak, r-process C,N,O, light-odd, α, Fe- peak, r- process H He light-odd, Li s-process C,N, C,N,O α, Fe-peak, r-process C,N,O, light-odd, α, Fe- peak, r- process H Fe-peak He light-odd, Li s-process C,N, General concepts: nucleosynthesis • H, He, Li were synthesized in the high-temperature phase of early universe (BB Nucleosynthesis, 3 to 20 min after BB)… • … but almost 100% of everything else was synthesized in stars. • Stellar nucleosynthesis products are reintroduced in ISM at the end of the star life. New stars will be then born enriched of the product of previous generations. • What matters is not what the star makes, but what it can eject.
    [Show full text]
  • Stellar Nucleosynthesis
    21 November 2006 by JJG Stellar Nucleosynthesis Figure 1 shows the relative abundances of solar system elements versus atomic number Z, the number of protons in the nucleus. A theory of nucleosynthesis should explain this pattern. One believes, of course, that all but the lightest elements (Z > 4) are made in stars rather than the early universe, and primarily through nuclear fusion. Figure 1: Solar abundances by number, i.e. vertical axis is log(XZ /A¯Z ) + constant, where XZ is the abundance of element Z by mass and A¯Z is the mean atomic weight of that element. (C. R. Crowley, U Mich). It is clear that the pattern in Fig. 1 is not the result of thermal equilibrium: if it were, then iron ( 56Fe) would be the most abundant element since it is the most tightly bound. In fact, nuclear masses can be approximated by the semi-empirical mass formula [1] M(A, Z) = (A − Z)mn + Z(mp + me) 2 2 2/3 (A/2 − Z) Z δ − a1A + a2A + a3 + a4 + a5 . (1) A A1/3 A3/4 The coefficients have the following approximate values measured in MeV/c2: a1 − 15.53, a2 = 17.804, a3 = 94.77, a4 = 0.7103, a5 = 33.6. The first two terms on the righthand side represent the “free” rest masses of the neutron, 2 proton, and electron: mn ≈ 939.57, mp ≈ 938.27, me ≈ 0.511 MeV/c . The term in a1 represents an increase in the binding energy (i.e., decrease in nuclear mass) due to nearest- neighbor interactions between nucleons: to lowest order, nuclei are rather like drops of liquid, in which the interactions are very short range, and are attractive at low pressure but are strongly repulsive under compression; consequently, the liquid prefers to maintain 14 −3 a roughly constant density, which for nuclei is ρnuc ≈ 2 × 10 g cm , correponding to an 1 1/3 interparticle spacing a0 ≡ (3ρnuc/4πmp) ≈ 1.3 fm.
    [Show full text]
  • Iron-Peak Elements in the Solar Neighbourhood Š
    The AMBRE project: Iron-peak elements in the solar neighbourhood Š. Mikolaitis, P. de Laverny, A. Recio–blanco, V. Hill, C. C. Worley, M. de Pascale To cite this version: Š. Mikolaitis, P. de Laverny, A. Recio–blanco, V. Hill, C. C. Worley, et al.. The AMBRE project: Iron-peak elements in the solar neighbourhood. Astronomy and Astrophysics - A&A, EDP Sciences, 2017, 600, pp.A22. 10.1051/0004-6361/201629629. hal-03118590 HAL Id: hal-03118590 https://hal.archives-ouvertes.fr/hal-03118590 Submitted on 22 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A&A 600, A22 (2017) Astronomy DOI: 10.1051/0004-6361/201629629 & c ESO 2017 Astrophysics The AMBRE project: Iron-peak elements in the solar neighbourhood?,?? Š. Mikolaitis1; 2, P. de Laverny2, A. Recio–Blanco2, V. Hill2, C. C. Worley3, and M. de Pascale4 1 Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio˙ al. 3, 10257 Vilnius, Lithuania e-mail: [email protected] 2 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS_34229, 06304 Nice Cedex 4, France 3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 4 INAF–Padova Observatory, Vicolo dell’Osservatorio 5, 35122 Padova, Italy Received 1 September 2016 / Accepted 24 November 2016 ABSTRACT Context.
    [Show full text]