Supernovae and Nucleosynthesis [1 ed.] 0691011486, 0691011478

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David Arnett

SUPERNOVAE AND NUCLEOSYNTHESIS An Investigation of the History of Matter, from the Big Bang to the Present

PRINCETON UNIVERSITY PRESS

Princeton, New Jersey

Copyright © 1996 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, Chichester, West Sussex

All Rights Reserved Ubrary of Congress Cataloging-in-Publication Data Arnett, David, 1940Supernovae and nucleosynthesis : an investigation of the history of matter, from the big bang to the present I David Arnett. p. cm.-(Princeton series in astrophysics) Includes bibliographical references and index. ISBN 0-691-01148-6 (alk. paper).-ISBN 0-691-01147-8 (pbk. : alk. paper) 1. Cosmology. 2. Stars-Evolution. 3. Supernovae. 4. Nucleosynthesis. 5. Nuclear Astrophysics. I. Title. II. Series. QB981.A66 1996 523.1-dc20 95-41534 CIP

This book has been composed in Times Roman Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton Academic Press 1 3 5 7 9 10 8 6 4 2 13579108642 (pbk.)

Contents

List of Figures

xi

List of Tables

xv

Preface

xvii

1 Introduction

1

2 Abundances of Nuclei

4

2.1 2.2 2.3 2.4 2.5 2.6

What Are Abundances? Solar System Abundances Stellar Atmospheres Meteorites Cosmic Rays Other Aspects

7 10 17 31 39 44

3

Some Aspects of Nuclear Physics 3.1 Nuclear Masses 3.2 Nuclear Stability 3.3 Coulomb Barrier 3.4 Resonances 3.5 Reverse Rates 3.6 Heavy-Ion Reactions 3.7 Weak Interactions in Nuclei 3.8 Sources of Rates

4

Nuclear Reaction Networks 4.1 Network Equations 4.2 Solutions: Steady State 4.3 Solutions: Equilibria 4.4 Solutions: General Method 4.5 Energy Generation 4.6 Mixing and Hydrodynamics 4.7 Freezeout

92 93 96 99 102 108 113 116

5

Cosmological N ucleosynthesis 5.1 Kinematics 5.2 Radiation and Particles 5.3 Weak Interaction Freezeout 5.4 Cosmological Nucleosynthesis 5.5 Further Implications

118 119 128 134 138 143

6

Some Properties of Stars 6.1 Stellar Evolution Equations 6.2 Standard Model

146 147 153

48 49 57 62 69 73 75 84 90

viii

CONTENTS Nuclear Energy Neutrino Processes Stellar Energy Ignition Masses Final States

161 165 169 174 178

Hydrogen-Burning Stars 7.1 Birth of Stars 7.2 Burning Processes 7.3 Main Sequence 7.4 Convective Cores 7.5 Shell Burning 7.6 Nucleosynthesis

182 183 185 190 196 202 211

6.3 6.4 6.5 6.6 6.7

7

8.1 8.2 8.3 8.4

Thermonuclear Features Ignition Core Nucleosynthesis Shell Nucleosynthesis 8.5 M-Ma Relation 8.6 Implications

222 223 229 233 239 241 247

Explosive Nucleosynthesis 9.1 Parameters 9.2 Carbon and Neon 9.3 Oxygen 9.4 Silicon and e-Process 9.5 Neutron Excess and Galactic Evolution 9.6 Yield Puzzle

249 250 253 260 267 275 277

8 Helium-Burning Stars

9

10 Neutrino-Cooled Stars 10.1 Neutrinos and Convection 10.2 Core Evolution 10.3 Stellar Structure 10.4 Shell Nucleosynthesis

284 285 292 298 311

11 Thermonuclear Explosions 11.1 Thermonuclear Flames 11.2 Degenerate Instability 11.3 Convection and U rca 11.4 Yields from Degenerate Instability 11.5 He Detonation 11.6 Pair Instability 11.7 Oxygen Burning and Beyond

324 325 333 342 355 365 372 375

12 Gravitational Collapse 12.1 Historical Overview 12.2 Neutronization and Dissociation 12.3 Neutrino Trapping

381 382 385 389

CONTENTS 12.4 Collapse 12.5 Bounce 12.6 Ejection of Matter

13 Supernovae 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8

An Overview Shock Emergence Expansion and Radiative Diffusion Radioactive Heating Recombination SN1987A Type II Supernovae and SN1993J Type I Supernovae

14 Galactic Evolution 14.1 14.2 14.3 14.4 14.5 14.6 14.7

Galactic Evolution Equations Initial Mass Functions One-Zone Models Absolute Yields The Galactic Disk Primordial Stellar Yields Critical Uncertainties

ix

392 395 407

414 415 417 421 424 429 436 444 451

459 460 467 484 491 497 501 512

Appendixes A

Solar System Abundances

519

A.1 Tables A.2 Notes: H to Kr A.3 Notes: Rb to U

519 524 531

B Equations of State B.1 Coulomb Interactions B.2 Integrals B.3 Photon Gas B.4 Fermi-Dirac Gas B.5 Equilibria B.6 Urca Rates

532

C Stellar Structure

548

C.1 Polytropes C.2 Gravitational Binding C.3 Energy Generation

532 533 534 535 539 540 549 552 555

D Supernova Light Curves D.1 Simple Cooling D.2 Heating

558

References

573

Index

595

558 567

28

ABUNDANCES OF NUCLEI

Typical Curves of Growth 2 Damping

Log a = -

1

o

-1

Linear Region

-2~~~~~~~~~~~~~~~~~~~~~~~~~

-2

-1

o

2

3

4

5

6

7

Log (cW.,/r..v)

Fig. 2.7. Curves of Growth

abundance (horizontal axis value) can be inferred. Unless the line width is narrow enough to be in the linear region, the determination of the curve of growth requires a determination of the Doppler broadening (value of log a in figure 2.7), which is an additional complication. It also requires either (1) a choice among theoretical models to determine the shape of the curve, or alternatively (2) a choice of an empirical reference curve of growth for estimating relative abundances between stars of similar atmospheres. It is the product Nf which is determined observationally. To find N requires that the oscillator strength be known. A revision of f -values for Fe led to an increase (by a factor of five to ten) in the determined values of the iron abundance in the solar photosphere [262, 273, 413], bringing them into agreement with meteoritic values. Prior to the revision the values were thought to be well known, and an unresolved discrepancy existed between the solar and the meteoritic determinations. Although we hope that such large revisions will no longer need to occur, it illustrates yet another difficulty in the thorny problem of stellar abundance determination. A difficulty arises when this procedure is applied [701]; the measured equivalent widths are larger than they should be. Struve and Elvey [594] attributed the additional width to nonthermal motion in the stellar

2.3

STELLAR ATMOSPHERES

29

atmosphere and called it microturbulence because the velocities must vary only on a small spatial scale. Worrall and Wilson [701] criticized the use of microturbulence as an adjustable parameter not based upon a correct physical model. In particular, they argue that it incorrectly compensates for non-LTE effects. Pagel [478] countered that while there are difficulties on the fiat (saturated) part of the curve of growth, these do not necessarily extend to the linear and square-root (damping) branches. Further, LTE gives an excellent approximation to the visible continuum in all but supergiants and the very hottest stars. Nevertheless, difficulties of this sort have spurred efforts to build more realistic procedures (see [671]). If differential coarse analysis (as devised by Greenstein and collaborators) is used-that is, equivalent widths of weak lines are compared with those in a standard star of otherwise similar properties-many uncertainties should divide out. Such relative determinations are less prone to error than absolute ones. Of course there may be difficulty in obtaining a sufficient range of standard stars. Several important results were obtained by this method. Greenstein [272] summarized them as follows: (a) in no star is X Fe = 0, even if [Fe] ~ -2.5 to - 3; (b) even if the ratio of a-particle nuclei to iron to heavy s-process elements is variable,3 the factors seldom exceed ten, i.e., [a-nuclei]-[Fe] :::: +1 and [s-process] - [Fe] :::: -0.5; (c) in unevolved stars, the range of [H/He] is less than 0.3, with values perhaps near 0.1. Recent reviews suggest that these conclusions are still intact; see [376, 680]. However, in 1969, Unsold [644]-one of the pioneers of stellar spectroscopy and founder of the Kiel school-made an interesting critique of the results 4 obtained at that time. In a slightly paraphrased form, his points were: (1) the proposed abundance differences were mostly the same order of magnitude as the average error of analysis; (2) since a star highly deficient in metals (HD 140283, analyzed by Baschek [80]) shows no such effects, why should these effects be large in stars that are less deficient in heavy elements (more like solar)? And, (3) it is remarkable that the observed deficiency is the same for carbon, members of the iron group, and heavy elements like strontium and barium, and shows no relation to the various types of nuclear effects described. s Unsold did not doubt that nuclear reactions are the source of stellar energy. Merrill's discovery [428] in 1952 of technetium in S stars (the most stable isotope 3See 4See in stars, 5 See

chapter 14. Wallerstein [662] for a summary of the astronomical evidence for nucleosynthesis as known then. chapter 14.

11.4 YIELDS FROM DEGENERATE INSTABILITY

363

for a time TO at constant conditions. If the matter expands and cools, less burning occurs. This must be compensated for by a shorter TO (more vigorous burning). Using dIn Yo/dt ~ (a/3)d In pf dt , we estimate that this occurs for TO ~ 0.1 (d In P/ dt) -1. Hydrodynamic times of the order of 0.1 s are typical of such explosions [49, 619]; TO ~ 0.01 s occurs for P = 1.2 X 107 g cm". This is close to the value found by direct hydrodynamic calculations of the deflagration model (see figure 5 in [619]). In a detonation, the transition occurs at a similar density [331, 349]. Both the deflagration model and the delayed detonation model utilize the same physical effect to preserve a layer of intermediate mass elements at the outer edge of the exploding object. These arguments are also relevant to detonation in sub-Chandrasekhar mass white dwarfs (see §11.5). For an n = 3 polytropic structure, 80 percent of the mass lies inside a radius at which the density is 6 percent of the central value. If we want the outer 20 percent of the degenerate object to avoid oxygen burning, this implies a central density of, roughly, Pc :s 2 x 108 g cm". The gravitational binding energy B of a white dwarf of mass M is (11.43) for Pc ~ 109 g ern>', where (B/ M)1 = 2.46 X 1017 erg g-l and PI = 2.7 X 107 g em -3. For smaller central densities, direct numerical evaluations are required. To reduce the central density from the value at ignition (Pc ~ 3 x 109 g cm") to the value that would allow an outer layer of intermediate mass elements, (Pc ~ 2 x 108 g cm"), requires about 1.5 x 1050 erg. This could be supplied by burning 0.15Mo of 12C to Ne and Mg; more energy would be needed if Urea or other losses were important. If this could happen during the epoch between ignition and flashing, it would provide another path to an acceptable explosion. Suppose that a parcel of matter does burn to form carbon-flash matter. How will it interact in an environment of unburned matter? An attempt to answer this question leads to a discussion of laminar flames [690, 622, 352, 399, 53]. Suppose the matter is in pressure equilibrium, and initially at rest. The hot matter will heat its surroundings, primarily by electron conduction of thermal energy. As the new fuel is heated it begins to burn, heating still more. If this new heat can be balanced by loss by conduction, then a stable flame front is at least possible. Consider a layer of width Sr, area A, and mass Sm = ApSr. The rate of energy release by burning is Sme = Ap Sre, while the cooling rate is FA, where the heat flux is F = -¥daT 4/dr. The temperature of the burned matter is much larger than for unburned matter, so F ~ ¥aT~flash/ Sr. Notice the different dependence of heating and

364

THERMONUCLEAR EXPLOSIONS

cooling upon the width of the zone. Reducing t::..r enhances cooling over heating. High heating rates demand small widths for balanced cooling. For K = 10- 3 em? g, P = 1.6 X 109 g cm", TCflash = 7 X 109 K, and 6cm is the zoning needed E = 1.2 X 1030 erg g-l, this implies t::..r ~ 5 x 10to resolve the burning front. Direct numerical calculation of such a front, using the physics in an old paper of Arnett [21], gives a propagation velocity of vflarne ~ 270 km S-l. This is less than a factor of three above the recent value of Timmes and Woosley [620], and is similar to that of Khokhlov [352]. Evidently such values are not controversial. For comparison, the sound speed is about 8 x 103 km s:': the flame motion is quite subsonic. The flame is a surface which grows to enclose more volume. A sphere is that geometrical shape which has a minimal surface area relative to its volume. The rate of increase in volume is proportional to the velocity of the flame and to the area of the surface. This will be increased if the surface is distorted, resulting in a faster rate of burning of matter. Numerical experiments by Muller and Arnett [445, 446] indicated that a spherical flame would be subject to instabilites with large length scales. Woosley [690] developed an ingenious scenario in which the crinkling of the flame front is assumed to be of a fractal nature, and gives a slow onset of burning which accelerates into an explosion. This ameliorates the electron capture problem by a stage of subsonic expansion prior to most of the burning. Thus we return to the flame problem discussed earlier. Could it be that the presence of intermediate mass elements in SNla is not a clue about the nature of the burning front, but about the geometry of the initial star? Steinmetz, Muller, and Hillebrandt [589] conducted a set of numerical experiments to investigate whether rotational flattening of a white dwarf could "tame" a detonation by allowing incompletely burned matter to be ejected. This is particularly relevant to scenarios in which the exploding white dwarf is in a binary. Their conclusion was that it is impossible to reproduce the desired 56Ni production in detonation models, whether they involve rapid rotation or off-center ignition. Thus we are still left with the question of how the ignition evolves to an explosion.

11.5 HE DETONATION

We have explored the idea that some supernova explosions involve carbon ignition under conditions of extreme electron degeneracy, with the burning initiated by the approach to the Chandrasekhar limiting mass.