Principles and perspectives in cosmochemistry lecture notes of the kodai school on synthesis of elements in stars held at kodaikanal observatory india april 29 may 13 2008

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Principles and Perspectives
in Cosmochemistry
Lecture Notes of the Kodai School
on ‘Synthesis of Elements in Stars’ held
at Kodaikanal Observatory, India,
April 29-May 13, 2008

Aruna Goswami
Editor
Indian Institute of Astrophysics,
Bangalore, India

B. Eswar Reddy
Editor
Indian Institute of Astrophysics,
Bangalore, India

123


Editors
Aruna Goswami
Indian Institute of Astrophysics
2nd Block, Koramangala
Bangalore 560034

India


B. Eswar Reddy
Indian Institute of Astrophysics
2nd Block, Koramangala
Bangalore 560034
India


ISSN 1570-6591
e-ISSN 1570-6605
ISBN 978-3-642-10351-3
e-ISBN 978-3-642-10352-0
DOI 10.1007/978-3-642-10352-0
Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2010921800
c Springer-Verlag Berlin Heidelberg 2010
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Preface

The origin of elements is among the fundamental aspects of our universe;
cosmochemistry tries to answer when, how and where the chemical elements
arose after hydrogen was created during primordial nucleosynthesis following
the Big Bang. However, quantitative answers to these fundamental questions
began to emerge only in the late fifties, with the pioneering works of Burbidge, Burbidge, Fowler and Hoyle, and Cameron. Since then there had been
significant progress in the understanding of synthesis of elements in stars.
Cosmochemistry, however, remains a fertile area of research, as there
remain many outstanding problems. A comprehensive approach to cosmochemistry requires a combination of a number of topics like primordial
nucleosynthesis, stellar nucleosynthesis, explosive nucleosynthesis and solar
abundance. The Kodai school on ‘Synthesis of elements in stars’ was organized to provide a glimpse of this exciting area of research to astrophysicists
of tomorrow, motivated young students from India and abroad. The lectures
are thus aimed at researchers who would like to venture deeper into this exciting arena.
The school drew strength from considerable in-house expertise at IIA in a
number of areas critical for the school. A highlight of the school, however, was
the faculty participation by a number of leading astrophysicists from different
parts of the world.
Following a traditional and inspiring invocation from Upanishad and a
brief inaugural function, the school was opened for technical sessions. David
Lambert set the tone of the scientific sessions with the lead talk on ‘Synthesis
of elements in stars: an overview’. The basic properties of nuclei were explained by Arun Mangalam in a series of lectures. The lectures by C Sivaram
put the primary issue in cosmochemistry in perspective through a discussion
on cosmological nucleosynthesis of light elements. Aruna Goswami discussed
some current issues in the present understanding of the Galactic chemical
evolution. Gajendra Pandey explained how stellar spectra can be analyzed
using ‘Curve of growth technique’. Kameswara Rao of IIA talked about the
high resolution Echelle spectrograph at VBO, Kavalur and discussed some

results obtained from analysis of data acquired using this instrument. These


VI

Preface

lectures provided the background for the series of lectures by other speakers
that followed. Apart from the regular class room lectures, students had ample
time for hands-on sessions coordinated by Goswami, Reddy and Pandey.
The book has been organized into three parts to address the major issues
in cosmochemistry. Part I of the book deals with stellar structure, nucleosynthesis and evolution of low and intermediate-mass stars. The lectures by
Simon Jeffery outline stellar evolution with discussion on the basic equations,
elementary solutions and numerical methods. Amanda Karakas’s lectures discuss nucleosynthesis of low and intermediate-mass stars covering nucleosynthesis prior to the Asymptotic Giant Branch (AGB) phase, evolution during
the AGB, nucleosynthesis during the AGB phase, evolution after the AGB
and massive AGB stars. The slow neutron-capture process and yields from
AGB stars are also discussed in detail by Karakas. The lectures by S Giridhar
provide some necessary background on stellar classification.
Part II deals with explosive nucleosynthesis that plays a critical role in cosmochemistry. The lectures by Kamales Kar provide essential background material on weak-interaction rates for stellar evolution, supernovae and r-process
nucleosynthesis. He also discusses in detail the solar neutrino problem. Massive stars, their evolution and nuclear reaction rates from the point of view
of astronomers and nuclear physicists are discussed by Alak Ray. His lectures also describe the various stages of hydrostatic nuclear fuel burning with
illustrative examples of how the reactions are computed. He also discussed
core-collapse (thermonuclear vs. core-collapse) and supernovae in brief. The
lectures by Marcel Arnould address the phenomena of evolution of massive
stars and the concomitant non-explosive and explosive nucleosynthesis. He
highlights a number of important problems that are yet unresolved but crucial for our understanding of Galactic chemical evolution. The p-process nucleosynthesis attributed to the production of proton-rich elements, a topic of
great importance but yet less explored is also discussed in his lectures.
The third and the final part of the book addresses use of solar system abundances to probe cosmochemistry quantitatively. The lectures by Bruce Fegley
address cosmochemistry of the major elements; while the lectures by Katharina Lodders discuss elemental abundances in Solar, meteoritic and outside
the solar system.

Cosmochemistry is still an evolving branch of astrophysics, with many
challenges. The book is expected to serve as a contemporary reference material
for research in cosmochemistry. We would like to take this opportunity to
thank all the contributors for making this book a reality.

Bangalore,
April 2009

Aruna Goswami
B. Eswar Reddy


Acknowledgement
This school would not have been possible without the dedicated support of
many. We extend our sincere thanks to professor Siraj Hasan, Director, Indian Institute of Astrophysics and professor Vinod Krishan for their all round
support for the school.
We are particularly grateful to the school faculty from India and abroad
for readily accepting to participate, prepare lecture notes and spend time with
the students.
The organization of the school is a collective effort of the coordinators, the
convener, the members of the local organizing committee and many others. We
are thankful to the administrative department of IIA and the staff members of
Kodaikanal Solar observatory for their help and support in various activities
of the school.


Contents

Part I Stellar Structure, Nucleosynthesis and Evolution of Low
and Intermediate-mass Stars

Stellar Structure and Evolution: An Introduction
C. Simon Jeffery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Nucleosynthesis of Low and Intermediate-mass Stars
Amanda I. Karakas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Spectral Classification: Old and Contemporary
Sunetra Giridhar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Part II Massive Stars, Core Collapse, Explosive Nucleosynthesis
Weak Interaction Rates for Stellar Evolution, Supernovae
and r-Process Nucleosynthesis
Kamales Kar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Massive stars as thermonuclear reactors and their explosions
following core collapse
Alak Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
The Evolution of Massive Stars and the Concomitant
Non-explosive and Explosive Nucleosynthesis
Marcel Arnould . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Part III Cosmochemistry and Solar System Abundances
Cosmochemistry
Bruce Fegley, Jr., Laura Schaefer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Solar System Abundances of the Elements
Katharina Lodders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Cosmochemistry: A Perspective
Aruna Goswami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419


List of Contributors

C. Simon Jeffery
Armagh Observatory, College
Hill, Armagh ET61 9DG,
Northern Ireland

Amanda I. Karakas
Research School of
Astronomy & Astrophysics

Sunetra Giridhar
Indian Institute of Astrophysics,
Bangalore 560034, India

Kamales Kar
Saha Institute of Nuclear Physics,
Bidhannagar, Kolkata 700064, India

Alak Ray
Tata Institute of Fundamental
Research, Mumbai 400005, India

Marcel Arnould
Institut d‘Astronomie et
d‘Astrophysique, Universite‘
Libre de Bruxelles, CP-226,
B-1050 Brussels, Belgium


Bruce Fegley
Planetary chemistry Laboratory,

Department of earth and
planetary sciences, Washington
University, St. Louis,
MO63130-4899, USA


Laura Schaefer
Planetary chemistry Laboratory,
Department of earth
and planetary sciences, Washington
University, St. Louis,
MO63130-4899, USA
laura

Katharina Lodders
Planetary chemistry laboratory,
Department of earth and planetary
sciences and McDonnell centre
for the space sciences, Washington
University, Campus box,
1169, One Brookings Drive, Saint
Louis, MO63130, USA



School Faculty
Marcel Arnould
Institut d‘Astronomie et d‘Astrophysique,
Universite‘ Libre de Bruxelles, CP-226, B-1050 Brussels, Belgium

Bruce Fegley
Planetary chemistry Laboratory
Department of earth and planetary sciences, Washington University
St. Louis, MO63130-4899, USA

Sunetra Giridhar
Indian Institute of Astrophysics, Bangalore 560034, India

Aruna Goswami
Indian Institute of Astrophysics, Bangalore 560034, India

C. Simon Jeffery
Armagh Observatory, College Hill, Armagh ET61 9DG, Northern Ireland

Kamales Kar
Saha Institute of Nuclear Physics, Bidhannagar, Kolkata 700064, India

Amanda I. Karakas
Research School of Astronomy & Astrophysics

David L. Lambert
McDonald Observatory, University of Texas at austin, Austin

Katharina Lodders
Planetary chemistry laboratory
Department of earth and planetary sciences and McDonnell centre for the
space sciences
Washington University, Campus box, 1169, One Brookings Drive, Saint Louis,
MO63130, USA

School Faculty

Arun Mangalam
Indian Institute of Astrophysics, Bangalore 560034, India

Gajendra Pandey
Indian Institute of Astrophysics, Bangalore 560034, India

N. Kameswara Rao
Indian Institute of Astrophysics, Bangalore 560034, India

Alak Ray
Tata Institute of Fundamental Research, Mumbai 400005, India

Eswar Reddy
Indian Institute of Astrophysics, Bangalore 560034, India

C. Sivaram
Indian Institute of Astrophysics, Bangalore 560034, India


XIII


List of Participants
Tiago Mendes de Almeida
Cidade Universitaria, Sao Paulo-SP-Brazil
Sonam Arora

Department of Physics, Punjab University, India
Andrea Borch
Indian Institute of Astrophysics, Bangalore-560034, India
Bhavya B.
Department of Physics, CUSAT, Cochin, Kerala, India
R. S. Keerthi Chandar
Department of Physics, Bharathiar University, Tamil Nadu, India
K. Chandrashekhar
Indian Institute of Astrophysics, Bangalore-560034, India
Sukanta Deb
Department of Physics & Astrophysics, Delhi University, Delhi, India
Nandita Debnath
Department of Physics, Tezpur University, Napam, Sonitpur - 784028, Assam,
India
Thubstan Dorje
Indian Astronomical Observatory, Hanle, Leh-Ladakh, India
Krithika Dota
Department of Physics, Mumbai University, Mumbai, India
Koshy George
ISRO, Bangalore - 560017, India
Suruchi Goel
Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India
Gagan Gupta
Department of Physics, Panjab University, Chandigarh, India
Singh Abhishek Indrajit
University of Mumbai, Kalina Campus , Santa Cruz, Mumbai - 400098, India


List of Participants

Vishal Joshi
Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India
Devika Kamath
Department of Physics, Christ College, Bangalore - 560029, India
Sreeja S. Kartha
Indian Institute of Astrophysics, Bangalore - 560034, India
Chrisphin Karthick
ARIES, Manora Peak, Nainital - 263129, India
Rajwinder Kaur
Punjab University, Patiala, Punjab, India
Pranav Kumar
Department of Physics & Astrophysics, University of Delhi, Delhi, India
Blesson Mathew
Indian Institute of Astrophysics, Bangalore - 560034, India
Ritesh K. Mishra
Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India
Rana Nandi
SINP, Theory Division, 1/AF, Bidhannagar, Kolkata - 700064, India
H. S. Nataraj
Indian Institute of Astrophysics, Bangalore - 560034, India
Vinicius Moris Placco
Cidade Universitaria, Sao Paulo-SP-Brazil
Ananta C. Pradhan
Indian Institute of Astrophysics, Bangalore - 560034, India
Yogesh Prasad
Dept. of Physics, H.N.B. Garhwal University
Srinagar Garhwal- 246174, Uttarakhand, India
Ashish Raj
Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India

XV


XVI

List of Participants

N. G. Rudraswami
Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India
Krishna Prasad Sayamanthula
Indian Institute of Astrophysics, Bangalore - 560034, India
Arul Selvam
Department of Physics, Madurai Kamaraj University, Tamil Nadu, India
S. Sujatha
M P Birla Inst. of Fundamental Research, 43/1 Race Course Road
Bharatiya Vidya Bhavan Campus, Bangalore - 560001, India
Ramya Sethuram
Indian Institute of Astrophysics, Bangalore - 560034, India
Bharat Kumar Yerra
Indian Institute of Astrophysics, Bangalore - 560034, India


Part I

Stellar Structure, Nucleosynthesis and
Evolution of Low and Intermediate-mass Stars


Stellar Structure and Evolution:
An Introduction

C. Simon Jeffery
Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland, UK

Summary. The synthesis of new elements takes place inside stars. How do stars
evolve and distribute this creation to the universe at large? This article starts with
the observables that the theory of stellar evolution aims to reproduce, and gives a
quick overview of what that theory predicts (Sects. 2–3). It presents the equations
governing stellar structure and evolution (Sects. 4–6) and the physics of stellar interiors (Sects. 7–9). Approximate and numerical methods for their solution are outlined
(Sects. 10–11) and the general results of stellar structure and evolution are discussed
(Sects. 12–13). The structure and evolution of horizontal-branch stars, hydrogendeficient stars and other stellar remnants are also considered (Sects. 14–15).

Keywords: Stars: interiors – Stars: evolution – Stars: horizontal-branch –
Stars: AGB and post-AGB – HR and C-M diagrams – Equation of state –
Convection – Atomic Processes – Nucleosynthesis

1 Introduction
What are the stars? How do they shine? What are they made of? These
questions have challenged mankind ever since he began to explore the world
around him and appreciate the awesome splendour of the night sky. Just as
challenging are questions about what we ourselves are made of, and where we
come from. Only in the last hundred years have we started to find answers
that approach a coherent understanding of the universe we inhabit.
Fundamental to understanding the stars are measurements of distance and
brightness, colour and constancy. Any theory of what stars are and how they
behave must be able to explain these observations. Deeper insight is gained
from measurements of chemical composition and the relationships between
stars and the interstellar medium. The big story will show how elements are
manufactured by nuclear reactions deep inside the stars – nucleosynthesis –
and then transported to the stellar surface and into the interstellar medium.

A. Goswami and B.E. Reddy (eds.), Principles and Perspectives in Cosmochemistry,
Astrophysics and Space Science Proceedings,
DOI 10.1007/978-3-642-10352-0 1, c Springer-Verlag Berlin Heidelberg 2010


4

C. S. Jeffery
Table 1. The Sun
Mass:
M
Radius:
R
Surface gravity:
g
Effective temperature:
Teff,
Luminosity:
L
Surface hydrogen mass fraction: X
Surface helium mass fraction:
Y
Surface metal mass fraction:
Z
Age:
t

= 1.98892(25) × 1030 kg
= 6.9599(7) × 108 m
= 2.7397(5) × 102 m s−2

= 5770(6) K
= 3.826(8) × 1026 W
= 0.71
= 0.265
= 0.025
≈ 4.567 × 109 y

The object of these lectures is to explain the physics of stellar interiors,
to use this physics to make stellar models and hence to understand how stars
work and evolve. The lectures will demonstrate how models of stars are constructed, and explain how these models predict stars should evolve.
This article starts by introducing some of the fundamental observational
material (Sect. 2), and by providing an early preview of the stellar evolution
theory (Sect. 3). Fundamental timescales and the equations of stellar structure
and evolution are derived in Sects. 4–6. The micro-physics (equation of state,
opacity and nuclear physics) are discussed in Sects. 7–9. Some methods for
calculating approximate solutions and full numerical solutions are presented
(Sects. 10–11). Subsequent sections deal with the evolution of main-sequence
stars (Sect. 12), white dwarfs and supernovae (Sect. 13), horizontal-branch
stars (Sect. 14) and hydrogen-deficient stars (Sect. 15).
The text is based on a series of six lectures given at the 2008 Kodai School
on Synthesis of the Elements in Stars1 and on a more extended course given
in the University of St Andrews and Trinity College, Dublin over a period
of some twenty years. At Kodaikanal, the core material comprised four lectures. Two more advanced lectures covered horizontal-branch stars (Sect. 14)
and hydrogen-deficient stars (Sect. 15). Development of the core material was
originally drawn from several seminal texts [1, 2, 3, 4, 5, 6, 7, 8, 9]. Section 15
and parts of Sect. 14 are based on [10, 11].
Variables
In considering stellar structure, we will meet a number of quantities. The most
important are:
•

•
•
1

stellar mass M : often given in solar units M ,
stellar radius R: often given in solar units R ,
stellar luminosity L: often given in solar units L ,
Kodaikanal Observatory, Indian Institute of Astrophysics, 2008, April 29 - May
13.


Stellar Structure and Evolution

5

Table 2. Physical Constants: CODATA 2006
speed of light in vacuum
gravitational constant
Planck constant
electron charge
electron mass
proton mass
Avogadro’s number
atomic mass unit
Boltzmann constant
Stefan-Boltzmann constant
Radiation constant
Wien’s displacement constants

•

•
•
•

c
G
h
e
me
mp
NA
mu
k
σ
a
b
b

= 2.997 92458 × 108
= 6.674 28(67) × 10−11
= 6.626 068 96(33) × 10−34
= 1.602 176 487(40) × 10−19
= 9.109 382 15(45) × 10−31
= 1.672 621 637(83) × 10−27
= 6.022 141 79(30) × 1023
≡ 10−3 kg mol−1 /NA
= 1.380 6504(24) × 10−23
= 5.670 400(40) × 10−8
≡ 4σ/c
= λmax T = 2.897 7685(51) × 10−3

= νmax /T = 5.878 933(10) × 1010

m s−1
m3 kg−1 s−2
Js
C
kg
kg
mol−1
kg
J K −1
W m−2 K−4
[J m−3 K−4 ]
mK
Hz K−1

surface gravity g: a force measured in m s−2 ,
effective temperature Teff : usually given in degrees Kelvin.
mass-fractions of hydrogen X, helium Y and other elements Z, respectively,
and age t: usually given in years, millions (t6 ) or billions of years (t9 ).

The flux emitted from the surface of a star is the product of the stellar surface
area (4πR2 ) and emissivity per unit area assuming that the surface radiates
as a black body:
4
.
(1)
L = 4πR2 σTeff
where σ is the Stefan-Boltzmann constant. The surface gravity is simply given
by

g = GM/R2 ,
(2)
where G is the gravitational constant. The conservation equation for chemical
composition can be simply written
X + Y + Z = 1.

(3)

In situations where the abundances of individual elements or nuclides are
important (e.g. nuclear reaction rates), relative abundances by mass will be
given as xi , where i is either the atomic number, or denotes the nuclide in some
other distinct way. Values for the Sun are given in Table 1; errors on the last
digits are shown in parentheses. Table 2 provides constants used throughout
the text and enables many equations to be evaluated.

2 The Hertzsprung–Russell Diagram
The most important correlations amongst stellar properties are contained in
a type of diagram developed independently by Ejnar Hertzsprung and Henry


6

C. S. Jeffery

Fig. 1. Hertzsprung-Russell diagram: a plot of luminosity (absolute magnitude)
against the colours of the brightest stars ranging from the high-temperature bluewhite stars on the left side of the diagram to the low temperature red stars on
the right side. Original image by Richard Powell licensed for derivative works and
redistribution under the Creative Commons Attribution ShareAlike 2.5 License

Russell [12, 13, 14]. The original Hertzsprung–Russell (HR) diagram showed

the distribution of spectral type and absolute magnitude (or brightness) for
stars with known distances (Fig. 1). The latter is required to convert an apparent brightness (e.g. mV ) to an absolute magnitude (MV ). The diagram
demonstrates that stars do not appear with any combination of spectral type
and brightness, but fall on well-defined sequences, e.g. the main sequence, the
giant branch, the white dwarfs, and so on.
A more convenient form is the colour – magnitude diagram, in which either
an apparent or absolute magnitude is plotted against a photometric colour
index, being the ratio of brightness at one wavelength to that at another.
Such a diagram is particularly useful for comparing the properties of stars in
a cluster, which may be assumed to lie at approximately the same distance.
The additional supposition that all stars in a cluster are of the same age has


Stellar Structure and Evolution

7

Fig. 2. Colour-magnitude diagram for the young galactic open clusters NGC 869
and NGC 884 (=h and χ Persei; based on [15])

important consequences for understanding stellar evolution – although the
supposition may not always be correct!
Wien’s displacement law states that there is a relation between the temperature of a black body and the wavelength at which the maximum energy
is emitted: λmax = b/T . From this it was recognised that there should be a
connection between the colour of a star and its effective (or surface) temperature. With a theory of stellar atmospheres, the relationship between spectral
type, colour index and effective temperature became concrete. In addition, a
correction to account for light emitted at unobserved wavelengths allows the
apparent visual magnitude to be converted to a bolometric magnitude, and
hence to luminosity. The use of an effective temperature – luminosity diagram
is common in theoretical work (cf. Fig. 8). It is important to recognise and

understand the connections and differences betweet earlier epochs. At later times, a QSE cluster
involving lighter nuclei develops, and all the clusters finally merge to lead to a
Nuclear Statistical Equilibrium (NSE) state.2 This regime has been described
in detail by e.g. [17], and is not reviewed here. Let us simply say that the
2

Note that weak interaction processes remain out of equilibrium as long as neutrinos are not equilibrated with matter and radiation. This is the case as long as
the density remains lower than about 1011 g/cm3 . At higher densities, a state of
so-called complete equilibrium is obtained.


Massive Stars Evolution and Nucleosynthesis

287

(p, g )39K(p, g )40Ca

(g , p)35Cl(g , p)34S(a, g )38Ar

(a, g )36Ar

(a, p )39K↑

(a, g )42Ca

(n, g )37Ar(n, a)34S↑

(16O, p)31P

(p, a)28Si(a, g )32S

(a, p )35Cl↑

(p, g )32S↑

(n, g )33S(n, a)30Si(a, g )34S↑

(g, p)30Si↑
(g , n)30Si↑
16

O

(16O, a)28Si↑
(g, p)30P( g , p )20Si
(16O, n)31S
(b +)31P↑

(a, n)32S↑

Fig. 7. The main reactions involved in the O burning in the core of massive stars
(here a Population I 25 M star). The reverse reactions of the underlined ones may
be activated at some point during the burning (from [15])


288

Marcel Arnould

30

z

20

10

0

0

5

10

15

20
N

25

30

35

40

Fig. 8. Illustration of the development of two QSE clusters during Si burning at
3.5 × 109 K in a Population I 25 M star (from [15])

abundances are obtained simply by solving a set of nuclear Saha equations
under the constraint of mass conservation and electrical neutrality. The resulting abundances do not depend on reaction rates, but only on temperature,
nuclear binding energies, nuclear partition functions and neutron excess. As
in the case of the QSE regime, the NSE abundances are subjected to time
variations as a result of temperature and neutron excess changes. In any case,
the NSE conditions favour the production of the most stable, that is the iron
peak, nuclides. The iron core represented in Fig. 1 results.
In the framework of stellar evolution models, Si burning has often been
approximated in different ways relying on the QSE cluster concept. These
approximations are not fully appropriate, particularly in view of the time
dependence of the QSE cluster boundaries. This has been stressed by [15] who
adopt instead for the QSE and NSE regimes a detailed Si-burning network
coupled to the stellar evolution equations.


Massive Stars Evolution and Nucleosynthesis

289

4 The explosive fate of massive stars
As said in Sect. 2, the iron core left over following Si burning suffers a dynamical instability as a result of endothermic electron captures and Fe photodidintegration. To a first approximation, this gravitational instability sets in near
the classical Chandrasekhar mass limit for cold white dwarfs, MCh = 5.83 Ye2 ,
Ye being the electron mole fraction. In the real situation of a hot stellar core,
collapse may start at masses that differ somewhat from this value, depending
on the details of the core equation of state. The reader is referred to [18]
(especially Chaps. 12 and 13) for a detailed discussion of the implosion mechanism and for its theoretical outcome and observable consequences. Here, we
just briefly summarise the situation.
The gravitational collapse of the iron core does not stop before the central
densities exceed the nuclear matter density ρ0 ≈ 2.5 × 1014 g cm−3 by about

a factor of two. At this point, the innermost (M <
∼ 0.5 M ) material forms
an incompressible, hot and still lepton-rich ‘proto-neutron’ star (PNS) whose
collapse is stopped abruptly, and which eventually bounces. A shock wave
powered by the gravitational binding energy released in the collapse propagates supersonically into the infalling outer layers. For many years, it has been
hoped that this shock could be sufficiently strong for ejecting explosively most
of the material outside the core, producing a so-called ‘prompt core collapse
supernova’ (PCCSN) with a typical kinetic energy of 1–2 × 1051 ergs, as observed. The problem is that the shock is formed roughly half-way inside the
iron core, and looses a substantial fraction of its energy in the endothermic
photodisintegrations of the iron-group nuclei located in the outermost portion
of the core. The shock energy loss is aggravated further by the escape of the
neutrinos produced by electron captures on the abundant free protons in the
shock-heated material. Detailed one-dimensional hydrodynamic simulations
conclude that the initially outgoing shock wave transforms within a few milliseconds after bounce into an accretion shock. The matter behind the shock
continues to accrete on the PNS. No recent simulation is able to predict a
successful PCCSN for a Fe-core progenitor star (M >
∼ 10 M ). This failure
is illustrated in Fig. 9 for a 15 M star.
Even so, some hope to get a CCSN of a non-prompt type has been expressed if there is a way to ‘rejuvenate’ the shock efficiently enough to obtain
an explosive ejection of the material outside the PNS. This rejuvenation remains a matter of intensive research. Neutrinos might well play a pivotal
role in this matter. They are produced in profusion from the internal energy
reservoir of the PNS that cools and deleptonises hundreds of milliseconds after bounce, and their total energy might amount to several 1053 ergs, that is
about 100 times the typical explosion energy of a SN II. The deposition of
a few percent of this energy would thus be sufficient to unbind the stellar
mantle and envelope, and provoke a ‘delayed’ CCSN (DCCSN) (these qualitative statements assume that a black hole is not formed instead of a PNS;
see below). Many attempts to evaluate the precise level of neutrino energy


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Marcel Arnould

104

radius [km]

103

102

101

100

0.0

0.2

0.4
0.6
time [s]

0.8

1.0

Fig. 9. Radial trajectories of several mass elements of the core of a 15 M star
versus time after bounce. The trajectories are plotted for each 0.02 M up to 1 M ,
and for each 0.01 M outside this mass. The thick dashed line indicates the location
of the shock wave. The prompt shock stalls within 100 ms after reaching 150 km,

and recedes down to below 100 km. No sign of a revival of the shock that possibly
leads to a successful D(elayed-)CCSN is seen either, even after 300 ms. Instead,
a stationary accretion shock forms at several tens of km. A PNS is seen to form,
reaching 1.6 M around 1 s after bounce (from [19])

deposition have been conducted over the last decades, based on more or less
controversial simplifications of the treatment of the neutrino transport (e.g.
[20] for a recent re-analysis of the problem, which is made even more complex by the due consideration of neutrino flavor mixing). In fact, theoretical
investigations and numerical simulations performed with increasing sophistication over the past two decades have not been able to come up with a clearly
successful CCSN for a Fe-core progenitor (M >
∼ 10 M ). This conclusion is
apparently robust to changes in the highly complex physical ingredients (like


Massive Stars Evolution and Nucleosynthesis

291

the neutrino interactions, or the equation of state), and in the numerical techniques (e.g. [20]). In fact, the neutrino-energy deposition should have to be
significantly enhanced over the current model values in order to trigger an
explosion. An illustration of a failed DCCSN is shown in Fig. 9.

Fig. 10. Simulation of an electron-capture supernova following the collapse of an
O-Ne core. The time evolution of the radius of various mass shells is displayed with
the inner boundaries of the O+Ne, C+O and He shells marked by thick lines. The
inner core of about 0.8 M is mainly made of Ne at the onset of collapse ( [21], and
references therein). The explosion is driven by the baryonic wind caused by neutrino
heating around the PNS. The thick solid, dashed, and dash-dotted lines mark the
neutrino spheres of νe , ν¯e , and heavy-lepton neutrinos, respectively. The thin dashed
line indicates the gain radius which separates the layers cooled from those heated by

the neutrino flow. The thick line starting at t = 0 is the outward moving supernova
shock (from [22])

This adverse circumstance may not mark the end of any hope to get a
DCCSN, however. In the case of the single stars considered here, one might
just have to limit the considerations to the stars in the approximate 9 to 10
M range that possibly develop O-Ne cores instead of iron cores at the termination of their hydrostatic evolution. Efficient endothermic electron captures
could trigger the collapse of that core, which could eventually transform into
a so-called electron-capture supernova that may be of the SN Ia or SN II