Download X-ray emission from supernova shock waves Tanja Kramer Nymark Department of Astronomy

X-ray emission from supernova
shock waves
Tanja Kramer Nymark
Department of Astronomy
Stockholm University
Cover image:
Composite image of the supernova remnant Cassiopeia A in infrared, optical
and X-ray emission. This is the remnant of the last supernova which exploded
in our galaxy in about 1670. The image is a composite of images from
NASAs spaceborne telescopes Spitzer (infrared), Hubble (optical) and
Chandra (X-rays).
Image credit: NASA/StSci
c Tanja Kramer Nymark, Stockholm 2007
ISBN 91-7155-377-0
Universitetsservice, US AB, Stockholm 2007
Department of Astronomy, Stockholm University
Doctoral Dissertation 2007
Stockholm Observatory
Department of Astronomy
SE-106 91 Stockholm
Abstract
A theoretical study of the interaction between supernovae and their surroundings is presented. Supernovae are the endpoint of the life of massive stars, and
are the dominant contributors to the chemical evolution of the Universe. During its life a massive star greatly modifies its environment. During and after
the explosion of the star it interacts with its surroundings in a number of ways.
A study of this interaction yields invaluable information about the late stages
of stellar evolution and the physics of supernova explosions. Recent advances
in observational facilities have given a wealth of observational data on interacting supernovae, and it is therefore essential to have good theoretical models
for interpreting the data.
This thesis presents an overview of the physics of supernovae and of their
interaction with a circumstellar medium. In particular the reverse shock created by the interaction is investigated. In most Type IIL and Type IIn supernovae this shock is radiative, and due to the high temperature most of the
radiation comes out as X-rays. A numerical model is presented which calculates the emission from the cooling region behind the reverse shock in a selfconsistent way, by combining a hydrodynamic model with a time-dependent
ionization balance and multilevel calculations. This has been applied to some
of the best cases of circumstellar interaction.
As a further application of the model the radio and X-ray emission from
Type IIP supernovae is discussed. We estimate the mass loss rate of the progenitors of Type IIP supernovae, and find that a superwind phase is not required.
VLT observations of the ring of SN 1987A show broad optical emission
lines coming from a range of ionization stages, in particular optical coronal
lines of [Fe X - XIV]. Models of the line emission indicate that the lines are
formed by cooling shocks with shock velocities in the range 310−390 km s−1 ,
confirming the picture of shocks striking the protrusions from the ring obliquely.
X-ray observations of the Type IIb SN 1993J and Type IIn SN 1998S are
analyzed. For SN 1993J we find that the spectrum is best fit with a CNOenriched composition. For SN 1998S we find that the high metal overabundance that has previously been claimed, is not necessary when a self-consistent
model of the cooling region is applied.
For Raymond
List of Papers
This thesis presents a study of the interaction between supernovae and the circumstellar medium. It consists of two parts. The first part gives an introduction
to supernovae in general, and to circumstellar interaction. Here I also present
a short description of the numerical model which we have developed, and the
results we have obtained. The second part consists of reprints and preprints of
the following four scientific publications, which are referred to in the text by
their Roman numerals.
I
II
III
IV
T. K. Nymark, C. Fransson, and C. Kozma 2006, “X-ray emission
from radiative shocks in type II supernovae”, A&A, 449, 171
R. A. Chevalier, C. Fransson, and T. K. Nymark 2006, “Radio
and X-ray emission as probes of type IIP supernovae and red supergiant mass loss”, ApJ, 641, 1029
P. Gröningsson, C. Fransson, P. Lundqvist, T. Nymark, N.
Lundqvist, R. Chevalier, B. Leibundgut, and J. Spyromilio
2006, “Coronal emission from the shocked circumstellar ring of
SN 1987A”, A&A, 456, 581
T. K. Nymark, P. Chandra, and C. Fransson 2006, “Modeling the
X-ray emission of SN 1993J and SN 1998S”, A&A, to be submitted
Reprints were made with permission from the publishers.
Contents
1
Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
2
3
3
2
Supernovae
2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Classification of supernovae . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Stellar Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Low mass stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 High mass stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 After the explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Supernova remnants . . . . . . . . . . . . . . . . . . . . . . . . . .
5
5
6
7
10
11
13
16
17
3
Circumstellar interaction
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Stellar winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Shocks in different environments . . . . . . . . . . . . . . . .
3.2 Physical scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Observational evidence for circumstellar interaction . . . . . . . .
3.3.1 SN 1987A (Type IIpec) . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 SN 1993J (Type IIb) . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 SN 1998S (Type IIn) . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Type IIP SNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
19
19
20
23
24
27
29
30
32
33
4
The model
4.1 Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Stationary flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Heat conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Radiative transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
35
35
36
36
36
36
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculating the emission . . . . . . . . . . . . . . . . . . . . . .
Atomic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fitting observed spectra . . . . . . . . . . . . . . . . . . . . . . .
37
38
39
40
41
5
Summary of the papers
5.1 Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Corrections to the atomic data . . . . . . . . . . . . . . . . . . . . . . . .
43
43
44
44
45
45
6
Future prospects
6.1 Multi-dimensional hydrodynamics . . . . . . . . . . . . . . . . . . . . .
6.2 Supernova remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Other projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Future observational facilities . . . . . . . . . . . . . . . . . . . . . . . . .
49
49
49
50
50
Svensk sammanfattning
51
Acknowledgements
55
Publications not included in this thesis
57
Bibliography
59
List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Classification scheme for supernovae . . . . . . . . . . . . . . . . . . .
Hertzsprung-Russell diagram . . . . . . . . . . . . . . . . . . . . . . . . .
Evolutionary tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Element distribution in the supernova progenitor . . . . . . . . . .
Exploding red supergiant . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cygnus loop supernova remnant . . . . . . . . . . . . . . . . . . . . . . .
Supernova light curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
8
9
14
15
15
17
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Temperature and density behind shock . . . . . . . . . . . . . . . . . .
The structure of a shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Density structure in the 4H47 model . . . . . . . . . . . . . . . . . . . .
Interaction of supernova ejecta with the progenitor wind. . . . .
Instabilities in the interaction region . . . . . . . . . . . . . . . . . . . .
Relation between peak radio luminosity and the time of the peak
HII-region around SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . .
The rings of SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
22
25
26
27
28
30
31
4.1
The structure of the code . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
5.1
5.2
5.3
Comparison of cooling and single-temperature spectra . . . . . . 44
Spectral fit for SN 1993J . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Spectra of cooling shocks with and without errors in Fe-emission 47
1
1
Introduction
Few subjects fascinate mankind like astronomy. Standing under the stars on a
dark night, the sheer immensity of space takes our breath away, and awakens
the desire to know more - the questions are as innumerable as the stars themselves. What are the stars? How far away are they? Do they ever change? How
big is space? Since the earliest times the night sky has been an object of speculation, fantasy and investigation, which makes astronomy one of the oldest
sciences. The regularity of the diurnal and annual motion of the sky made it a
perfect tool for time-keeping and navigation, and the apparent changelessness
of the individual stars was a solid point in an otherwise chaotic world. In the
past century we have come to realize that the Universe is far from unchanging.
The Universe on large scales is expanding, probably at an increasing rate, and
even at smaller scales nothing is constant. Stars are born and die, and even
our Sun will not last forever. However, on the small scale of our daily life the
sky still seems unchanging. This makes it especially noticeable when a star
occasionally and spectacularly lights up and outshines the other stars. This
phenomenon is rare, at least to the naked eye, but when it has occured, it has
both fascinated and frightened those who had the fortune to witness it. We now
know that these “new stars”, or supernovae, are the violent death of massive
stars in an explosion which in some cases disrupts the whole star. In other
cases it leaves only a small compact remnant while the main part of the star
is blown into space, where it mixes with the surrounding gas. The interaction
between the expelled gas and the surroundings is the topic of this thesis.
1.1
Background
It is through the expulsion of gas from exploding stars that heavy elements are
spread in the Universe. To begin with almost all gas in the Universe was in
the form of the lightest elements, hydrogen and helium. It is only in stars that
these elements are fused into heavier elements, and mainly in supernova explosions that elements heavier than iron are created. Such explosions are also
the most important means for spreading those elements into the surroundings.
It may also trigger star birth in nearby gas clouds, which have now been contaminated with those heavy elements which are essential for life. Supernovae
are therefore an essential part of the evolution of life, and understanding them
is important for understanding our own origins, and the possible spread of life
throughout the universe. They are in fact an essential piece in the large puzzle
2
Introduction
of Life, the Universe and Everything, a puzzle which involves many disciplines, and it is impossible for one person to attack all of it, however much we
may wish to. This thesis does not aspire to do so, but contributes with one part
of the puzzle - by investigating the interaction between supernovae and their
surroundings.
A supernova interacts with its surroundings in a number of ways. The first
interaction takes place at the time of explosion, when the light emitted by the
shock breaking through the stellar surface ionizes the circumstellar medium,
and heats it to a temperature of a few times 104 K. The ionized material recombines, giving rise to narrow emission lines characteristic of the slow-moving
circumstellar medium. Later, the material ejected in the explosion emits ionizing radiation, which again ionizes the circum-supernova gas. Finally, the
ejected material rams into the surrounding gas, sweeping it up and heating it.
The latter form of circumstellar interaction is the subject of this study, and
will be described in more detail in later chapters.
1.2
Motivation
The study of circumstellar interaction is important for a complete understanding of the physics of supernovae. At the moment it is far from clear exactly
what takes place during the explosion, and although many models have been
developed, none of these have reproduced all aspects of the observations.
Since the strength of the interaction depends closely on the explosion physics, in particular the structure of the ejected material, a study of circumstellar
interaction and its observable effects can help distinguish between explosion
models.
The explosion physics and the post-shock ejecta structure also depend on
the structure and evolutionary state of the progenitor star. It is impossible to
observe what goes on inside a star, although there are theoretical models for
this. During the explosion, however, the material created deep inside the progenitor is expelled. The ejected material still retains signatures of the processes which created it, and the interaction between this and the surrounding
gas therefore yields information on the processes that occured inside the star
during its lifetime.
The strength of the interaction also depends on the properties of the wind,
i.e. the wind velocity and mass loss rate of the progenitor as well as the composition of the wind. The latter reflects the composition of the outer layers
of the progenitor star at the time when the wind was ejected from the star.
The supernova shock moves quickly through the circumstellar gas, sweeping
up within weeks material that was ejected over thousands of years. Thus the
shock acts as a time machine, probing the earlier mass loss history of the progenitor on timescales much shorter than those at which the mass loss occured.
1.3 Method
3
Thus, in several ways the interaction between the supernova and the circumstellar gas can be used to deduce the structure of the progenitor star and
its evolutionary history, giving important input to the understanding of late
stages of stellar evolution.
1.3
Method
In order to investigate the emission from the interaction region, and in particular the X-ray emission from the reverse shock, we have developed a numerical model which calculates the X-ray emission from a radiative shock. This
model combines hydrodynamic calculations for a stationary flow with timedependent ionization balance and multi-level calculations. When analysing
X-ray observations of supernovae, it is common to use a single temperature
for the emitting region. While this may be a reasonable approximation for an
adiabatic shock, it is not sufficient to reproduce the emission from a radiative
shock. In a radiative shock gas at several temperatures is present, and therefore
many ionization stages of the elements contribute to the emission. If this is not
taken into account in the analysis, the deduction of elemental abundances from
the spectrum will be wrong. In combining hydrodynamic calculations with an
emission code, our model traces the cooling region better, and gives correct
weight to all the different emitting regions.
The model is described in detail in chapter 4.
1.4
Outline of the thesis
The main part of this thesis consists of four papers, denoted here by paper
I-IV. In addition an introduction is given in chapters 2–5. The purpose of this
introduction is to give the reader a general background to the field and a more
thorough description of the theory than is given in the papers. To this end I
start with a general description of supernovae in chapter 2. In chapter 3 I give
a more detailed description of circumstellar interaction, while my numerical
model is described in chapter 4 along with a background on shocks and spectral theory. In chapter 5 the main results from each paper is given, and in
chapter 6 some possible future projects are discussed.
5
2
Supernovae
2.1
History
The field of supernova research is a quite new one, compared with astronomy
in general – it is only about eighty years since astronomers first became aware
that some of the “new stars” which occasionally appeared were far too energetic to be understood in the context of what was at the time known about
stars. Bright new stars had been seen before, but their nature unfathomed,
these stars were often seen as portents sent by the gods to herald some important event. So it was that the “guest star” observed by Chinese astronomers in
1054 AD was interpreted as a sign “that there is a person of great wisdom and
virtue in the country”, while further north, in the Liao kingdom, it was taken
as an omen that their king would die (Mitton 1979). The guest star was set
on record as rivalling Jupiter in brightness. Visible in the daytime for 23 days
and by the naked eye at night for 22 months it must have been a remarkable
sight, although not quite as spectacular as the new star of 1006, which was
compared to the new moon in brightness (Clark & Stephenson 1977).
Bright new stars were also observed in Europe in 1572 by Tycho Brahe
and in 1604 by Johannes Kepler. Brahe was the first to use the term “stella
nova” (new star) to describe a star which appeared where none so bright had
been seen before, but it was only in the early twentieth century that it became clear that novae came in two separate classes, and that some novae were
much brighter than others. Although Tycho’s and Kepler’s novae were clearly
visible to the naked eye, most novae could only be seen with telescopes. Almost 400 years were to pass before the next naked-eye supernova occurred,
SN 1987A in the Large Magellanic Cloud. However, with a telescope even
faint novae could be observed, and as the telescopes improved, ever more
novae were found. It was noted that many novae were associated with spiral
nebulae. In the 1920s astronomers began to realize that spiral nebulae were
in fact galaxies like our own, but very far away. If the novae really occured
in those galaxies, this implied that they must be extremely bright to be seen
from Earth. Lundmark realized that if the computed distance to M31 (the Andromeda galaxy) was correct, the nova which appeared there in 1885 (S Andromedae) must be more energetic than any other event that was known at
the time - or in his words, “One might hesitate to accept such a luminosity”
(Lundmark 1925). This makes it the first supernova to have been observed in
modern times, i.e. after the invention of large telescopes. Lundmark divided
the novae into two classes; “upper class” novae, which reach a magnitude of
6
Supernovae
No hydrogen lines
Helium and
silicon
Hydrogen lines
No helium
No silicon
Helium
No silicon
Thermonuclear
supernovae
Plateau in
lightcurve
Linear
decay
Narrow hydrogen
lines
Hydrogen lines
disappear
Core-collapse
supernovae
Figure 2.1: Classification scheme for supernovae
the order of the galaxy in which it resides, and “lower class” novae, which are
much fainter. The term super-nova was coined by Baade and Zwicky in 1934,
and in the same paper they suggested that the source of such large energies
was the collapse of a normal star to a neutron star (Baade & Zwicky 1934).
Later research has shown that this is indeed the cause of one class of supernova, while another type is caused by the complete disruption of a special
type of star, a white dwarf, after mass transfer from a companion star. In the
following I will review the different types of supernovae, and the evolution
leading up to the explosion.
2.2
Classification of supernovae
The classification of supernovae (SNe) is, for historical reasons, based purely
on observational characteristics. The presence or absence of hydrogen in the
spectrum divides the supernovae into the two main types: the spectra of Type I
SNe do not show any hydrogen lines, while those of Type II SNe do. For Type I
2.3 Stellar Evolution
7
SNe a further division is based on the presence of helium and silicon lines.
Type Ia SNe contain both helium and silicon, Type Ib SNe contain helium but
no silicon and Type Ic SNe contain neither helium nor silicon. For Type II SNe
the division into subclasses is based on a combination of the shape of the light
curve and the lines present in the spectrum. Type IIL SNe have a linear decline
after maximum, while Type IIP SNe have a plateau in the light curve with
more or less constant luminosity before they start to decline. Type IIn SNe
have narrow emission lines of hydrogen in the spectrum while for Type IIb
SNe the hydrogen lines soon disappear, and the spectrum comes to resemble
that of a Type Ib. The classification is illustrated in Fig. 2.1, and the physics
behind the differences is discussed in sect. 2.5.
The spectroscopic classification is a relic from the early days of supernova
research when little was known about these objects, and does not reflect the
physical mechanisms behind them. A more physically, or at least theoretically,
correct classification might be to divide the SNe into thermonuclear SNe and
core-collapse SNe.
A thermonuclear SN is thought to occur when mass transfer from an
evolved star onto a massive white dwarf causes the white dwarf to explode.
This is described in more detail below. Core-collapse SNe occur when the
core of a massive star collapses under its own gravity. In order to understand
how such a thing can occur, we need to understand the basics of stellar
evolution. I will therefore start by reviewing the life of a star which will
eventually end in an explosion.
2.3
Stellar Evolution
The following gives a basic background on stellar evolution. More details on
the theory of stellar structure and evolution can be found in e.g. Clayton (1968)
and in Arnett (1996). A recent review of late stages of stellar evolution is given
by Woosley & Janka (2005).
The evolution of stars can be illustrated by the Hertzsprung-Russell diagram
(Fig. 2.2). This diagram shows the relation between temperature and luminosity of different stars. Most stars fall along a more or less diagonal line, the
main sequence, with the least massive stars in the bottom right and the most
massive, and also hottest and most luminous, stars in the upper left. Fig. 2.3
(Meynet & Maeder 2000) shows evolutionary tracks in the HR-diagram for
massive stars, i.e. the ones located in the upper left of the upper panel. As
these evolve, they move to the right, into the supergiant branch.
A star is born from a cloud of mainly hydrogen gas which contracts under
its own gravity. When the material contracts, the temperature increases. Eventually the temperature and pressure are so high that hydrogen fusion starts. A
star begins its life to the right of, and above, the main sequence, and moves
onto the main sequence when hydrogen ignites (see below). While hydrogen
Supernovae
O
B
Spectral class
A
Luminosity (Lsun)
104
F
G
K
M
-10
-5
Supergiants
Giants
Main sequence
102
0
1
+5
White dwarves
10-2
10-4
25000 10000
+10
6000
3000
Absolute magnitude
8
+15
Temperature (K)
Figure 2.2: A schematic Hertzsprung-Russell diagram, which illustrates the relation
between temperature and luminosity of different stars.
is burning it moves slowly to the left and up on the main sequence. Towards
the end of its life the star moves away from the main sequence toward the right
in the diagram.
To put it simply, hydrogen fusion means that four hydrogen nuclei combine
to form one helium nucleus. This can happen in one of two ways, depending
on the temperature. The first, the so-called proton-proton chain, starts with
three protons, 1 H, forming one 3 He:
1H + 1H
→ 2 D + e+ + ν
2D + 1H
→ 3 He + γ
At low temperatures the reaction chain ends as:
3
He + 3 He → 4 He + 1 H + 1 H
(2.1)
At temperatures above 1.4 × 107 K the end of the reaction goes as follows:
3 He + 4 He
→ 7 Be + γ
7 Be + e−
→ 7 Li + ν
7 Li + 1 H
→ 4 He + 4 He
2.3 Stellar Evolution
9
Figure 2.3: Evolutionary tracks for massive stars (Meynet & Maeder 2000), showing the difference in the evolutionary tracks of rotating (solid line) and non-rotating
(dotted line) stars.
In stars more massive than the sun, carbon, if sufficiently abundant, can act
as a catalyst, and in this case hydrogen fusion can follow the CNO-cycle:
12
C +1 H → 13 N + γ
13 N
13
14
C +1 H → 14 N + γ
N +1 H → 15 O + γ
15 O
15
→ 13 C + e+ + ν
→ 15 N + e+ + ν
N +1 H → 12 C + 4 He
Whichever way fusion occurs, the net result is that four protons are turned
into one helium nucleus (also called an alpha-particle), two positrons, two
neutrinos and radiation. The final helium atom is less massive than the original
four hydrogen atoms. The excess mass is converted to energy, and radiated
away. When this process starts, the star is born. The energy produced in the
fusion process creates a pressure which counteracts the gravitational pull, and
the contraction stops. An equilibrium is created between gravity and pressure,
and as long as this equilibrium persists, the star lives safely, shining steadily
as the excess energy is radiated away. When hydrogen fusion starts, the star
moves onto the main sequence (see Fig. 2.2), where it will spend most of its
life. The mass of the star determines its colour and its position on the main
sequence. Low mass stars are red, and located in the far right of the diagram,
in the lower part of the main sequence. The higher the mass of the star, the
10
Supernovae
further up on the main sequence it will be. The most massive stars are blue
supergiants (BSG) and located in the upper left of the main sequence.
2.3.1
Low mass stars
One effect of the fusion is that since four particles are converted to one (larger)
particle, the particle pressure is reduced. When about 80% of the hydrogen in
the core of the star has been converted to helium, the particle pressure becomes too small to counteract gravity. For the Sun this occurs after 10 billion
years. Lower mass stars continue to burn hydrogen much longer, but eventually fusion in the core stops. Outside the core where there is still hydrogen
left, fusion continues. The star’s time on the main sequence is now over. In
order to accomodate the change in pressure, the whole star is restructured. It
swells up while at the same time the core contracts. The larger surface area
causes the surface temperature to drop, and the star becomes redder - a red
giant. It moves off the main sequence, to the right, onto the red giant branch.
During the contraction of the core, the temperature in the core increases. As
the matter is packed ever closer, the motion of the electrons is restricted, and
they attain as low energy states as possible. The Pauli exclusion principle,
which forbids two electrons to occupy the same quantum state, sets a limit
to how closely the electrons may be packed. When this limit is reached, the
contraction stops. The electrons are now said to be degenerate. In stars smaller than the Sun electron degeneracy sets in before the temperature becomes
high enough for helium to ignite, and no further fusion is possible. The core is
now a dense ball of electron degenerate gas, with a temperature of about 100
000 K. This heat is radiated away, and the outer layers of the star are blown
away by the strong radiation. What remains is a white dwarf, which gradually
cools and fades, and for a short while a planetary nebula which glows as the
expelled gas is excited and ionized by the radiation from the cooling white
dwarf.
In the Sun, as well as in more massive stars, the temperature in the core
becomes high enough for helium to ignite, producing carbon and oxygen. Helium burning occurs via the triple-alpha process, where three alpha-particles
combine to form one carbon nucleus:
4 He + 4 He
→ 8 Be
8 Be + 4 He
→ 12 C + γ.
Some of the carbon nuclei thus produced combine with alpha-particles to
produce oxygen:
12 C + 4 He
→ 16 O + γ.
(2.2)
2.3 Stellar Evolution
11
When the helium is exhausted, the core once again contracts while the outer
parts expand, and the star moves onto the asymptotic giant branch. If the temperature in the core does not become sufficiently high for further fusion to
start, also this star ends up as a white dwarf. This is the destiny of all stars
with an initial mass less than 8–10 M . All white dwarfs are thought to have
more or less the same mass, of about one solar mass. A white dwarf by itself
can never become a supernova.
The situation is different if it has a less evolved companion star. When the
companion expands as part of its own evolution, it may start transferring mass
to the white dwarf. If the mass of the white dwarf is increased beyond 1.4 M
(also known as the Chandrasekhar limit), it collapses. The temperature increases due to the collapse, but because the pressure of degenerate material
is independent of the temperature, it remains constant. This means that it is
impossible for the star to compensate for the temperature increase by expanding. As a result, the whole star ignites at the same time, causing explosive
nucleosynthesis which completely disrupts the white dwarf, leaving no remnant. Type Ia SNe are thought to be of this type, which explains the lack of
hydrogen in these SNe: only the core of the original star remains before the
explosion. This explanation is also borne out by the fact that Type Ia SNe, unlike the other types, are found in all galaxy types, and both within and outside
spiral arms, indicating that the progenitors are old stars. These SNe are the
most luminous, and since they originate in stars with more or less the same
initial mass, they are believed to have the same luminosity irrespective of their
environment. This has led to their remarkable usefulness as standard candles
in cosmology. However, since Type Ia SNe usually do not show strong circumstellar interaction, we will leave them, and concentrate on the other types.
2.3.2
High mass stars
In stars that are initially more massive than 8 M , helium burning in the core is
followed by carbon burning, and then ever heavier elements are fused. Carbon
fusion occurs at temperatures of 7 − 8 × 108 K, and lasts for a few hundred
years. During carbon burning, the star, which was a blue supergiant on the
main sequence, has swollen and become a red supergiant (RSG). Nothing can
be seen on the surface of what is happening in the core, but deep inside the
star the fusion of ever heavier elements is proceeding at an increasingly faster
pace. The main reaction of carbon burning is
12 C + 12 C
→ 24 Mg∗ + γ
The magnesium created in the reaction is highly excited, and quickly decays
through one of three channels:
12
Supernovae
γ+
24 Mg∗
→ 23 Mg + n
24 Mg∗
→ 20 Ne + 4 He + γ
24 Mg∗
→ 23 Na + p + γ
(2.3)
The proton, neutron and alpha-particle created in this process react with
other nuclei, resulting in a large number of reactions. The main products are
16 O, 20,21,22 Ne, 23 Na, 24,25,26 Mg, 26,27 Al, as well as some 29,30 Si and 31 P. The
composition following carbon burning is dominated by 16 O, 20 Ne and 24 Mg.
After carbon is exhausted in the centre of the star, the core once again contracts until the temperature has reached 1.5 billion degrees, at which point
neon ignites. Neon fusion occurs in several steps, starting with the photodisintegration of 20 Ne
γ + 20 Ne
20 Ne + 4 He
→ 16 O + 4 He
→ 24 Mg + γ
(2.4)
The net result is that two neon nuclei produce one oxygen and one magnesium. Additional nuclei produced in secondary reactions are Al, S and P.
The resulting composition consists mainly of O, Mg and Si, as well as traces
of Al, Si, P and S.
Following neon burning, oxygen ignites when the central temperature is
two billion degrees. The main reaction is fusion of two oxygen nuclei into one
sulphur nucleus:
16
O + 16 O → 32 S∗
(2.5)
The excited sulphur nucleus decays through four channels
γ+
32 S∗
→ 31 S + n + γ
32 S∗
→ 31 P + p + γ
32 S∗
→ 30 P + d
32 S∗
→ 28 Si + 4 He + γ
(2.6)
Also in this case a host of secondary reactions occur, producing mainly
and 40,42 Ca. 90% of the final composition consists of 28 Si and 32 S in almost equal amounts, which is the fuel for the
final stage of hydrostatic nuclear burning.
28 Si, 32,33,34 S, 35,37 Cl, 36,38 Ar, 39,41 K
2.4 Explosion
13
During silicon burning 28 Si is photodisintegrated into protons, neutrons and
alpha-particles. These react with other elements to build up new elements,
notably the iron group elements, resulting in an iron-rich core. The iron group
elements are the most tightly bound nuclei, which means that no further energy can be extracted through fusion. Instead, the creation of heavier elements
consumes energy, so that if such reactions do occur, they drain the star of energy. Consequently, when the iron core begins to contract, no additional fusion
processes can ignite to halt the collapse.
As ever heavier elements burn in the core, fusion of lighter elements goes
on in layers outside the core, so that finally the star has an onion-like structure,
with light elements furthest out, and heavier elements in layers inwards to the
core (Fig. 2.4).
After helium fusion the temperature is high enough for electrons and
positrons to be created. These in turn produce neutrinos by pair annihilation.
Since the neutrinos have a very small interaction cross section, they leave the
star easily, carrying their energy with them. These losses dominate the photon
production by orders of magnitude. This process, in combination with the
fact that the available energy to be extracted from one fusion event decreases
for more advanced burning stages, has the consequence that the burning has
to proceed ever faster in order to maintain the pressure. Therefore, each
consecutive burning stage lasts shorter than the previous ones. The duration
of each burning stage depends on the mass of the star - the more massive
the star, the more violent the burning will be, and the sooner the fuel will
be consumed. For a 20 M star hydrogen burning takes 8 million years,
while oxygen burning takes 1.3 years and silicon burning only about 10 days
(Heger et al. 1993).
2.4
Explosion
When nothing remains to hinder the gravitational contraction, the core collapses rapidly. When the density in the core, which is now neutron rich, becomes sufficiently high, the repulsive part of the nuclear force becomes strong
enough to halt the collapse. The contraction stops abruptly, creating a rebound shock which moves out from the core. The infalling matter bounces
off the inner core, and the collapse turns into an explosion as a shock builds
up, moving through the star. As the neutron star is forming, copious amounts
of neutrinos are emitted. In the space of a few seconds ∼ 10% of the mass
of the neutron-rich core is radiated as neutrinos, giving a neutrino luminosity
of ∼ 1053 ergs s−1 . Due to the low interaction cross-section of neutrinos with
ordinary matter, however, this neutrino burst is practically invisible to us. The
only supernova from which neutrinos have been observed is SN 1987A. A
total of 19 neutrinos were observed in a 10 s burst - a small number, considering that ∼ 1058 neutrinos were produced in the explosion. The heavy neutrino
14
Supernovae
Figure 2.4: A supernova progenitor has an onion-like structure, with an iron core
and progressively lighter elements further out. This structure is also evident in the
ejected material. This plot of the element distribution in the model 4H47 (Nomoto
& Hashimoto 1988; Shigeyama et al. 1994) shows the distribution in mass of the
elements in the ejected material after the explosion.
losses in combination with photodisintegration drain the outflowing material
of energy, causing the shock to stall, and the matter begins to fall back. If this
fallback is not prevented, a black hole will form within seconds. However,
a combination of mixing, convection and heating of the material behind the
shock by the neutrinos is thought to give the shock sufficient energy to eventually make the star explode. The outer layers are ejected violently, leaving
a neutron star in the centre. Some of the ejected material falls back, and if
the mass of the fallback material is sufficiently large, the neutron star may
collapse further and turn into a black hole. Meanwhile the shock moves out
through the star. At the high temperatures present behind the shock, elements
heavier than iron can be produced. As the shock passes through the onion-like
outer layers, Rayleigh-Taylor instabilities develop at the interfaces between
the different zones. Fig. 2.5 shows the density structure in a two-dimensional
model calculation of the explosion of a 15 M red supergiant, as well as the
distribution of the elements following the explosion (Kifonidis et al. 2000).
The instabilities evident in the figure contribute to mixing the material created
deep in the interior with the less processed material further out.
2.4 Explosion
15
Figure 2.5: The density distribution and mixing of elements in an exploding red supergiant of 15 M (Kifonidis et al. 2000)
Figure 2.6: The Cygnus loop supernova remnant is the remains of a star which exploded 15,000 years ago. The image was taken with the Wide Field Planetary Camera
aboard the Hubble Space Telescope. (Image credit: NASA/STScI.)
16
2.5
Supernovae
After the explosion
When the shock breaks through the stellar surface, this results in a bright flash,
mainly in UV and X-rays. The optical emission becomes visible after a few
hours, but soon fades due to the high opacity in the ionized hydrogen gas. A
lot of information can be gained by studying the light curve of the supernova.
A light curve is a plot of luminosity versus time. A sample of supernova light
curves is given in Fig. 2.7. The shape of the light curve is indicative of the
type of supernova, but some features are common for all SNe. After the initial
burst, a minimum is reached after about 10 days, after which the luminosity
again increases. This is thought to be caused by diffusion of radiation from
the supernova. Initially, the outer layers of the atmosphere are ionized, and
opaque to the radiation created in the explosion. This radiation comes partly
from the kinetic energy of the shock, and partly from radioactive decay, but
because of the high opacity, the radiation is trapped, and diffuses only slowly
out. The minimum occurs when the gas in the outer layers has cooled sufficiently for hydrogen to recombine. Since neutral hydrogen is transparent, the
emitted radiation in the outer layers escape, which leads to an increase in the
luminosity from the supernova. As the supernova expands, ever deeper layers
cool to the point of recombination - or in other words, a recombination front is
formed, which moves inward through the hydrogen envelope. The maximum
luminosity is reached after ∼ 100 days. After this, the luminosity begins to
decrease, with a decline rate which depends on the type of supernova. If the
kinetic energy of the explosion were the only source of energy, all supernovae
would fade completely within a few weeks or months, as the expansion cools
the gas. There are, however, several processes which contribute to powering
the light curve for a long time.
For thermonuclear SNe (Type Ia) the principal energy source after a few
months is the decay of radioactive isotopes created in the explosion. Particularly important is 56 Ni, which decays first to 56 Co with a half-life of 6 days,
and then to stable 56 Fe with a half-life of 77 days. This is the cause of the
characteristic shape of the light curves of SN Ia, as seen in Fig. 2.7, with a
steep decline during the first few weeks after maximum, and a slower decline
as the decay of 56 Co comes to dominate the emission. For core-collapse SNe
which have lost their hydrogen envelope (Type Ib/c) the light curve resembles
that of thermonuclear SNe.
Type II SNe are divided into the two main categories Type IIP (plateau)
and Type IIL (linear). As the names suggest, the light curves of Type IIL SNe
decay linearly after the maximum, while for Type IIP SNe the emission stays
constant for months, giving a characteristic plateau in the light curve. The
cause of this behaviour is thought to be the size of the hydrogen envelope.
Type IIP SNe are thought to arise from progenitors which have retained a large
hydrogen envelope, and the emission stays constant as long as the recombination front is moving inward in this envelope. Type IIL SNe, on the other hand,
2.5 After the explosion
17
Figure 2.7: A schematic overview of the different types of supernova light curves.
From Filippenko (1997)
have a smaller hydrogen envelope, leading to a recombination front of shorter
duration, and a faster decline. At late times the light curves of Type II SNe are
powered by radioactive decay, similarly to Type I SNe.
Most SNe fade away completely as the envelope expands and thins out, and
the radioactive elements decay to stable isotopes. For some SNe, however, the
interaction with a dense circumstellar medium can power the light curve for
much longer. This is particularly evident at radio and X-ray wavelengths, but
also the optical light curve flattens and stays constant for many years. This
interaction is the topic of this thesis, and will be described in more detail in
the next chapter.
2.5.1
Supernova remnants
As the supernova expands, it sweeps up interstellar gas. This gas usually has a
low density, and because of the high shock velocity, the ambient gas is heated
and compressed without affecting the dynamics of the supernova shock. The
supernova is said to be freely expanding. The interstellar gas builds up behind
the shock, however, and when the mass that has been swept up is comparable
to the mass ejected by the supernova, the shock begins to slow down. The
shocked gas cools, and eventually the temperature has fallen to 106 − 107 K.
At this point the heaviest ions start capturing electrons (recombining), releasing energy as photons in the process. This drains the gas of energy, causing
it to cool even more, allowing more ions to recombine. This starts a runaway
process in which the gas collapses to form a thin shell, which radiates strongly.
The expanding structure, a supernova remnant, can be seen for thousands of
years (Fig. 2.6). The main cause of the radiation is the emission of photons
from recombination and excitation, which release the kinetic energy from the
supernova explosion. An additional source of power may, however, be a neut-
18
Supernovae
ron star at the centre of the supernova remnant. If the neutron star, which was
formed during the collapse, is a pulsar, it emits relativistic particles, which
interact with the supernova ejecta. One example of this is the Crab supernova
remnant, which contains a pulsar in the centre.
19
3
Circumstellar interaction
3.1
Background
When a star explodes as a supernova, a strong shock is driven into the surrounding material. If the circumstellar medium (CSM) is dense, the interaction between the shock and the CSM will be strong. Such a CSM may be set
up in binary systems where some of the mass has been lost through Roche
lobe overflow, or around single stars with dense, slow-moving stellar winds,
like red supergiants. In order to understand the physics of this it is necessary
to know something about stellar winds and about shocks. I will therefore start
this chapter with a short description of these phenomena.
3.1.1
Stellar winds
All stars lose mass to a varying degree at different stages of their lives. At
the surface of the star gas is pushed outward by radiation pressure or hydrodynamic shocks, creating a wind which streams away from the star. The
properties of this wind depend on the chemical composition and temperature
in the stellar atmosphere as well as the surface gravity (i.e. the mass and the
radius). As these parameters change during the evolution of the star, so does
the mass loss rate of the stellar wind. Our Sun, for instance, loses mass at a
rate of ∼ 10−14 times its own mass every year (Ṁ ∼ 10−14 M yr−1 ), with a
wind velocity of vw ∼ 500 km s−1 . When it eventually evolves into a red giant
in five billion years time, the temperature and surface gravity will drop due to
the expansion. The lower temperature in turn reduces the radiation pressure,
but this is more than compensated for by the reduced surface gravity. The resulting low escape velocity means that even low-velocity gas will escape from
the atmosphere, and a slow, dense wind results.
Stars more massive than the Sun have a considerably stronger wind already
on the main sequence. A blue supergiant, which has temperatures of T =
20, 000 – 50, 000 K, loses mass at 10−6 − 10−5 M yr−1 with velocities of
500 – 3, 000 km s−1 . As this star evolves it expands and cools, and turns into
a red supergiant, whose lower surface gravity gives rise to a slow, dense wind,
with Ṁ = 10−6 − 10−4 M yr−1 and vw ∼ 5 – 50 km s−1 (Salasnich et al.
1999). By then it is surrounded by a very dense medium, and if it explodes at
this point, the interaction between the supernova shock and the CSM will be
strong. At the very end of the evolution strong pulsations may drive a ’super-
20
Circumstellar interaction
4
wind’, with even higher mass loss during a short period (<
∼ 10 years) (Heger
et al. 1997).
In some cases, however, the star could evolve back to the blue supergiant
stage. The resulting fast wind will then blow a bubble in the surrounding gas,
as it sweeps up the remains of the red supergiant wind. The latter then forms
a dense shell, or possibly a ring if the red supergiant wind is asymmetric.
An explosion in this environment will initially lead to very little interaction.
However, as the supernova shock overtakes the dense shell or ring, a stronger
interaction ensues. This is the case for SN 1987A, which is described in more
detail in sect. 3.3.1.
The composition in the atmosphere of the star can change, either because
material created by nuclear fusion is mixed upwards and enriches the atmosphere, or because the outer atmosphere, consisting mainly of hydrogen,
is lost. This can happen as a result of very strong winds, or through mass
transfer to a binary companion. Some very bright stars, known as Wolf-Rayet
stars, have extremely strong winds, with Ṁ ∼ 10−5 M yr−1 and vw ∼ 1000 –
5000 km s−1 . These stars have already lost most of their hydrogen envelope.
It is not known exactly what causes a star to become a Wolf-Rayet star. Binary interaction could play a role for some of them, although heavy mass loss
on the main sequence and the red supergiant branch are likely to be the most
important factors. The strong wind essentially causes most of the remaining
outer layers of the atmosphere to be pushed away, and the star to be shrouded
in a dense cloud of gas. Since these stars have lost the hydrogen envelope, and
in some cases even the helium envelope, they are believed to be the progenitors of Type Ib/c SNe.
Several processes can modify this simplified picture of spherical mass
loss. Rotation, magnetic fields and interaction in a binary system can create
a non-spherical wind. Pulsation, which is common at many stages of stellar
evolution, can also modify the CSM. Since circumstellar interaction depends
closely on the structure of the CSM, the physics of the interaction will vary
depending on the evolutionary state of the star. For this reason a careful study
of circumstellar interaction can help map out the mass loss history of the
progenitor star.
3.1.2
Shocks
Shocks abound in space, occuring in a wide range of circumstances, from star
births to deaths, within molecular clouds, in stellar winds and planetary atmospheres as well as inside stars. A shock forms when movement occurs faster
than the local sound speed. When this happens, the medium through which the
gas is moving does not have time to react in a smooth way to the change, and
a shock front is formed. As the shock moves forward, the material which it
passes is heated and accelerated, but once the shock has passed, the gas, now
denser and hotter than before, gradually cools. The cooling occurs mainly
3.1 Background
21
through line emission as ions which were ionized and excited by the passing
shock, gradually return to their ground state, sending off the excess energy as
8
photons. If the temperature is sufficiently high (T >
∼ 10 K), the gas is completely ionized, and no line emission can take place. The energy loss by radiation is therefore small, although some energy is lost as bremsstrahlung in interactions between free electrons and ions. If the shocked region expands more
quickly than it cools, i.e. if the cooling timescale is much longer than the expansion timescale, the expansion may be considered to be energy-conserving.
Such a shock is known as an adiabatic shock1 .
For temperatures below ∼ 108 K, the electrons and ions begin to recombine. Line emission from these highly ionized, but not completely stripped
species, drains the gas of energy, and it cools rapidly, causing even more ions
to recombine. This is a highly unstable situation, which causes a rapid cooling
to ∼ 104 K, at which temperature hydrogen recombines. Whether the gas has
time to cool or not depends on the cooling rate, which in turn depends on the
temperature and density. An estimate of the cooling time is given by
tc =
3kTe
.
ne Λ(Te )
(3.1)
If this timescale is shorter than the age of the SN, the shocked gas will cool.
In paper I we discuss the conditions for this to take place, which obviously
depends on the density and shock velocity, i.e. the shock temperature.
A shock where this condition holds is known as a radiative shock, or a
cooling shock. One effect of the energy loss is that the pressure drops, and
the shocked region collapses and forms a thin, cool shell. This is the cause
of the thin filaments which are seen in many old supernova remnants like the
Cygnus loop nebula (Fig. 2.6) or in star-forming regions, where winds and
jets from newly born stars form shocks in the surrounding gas cloud (HerbigHaro objects). In the latter objects molecular cooling is also important below
∼ 104 K.
Since in the following the shocks surrounding a supernova will be described
in more detail, it is useful to review the terminology of shocks. The structure of a shock is illustrated in Fig. 3.1. The region which the shock has not
yet passed is denoted as upstream, and the region behind the shock front is
denoted as downstream. All upstream quantities are labelled with 1, and all
downstream quantities with 2. Quantities relating to the shock itself are labelled with s. Fig. 3.2 shows the density (dashed line) and temperature in
front of and behind the shock front, for a shock velocity of Vs = 800 km s−1 .
The shock is moving to the left in this picture. In front of the shock the temperature and ionization increase due to the radiation from the shocked gas. As
the gas passes the shock, both density and temperature increase drastically.
Behind the shock the gas cools gradually until catastrophic cooling sets in. At
1 An
adiabatic process is one which occurs without gain or loss of heat or entropy.
22
Circumstellar interaction
Shock front
Up
stream
Downstream
Vs
n1 , p1
T1, v1
Neutral,
unshocked
gas
Unshocked gas
Photoionized
by radiation
from the shock
n2 , p2
T2, v2
Hot, shocked
gas
Cooling,
collisionally
ionized
Cool shell
Photoionization
region
Figure 3.1: The structure of a shock. The shock front is moving to the left in the
picture. n is density, p is pressure, T is temperature and v is velocity.
Figure 3.2: Density (dashed) and temperature structure in front of (left) and behind
(right) a shock front with velocity Vs = 800 km s−1 , which is moving to the left in the
picture. Note the different spatial scales on each side of the shock (C. Fransson, priv.
comm.)
this point the temperature drops, while the density increases dramatically. The
gas then cools to ∼ 104 K, when photoelectric heating by the radiation from
the shock stabilizes the temperature in a thin zone. Although the cooling zone
is extremely thin, this is where most of the radiation is emitted. It is therefore
observationally very important.
The structure of the gas is described by the Euler equations. In one
dimension, in the absence of any sources of energy, and when time-dependent
effects are not important, these can be written as follows.
Conservation of mass:
d(ρv)
= 0.
dx
(3.2)
3.1 Background
23
Conservation of momentum:
d
(ρv2 + p) = 0.
dx
(3.3)
d
[(E + p)v] = Λni ne .
dx
(3.4)
Conservation of energy:
Here ρ = µmu ni is the number density, ne and ni are the electron and ion
number densities respectively, v is the velocity, the pressure is given by p =
(ne + ni )kT and
1
p
E = ρv2 +
(3.5)
.
2
γ −1
The faster the shock, the greater the compression, and the higher the temperature. In a supernova explosion the outgoing shock is very fast, with velocities
a few times 104 km s−1 . In sect. 3.2 we will look closer at what happens when
the medium into which the shock ploughs is dense.
3.1.3
Shocks in different environments
The treatment of adiabatic shocks is simpler than for radiative shocks in that
the post-shock region is relatively restricted in temperature and density, and
therefore computing the emission is relatively straightforward. Often a single
temperature is assumed for the whole region, but as found by e.g. Gronenschild & Mewe (1982), this is not sufficient when non-equilibrium ionization is important. However, because of the negligible radiative losses in these
shocks, the radiation mechanisms can be decoupled from the hydrodynamics,
which simplifies the calculations. In young supernova remnants, which are
a few hundred years old, both the circumstellar and the reverse shocks (see
sect. 3.2) are usually adiabatic. X-ray emission from supernova remnants have
been computed by e.g. Shull (1982), Kaastra & Jansen (1993), Borkowski
et al. (2001) and Badenes et al. (2003). The main difference between these
shocks and the cases which we study is that the reverse shock is usually radiative in our cases. We therefore need to take into account the cooling and
emission of the post-shock gas, representing a wide range of temperatures,
and we need to couple the cooling to the hydrodynamics. This is described in
detail in Chapter 4.
Radiative shocks have been modeled extensively for more than three decades. The first numerical models of cooling shocks were made by Cox (1972),
who considered a planar shock with a velocity of 100 km s−1 and applied
the results to the Cygnus Loop. Later, improved models were developed by
Raymond (1979), Dopita (1976, 1977), Hartigan et al. (1987) and others (see
Dopita & Sutherland 1996, and references therein). These models were intended for such diverse phenomena as old supernova remnants, Herbig-Haro
24
Circumstellar interaction
objects and narrow line emission regions in active galactic nuclei, but are
in general not applicable to young supernovae. The reason for this is that
for the low densities in supernova remnants the shock is not radiative above
∼ 200 km s−1 . In addition, because of the higher densities collisional deexcitation processes become important.
The effects of composition on the properties of the cooling gas in radiative
shocks have been studied by Itoh (1981a,b, 1986, 1988), Borkowski et al.
(1989) and Borkowski & Shull (1990). The main difference between these
studies and the present one is again the lower velocity and density in their
models.
Plewa & Różyczka (1992) and Plewa (1993, 1995) calculated the hydrodynamic evolution of fast shocks evolving in a dense medium, and applied
these calculations to AGNs and young supernova remnants. Their models
could in principle also be applicable to supernovae if the composition is close
to solar, but their treatment of the cooling in a time-independent formalism
makes it less applicable to the reverse shock. In paper I we find that a higher
metallicity, as appropriate for the reverse shock, leads to a stronger cooling,
and thereby a need for a time-dependent calculation of the ionization balance
and cooling. Plewa & Różyczka (1992), and Plewa (1993, 1995) also treated
the emission in a simplified manner by assuming collisional ionization balance
and computing the emission in the cooling region from given line intensities,
with a fairly limited number of lines. In contrast, we compute the emission
from transitions in multi-level ions, and couple the resulting cooling to the
hydrodynamics, resulting in detailed and self-consistent spectra.
3.2
Physical scenario
In the calculations in this thesis we mainly assume that the exploding star is
surrounded by the remains of the stellar wind of the progenitor, the density of
which is given by
Ṁ
ρw =
4πR2∗ vw
R∗
r
s
,
(3.6)
where R∗ is a reference radius, and the index w refers to the wind. A constant mass loss rate and wind velocity corresponds to the exponent s = 2, but
as described in section 3.1.1, the structure of the wind can be modified by
successive periods of fast and slow winds, as well as by pulsation and binary
interaction, all of which could contribute to changing the density gradient of
the circumstellar medium.
Models of supernova explosions have indicated that the density structure of
the outer ejecta can be approximated by a power law (Chevalier & Fransson
1994)
3.2 Physical scenario
25
Figure 3.3: Density structure in the 4H47 model (Nomoto & Hashimoto 1988; Shigeyama et al. 1994).
−3 η
V0t
t
ρe j = ρ0
,
t0
r
(3.7)
where ρ0 is the density at time t0 and velocity V0 . The density gradient η is
usually in the range 7-12, but can be as large as ∼ 20. Models of red supergiants indicate that in the outer layers η ∼ 10 (Matzner & McKee 1999). The
passage of the shock during the explosion can modify this structure, and realistic explosion models for SN 1993J show a steep outer gradient, with η ∼ 20,
a shallow middle part, with η ∼ 5, and a steep inner region (Fig. 3.3, Nomoto
& Hashimoto 1988; Shigeyama et al. 1994).
If the circumstellar medium is dense, the ram pressure which it exerts on
the outgoing shock (hereafter called the circumstellar or outer shock) creates
another shock (the reverse shock) which is driven backwards into the ejected
material (see Fig. 3.4). While the reverse shock is travelling backwards in
mass, both shocks usually travel outward in radius with the expansion velocity
of the ejecta. A layer is created consisting of the two shocks and two shells
between them; the outermost containing shocked circumstellar gas, which has
been shocked by the outgoing shock; and the other containing shocked ejecta
which have been shocked by the reverse shock. The interaction shell is dense
and hot, and produces high energy emission and particles. Immediately behind
the circumstellar shock the temperature about a month after the explosion is
Tcs ∼(1–5)×109 K, and the density ncs ∼ 106 – 108 cm−3 , depending on the
mass loss rate and velocity of the stellar wind The gas behind the reverse
shock is cooler and denser, with Trev ∼ 1 × 107 – 5 × 108 K and nrev ∼ 109 –
1011 cm−3 .
Where the two density distributions meet, there is a discontinuity in
density and temperature, known as the contact discontinuity. At this border
between the two regions Rayleigh-Taylor instabilities are likely to develop,
causing fingers of cool, shocked ejecta to penetrate into the hot region behind
26
Circumstellar interaction
Outer
shock
Contact
discontinuity
Reverse
shock
Ionized ejecta
Shocked ejecta
T~ 107 K
Neutral
ejecta
Ionized wind
Cool shell
Shocked wind
T~ 3x108 K
Figure 3.4: Interaction of supernova ejecta with the progenitor wind.
the outer shock. This is shown in Fig. 3.5, from Chevalier et al. (1992). The
whole structure moves outward with the expansion velocity of the ejecta,
according to Rs = V t .
The outer shock is adiabatic, except for the earliest epochs when inverse
Compton cooling may be important (Fransson 1984; Lundqvist & Fransson
1988), or in the case where the shock is moving into a very dense medium.
This is the case for SN 1987A, where the ejecta has now caught up with
the dense circumstellar ring (see Sect. 3.3.1). When radiative losses are
important, the hot region behind the reverse shock collapses to a very thin
shell, and a cool shell is created downstream from the reverse shockfront.
Most of the high-energy emission in the outward direction from the reverse
shock is then absorbed by the cool shell. In this case the observed X-ray
emission in the first weeks or months comes mainly from the shocked
windthe cool shell is transparent. At later times the X-ray luminosity of the
outer shock is too low to be observed, and as the optical depth of the cool
shell decreases, the reverse shock comes to dominate the X-ray emission. As
long as the reverse shock is radiative, its luminosity remains more or less
constant. Therefore, line emission from the reverse shock can be observed,
even at very late times.
Although most of the X-rays from the reverse shock are absorbed by the
dense shock this has important observational implications, since this flux is
re-emitted as optical and UV emission (Chevalier & Fransson 1994).
3.3 Observational evidence for circumstellar interaction
27
Figure 3.5: Density structure of the interaction region in hydrodynamic calculations
for η = 7, s = 2. The reverse shock is radiative and Rayleigh-Taylor instabilities at the
contact discontinuity creates fingers of shocked ejecta which protrude into the shocked
circumstellar material (Chevalier et al. 1992).
3.3
Observational evidence for circumstellar interaction
The main observational indications of circumstellar interaction are the detection of narrow emission lines from ionized circumstellar gas, broad emission
lines from ejecta ionized by radiation from the interaction region, radio synchrotron emission, and wavelength dependent turn-on of the observed radio
emission. The turn-on of the radio emission is caused either by synchrotron
self-absorption or, in the case that the external medium dominates the absorption, by the decreasing free-free optical depth in the circumstellar gas (Chevalier & Fransson 2003).
At early times, the free-free absorption in the ionized gas is so high that the
emission cannot escape. As the supernova expands, the optical depth, τ , drops,
and as it drops below unity, the emission becomes visible. Since τ ∝ λ 2 the
emission will first appear at short wavelengths, then later emission becomes
observable at successively longer wavelengths. The connection between the
peak radio luminosity (Lp ) and the time of the peak (tp ) can be used for determining which of the two absorption processes dominates. In Fig. 3.6 this
relation is shown for a number of supernovae. If synchrotron self-absorption
dominates, there will be a relation between the peak luminosity and the time
since explosion which depends on the SN expansion velocity. In the figure the
deduced velocity as a function of Lp and tp corresponding to synchrotron selfabsorption is shown as dashed lines. If the maximum observed ejecta velocity
of a supernova is higher than its position in the diagram indicates, synchro-
28
Circumstellar interaction
Figure 3.6: Relation between peak radio luminosity (Lp ) and the time of the peak
(tp ) (paper II). The dashed line represent the lower limit to the ejecta velocity if
synchrotron self-absorption is the only cause for absorption of the radio emission.
tron self-absorption is a likely cause for the early absorption and wavelengthdependent turn-on of the radio emission. If, on the other hand, it is lower, the
absorption is probably caused by free-free absorption in the external gas, or a
combination of the two. If synchrotron self-absorption is dominating, this can
be used for deducing the magnetic field and the density (Fransson & Björnsson 1998, 2005). If free-free absorption dominates the mass loss rate of the
progenitor can be found.
At late times, the circumstellar interaction gives rise to optical emission,
causing the optical light curve to flatten when the emission from radioactive
decay fades away. This is caused by the absorbed X-ray emission from the
reverse shock which is transformed into optical/UV radiation. The emission
from the interaction powers the light curve for a long time, as can be seen
e.g. for SN 1979C, which showed a more or less constant optical emission
between 1990 and 1994, i.e. up to 15 years after the explosion (Fesen et al.
1999).
SN 1979C was also the first supernova in which the importance of circumstellar interaction was evident. The early observations showed strong, broad
emission lines in the UV and narrow Hα emission. After about a year radio emission appeared, first at short wavelengths, later at successively longer
wavelengths (Weiler et al. 1986). However, X-rays from SN 1979C were
not observed until 16 years after the explosion, when they were detected by
ROSAT in 1995 (Immler et al. 1998). The reason for the delay in the X-rays
is likely to be strong absorption in the cool shell behind the reverse shock,
3.3 Observational evidence for circumstellar interaction
29
which prevented the X-rays from escaping sooner. Later this supernova has
been detected both by ASCA and Chandra.
Since then a number of other supernovae have shown evidence of circumstellar interaction, and quite a few of these have shown strong X-ray emission
at an early stage. A general result of these observations is that the strongest
X-ray emitting SNe all belong to either Type IIL, IIn or IIb SNe, while the
more common Type IIP SNe are weaker. A few Type Ic SNe related to GRBs
have shown very luminous X-ray emission. In these cases the emission is,
however, non-thermal. No X-rays have been seen for normal Type Ia SNe. At
the time of writing, 31 supernovae have been observed in X-rays shortly after
the explosion, a number which will certainly increase2 . Reviews of X-ray observations of supernovae are given by Schlegel (1995) and Immler & Lewin
(2003). I will here briefly describe the supernovae which are discussed in the
papers included in this thesis, which also include the best studied cases of
circumstellar interaction.
3.3.1
SN 1987A (Type IIpec)
SN 1987A in the Large Magellanic Cloud (LMC) is the closest supernova
for centuries, and as such has been extensively observed. The progenitor of
SN 1987A was a blue supergiant (Sanduleak −69◦ 202), a fact which surprised the astronomical community, since theory predicted that only red supergiants should explode. It is now thought that red supergiants can in some
circumstances evolve back to blue, and in the case of SN 1987A this is thought
to be caused by a binary merger (Podsiadlowski et al. 1990), or possibly by the
low metallicity in the LMC. In any case, the immediate surroundings of the
supernova was tenuous. It soon became evident, however, that the supernova
was surrounded by dense remnants of earlier episodes of mass loss. These
were ionized by the EUV burst at shock breakout, and gave rise to narrow
emission lines which were observed by the International Ultraviolet Explorer
(IUE) after 100 days (Fransson et al. 1989). Radio observations during the
first few weeks also indicated the presence of dense gas in the vicinity of the
supernova. Gradually, the now well known three-ring structure (Fig. 3.7) appeared, and was observed by the Hubble Space Telescope (HST) (Burrows
et al. 1995). The inner ring is thought to have been caused by a fast wind in
the blue supergiant stage overtaking the slower and denser wind of the earlier
red supergiant stage. The red supergiant wind was likely asymmetric, with a
higher density in the equatorial plane, so that the fast wind was slowed down
there, sweeping up the slower and denser material into a ring (Blondin & Lundqvist 1993). The origin of the outer rings is less well understood. They could
be connected with large lobes of material caused by the fast blue supergiant
wind, which escaped more freely along the poles, or by mass loss during a
2A
complete list of the X-ray supernovae is maintained by Stefan Immler, and may be found on
http://lheawww.gsfc.nasa.gov/users/immler/supernovae_list.html
30
Circumstellar interaction
Figure 3.7: The possible structure of the HII-region around SN 1987A, which is
probably the cause of the inner ring, and possibly even the outer rings (Chevalier
& Dwarkadas 1995).
binary merger (Morris & Podsiadlowski 2006). The latter could also be the
origin of the asymmetric mass loss in the red supergiant stage.
Since the rings first showed up, they have gradually faded. However, as
the gas from the explosion has caught up with the inner ring, its emission
has increased in all wavebands. Signs of shock interaction first appeared as
“hot spots” on the inner part of the ring, which are thought to be caused by
the expanding supernova ejecta hitting protrusions in the ring (Michael et al.
2002; Pun et al. 2002). The hot spots have increased in number, until they
now encompass most of the ring. The increasing X-ray emission from the
collision has been followed by Chandra (Zhekov et al. 2005, 2006) and XMM
(Haberl et al. 2006). The fastest rising component is the soft X-rays, where a
number of high ionization lines have been observed, mainly from H-like and
He-like ions of N, O, Ne, Si, Mg and S, as well as Fe XVII– XVII. Zhekov
et al. (2005, 2006) argue that these lines originate mainly in radiative shocks
which are caused by the blast wave hitting the protrusions at oblique angles.
In paper III we disuss the optical emission from these shocks. Our results are
described in more detail in chapter 5.
3.3.2
SN 1993J (Type IIb)
The bright Type II SN 1993J is by far the best studied case of circumstellar
interaction. It was discovered in March 1993 (Ripero & Garcia 1993), and
because of its proximity (∼ 3.6 Mpc), it has been extensively studied in all
wavebands. It was classified as a Type II supernova, based on the detection
of strong hydrogen Balmer lines in the early spectra, but the hydrogen lines
3.3 Observational evidence for circumstellar interaction
31
Figure 3.8: The rings around SN 1987A (upper, image credit: SINS team), and the
collision between the ejecta and the inner ring (lower, image credit: SAINTS team).
32
Circumstellar interaction
soon faded and helium lines became apparent (Filippenko et al. 1993). The
spectrum thus came to resemble a typical spectrum of a Type Ib supernova.
This indicates that the progenitor had only a thin hydrogen layer, the bulk of
the hydrogen envelope having been expelled by the progenitor, possibly as a
result of binary interaction (Nomoto et al. 1993; Woosley et al. 1994; Podsiadlowski et al. 1993). In this respect SN 1993J is a link between Type II SNe
and Type Ib/c SNe, indicating that the distinction of the different supernova
types does not reflect a real difference, but rather that there is a continuous sequence of progenitors depending on the mass of the hydrogen envelope, with
Type IIP SNe at one end, with a massive hydrogen envelope, and Type Ib/c
SNe at the other end, with no remaining hydrogen envelope.
SN 1993J showed signs of circumstellar interaction early on, first through
the detection of radio emission 5 days after the explosion (Weiler et al. 1993),
and shortly thereafter through X-ray observations. The first X-ray detection
was made by ROSAT as early as 6 days after explosion (Zimmerman et al.
1994), while ASCA first observed SN 1993J on day 8 (Kohmura et al. 1994)
and OSSE aboard the Compton Gamma Ray Observatory observed it after
10 days (Leising et al. 1994). At the very early times the X-ray spectrum
was dominated by a very hard component, which was too hard for ROSAT to
resolve properly, but which was easily observed by OSSE. This component
faded rapidly, however, and after three months was too weak for OSSE to
see. After this SN 1993J disappeared behind the Sun, but when it reappeared
at an age of six months, ROSAT and ASCA observations showed the X-ray
spectrum to be dominated by a soft component. The spectrum thus underwent
a transition from a hard to a soft spectrum. This is in agreement with the
theory, which predicts that the early spectrum is dominated by hard emission
from the forward shock, while the softer emission from the radiative reverse
shock is absorbed by the dense, cool shell. At later times the hard component
is fainter, while the soft component now penetrates the cool shell (Fransson
et al. (1996) , hereafter FLC96).
In paper IV we investigate the late X-ray emission from SN 1993J, and this
is also described in more detail in chapter 5.
3.3.3
SN 1998S (Type IIn)
The Type IIn SN 1998S in NGC 3877 was discovered soon after the explosion, and has been well studied at all wavelengths (e.g. Filippenko & Moran
1998; Fassia et al. 2001; Leonard et al. 2000; Lentz et al. 2001; Pooley et al.
2002; Chugai et al. 2002; Pozzo et al. 2004). It was observed by Chandra on
five occasions from day 678 to day 1324 (Pooley et al. 2002). The brightness
of the X-ray emission indicates interaction with a circumstellar medium.A
number of emission lines from metals were observed at energies above 1 keV,
among them lines from Ne, S, Si and Fe. The strength of the observed lines
have been claimed to indicate a high overabundance of metals with respect to
3.3 Observational evidence for circumstellar interaction
33
solar values , which in turn implies that the observed X-ray emission comes
mainly from the shocked ejecta, since such abundances are not expected in
the CSM. Another implication is that the heavy elements must be mixed to a
high velocity, possibly caused by an aspherical explosion (Pooley et al. 2002).
However, that conclusion disagrees with optical observations with the HST
(Fransson et al. 2005), where no evidence of overabundance of metals was
seen. We argue in paper IV that the X-ray analysis suffered from the lack of
a consistent model of the cooling region behind the reverse shock, and when
this is taken into account, the metal overabundance is not needed.
3.3.4
Type IIP SNe
Type IIP SNe show a long plateau in the light curve up to ∼ 100 days after
explosion, caused by the diffusion of radiation in the massive hydrogen envelope of the progenitor star. The progenitor of a Type IIP SN is now known
to be a red supergiant which have retained most of the hydrogen envelope,
due to a comparatively weak stellar wind. This class of SNe come from the
lower mass range resulting in a core collapse. They are consequently the most
common of all SNe. The surroundings of these stars are consequently less
dense than for Type IIn, IIb or IIL SNe, and the ensuing interaction between
ejecta and wind is not strong enough to give rise to a radiative reverse shock.
The hot, shocked region therefore consists of two adiabatic shocks, and the
X-ray emission from the region is generally harder than that from Type IIn,
IIb or IIL SNe. In addition to this there is weak radio synchrotron emission
from relativistic electrons (Weiler et al. 1986; Chevalier & Fransson 2003).
Chandra, XMM-Newton, and recently also Swift, have now detected a number of Type IIP SNe.
35
4
The model
Calculating the emission from the interaction region is a many-faceted problem. One has to consider not only the physics of the collision itself, i.e. the
shock hydrodynamics, but also the microscopic processes within the gas, in
particular the transitions within an ion leading to emission or absorption of
photons, as well as the particle interactions leading to changes in the state of
ionization. If we were to take all processes into account, we would also have
to include the radiative transfer, i.e. the movement of photons through the gas;
the effects of magnetic fields, and of the external radiation field; the conduction of heat in the gas; turbulence and instabilities - and of course this should
be done in three dimensions and in a time-dependent formalism, starting from
the time of the explosion. However, such a problem soon becomes intractable.
Therefore, as in all models, we have made simplifications in order to bring
down the problem to a level where it can be studied with a reasonable amount
of computer power. The main emphasis of this thesis is on the radiative emission from the shocks, so we have made a number of simplifications for the
hydrodynamics. I will start this chapter by listing the simplifications we have
made, along with the reasons why we believe them to be acceptable. I also
describe earlier models of similar problems, and the reasons why these are
not applicable to our case. Our model is then described briefly, but for details
I refer to paper I.
4.1
Simplifications
4.1.1
Stationary flow
The main simplification of the model is the assumption of a stationary flow.
That is, we assume that any process occurs on a timescale shorter than the time
since the explosion. We can then ignore the expansion of the SN in the calculations of the shock structure and consider the shock velocity and pre-shock
density as constant for each model. In paper I we discuss this simplification,
and estimate the ratio between the cooling time and the expansion time. Fig. 5
of paper I shows this ratio for a number of cases, and we find that the cooling
time is in most cases sufficiently short for several years after the explosion.
We also find that the higher the metallicity, the longer this approximation will
be valid.
36
4.1.2
The model
Heat conduction
We also ignore heat conduction between the different zones in the model.
Studies by Borkowski et al. (1989) and Borkowski & Shull (1990) have indicated that for high metallicity, this approximation is not valid. In paper I
we estimate the importance of conduction in our models, and find that for the
cases of interest to us, it turns out not to be important. The reason for the difference between our results and those of Borkowski et al. (1989); Borkowski
& Shull (1990) is that our model has higher shock velocities, which means
that the pre-shock gas will be fully ionized, and therefore that the cooling in
the post-shock gas will be lower.
4.1.3
Radiative transfer
Radiative transfer is treated by using an escape probability formalism. That
is, we compute the probability, β , that a given photon emitted by the gas will
escape from the region. If β = 1, all photons escape; if β = 0, all photons are
absorbed in the gas. In the latter case this formalism will only be approximate.
In an exact treatment the absorption of each photon and the reemission at other
wavelengths should be computed in detail. However, as we discuss in paper I,
for most of the relevant emission lines, β is sufficiently close to unity that this
approximation is valid.
4.1.4
Instabilities
It is likely that instabilities develop in the cooling flow, due to differential
pressure between adjacent cooling regions. This can lead to secondary shocks
within the cooling flow (e.g. Chevalier & Imamura 1982; Plewa & Różyczka
1992; Plewa 1993, 1995; Dopita & Sutherland 1996; Sutherland et al. 2003).
In paper I we discuss the importance of instabilities for the cases of interest to
us. The effects are most likely small for the X-ray emission, except possibly
for a spread in reverse shock velocities. This means that the spectrum is a
superposition of spectra from different cooling regions, and can be simulated
by adding spectra for a number of shock temperatures. This is similar to the
case where the reverse shock encounters clumpy ejecta, which we discuss in
paper IV for the case of SN 1993J.
4.2
Modelling
Our model consists of two main parts - the hydrodynamic code and the emission code. The connection between the two is described in sect. 4.2.4, and
is illustrated in the flowchart in Fig. 4.1. In the following, I summarize the
most important aspects of the interaction between the supernova ejecta and
the wind.
4.2 Modelling
4.2.1
37
Hydrodynamics
After a few days it is safe to assume that the interaction shell is thin compared
to its radius. In this case many of the properties of the interaction region may
be evaluated by a simple treatment, which was first described by Chevalier
(1982a,b) and by Nadyozhin (1985).
If the circumstellar medium is taken to be stationary, the pressure which the
neutral gas exerts on the outer shock is given by:
Pcs = ρcsVs2 ,
(4.1)
while the pressure exerted by the ejecta on the shocked gas is
2
Prev = ρejVrev
= ρej (V −Vs )2 .
(4.2)
The pressures are balanced by the change in the momentum of the shock.
The interaction shell is accelerated by the ejecta pressure, and decelerated by
the circumstellar pressure. The deceleration of the shell due to the interaction
with the surroundings may thus be written (Chevalier 1982b):
dVs
= 4πR2s (Prev − Pcs ).
dt
The mass which has been swept up by the circumstellar shock is:
(Mcs + Mrev )
(4.3)
Mcs = 4πρw R2 dR = Ṁ(Rs − R0 )/vw ,
(4.4)
where R0 is a reference radius. The mass swept up by the reverse shock is:
Z Rs
Mrev = 4π
Vmax t
ρej (R)R2 dR,
(4.5)
where Vmax is the maximum velocity of the ejecta at the time when the shock
forms. Using Eq. 3.7 for the ejecta density, this becomes
Mrev =
4π[R3−η
s
3 η
3−η η−3 ρ0t0 V0
− (Vmaxt)
]t
(η − 3)
.
(4.6)
After a few expansion times the radius of the shock is so large that R0 may
be neglected in Eq. 4.4, and Vmaxt may be neglected in Eq. 4.6. In this case
Eq. 4.3 may be solved, and gives the radius (Chevalier 1982a):
8πρ0t03V0η
Rs =
(η − 4)(η − 3)
1/(η−2)
t (η−3)/(η−2) .
(4.7)
This solution can be used to determine ratios of the physical quantities in the
two shocks, so that the density, temperature and mass of the reverse shock can
be expressed as (FLC96):
38
The model
ρrev =
(η − 3)(η − 4)
ρcs ;
(3 − s)(4 − s)
(4.8)
(3 − s)2
Tcs ;
(η − 3)2
(4.9)
n−4
Mcs .
4−s
(4.10)
Trev =
Mrev =
The temperature of the circumstellar shock is
Tcs = 2.27 × 109 µs
(η − 3)2 2
V K,
(η − s)2 4
(4.11)
where V4 = Vs /104 km s−1 and the density behind the circumstellar shock is
related to the wind density (Eq. 3.6) through the shock jump condition
ρcs =
γ +1
ρw .
γ −1
(4.12)
With γ = 5/3 this becomes ρcs = 4ρw .
Once the temperature and density behind the shock front have been determined, the behaviour of the post-shock gas can be computed from the Euler
equations (Eqs. 3.2–3.4). In order to solve these equations we need to discretize them. That is, we create a spatial grid, where the zones are separated by a
fixed density step. For each zone the temperature and velocity are computed
according to Eqs. 3.2–3.4. The density and temperature are then used as input
to the emission routine.
4.2.2
Calculating the emission
Once the temperature and density have been computed, the ionization state
of the gas can be calculated, as well as the level populations in each ion.
We assume that collisions between ions and thermal electrons are the main
cause of ionization and recombination in the gas, and of excitation of electrons
within each ion. De-excitation of electrons can occur either through collisions,
or by radiative decay. Radiative decay gives rise to the emission of a photon
at a specific wavelength corresponding to the energy difference between the
levels. The volume emissivity of each emission line is then
εk j = nm,k Ak j Ek j βk j ,
(4.13)
where Ek j is the energy difference between levels k and j, Ak j is the probability that the transition will occur, βk j is the escape probability and nm,k is
the number density of ions in ionization stage m whose electrons have been
excited to level k. In addition to this, continuum processes contribute to the
4.2 Modelling
39
emission. The emissivity from continuum processes can be written as (Sutherland & Dopita 1993)
ελ
= 2.05 × 10−19 n2e Gc λ −2
×e−E/kT T −1/2
−1
ergs s−1 cm−3 Å ,
(4.14)
where Gc is the total Gaunt factor, which describes recombination, two-photon
emission and free-free radiation.
The observed spectrum is the sum of the line and continuum processes. The
radiation from the region drains the gas of energy, leading to a cooling of the
gas. The total cooling per unit volume in Eq. (3.4) is calculated by adding the
contributions from line emission and continuum processes
∑ ελ ∆λ + ∑ εk j = ne ni Λ(Te ).
λ
(4.15)
k, j
Once the cooling has been found, the size of the region is calculated by
integrating Eq. 3.4 to find the distance that corresponds to a given value of the
cooling:
Z ni
1
2A B
x=
+ 04 dn0 ,
(4.16)
0
0
05
n
n0 Λ[T (n ), n ] n
where A and B are constants.
The emission routine is a separate unit, and can be used with any hydrodynamical model. The only requirement is that we know the density and temperature, as well as the chemical composition. This fact is exploited in paper
II, where an adiabatic shock model is used to compute the temperature and
density, which are then used as input to the emission code.
4.2.3
Atomic data
It is evident from the equations in the preceding sections that in order to solve
the equations a large quantity of data are needed. The wavelengths, energy
levels and rates for transitions, ionizations and recombination all need to be
specified in order to get to the final result - the spectrum. The aim of all this
is, of course, to be able to interpret the observed spectra, but this can only be
done if the rates of the various processes responsible for creating the emission are known. Because of the importance of reliable atomic data for astrophysical applications an enormous amount of work has been done by various
groups in order to build up databases of atomic data. These databases are continuously updated as new and improved rates are calculated, and a modeller
with pretensions to being up to date must update her numerical code regularly.
Sometimes, however, a modeller needs to weigh the gains of updating the data
against the time needed, as well as the computer power necessary to handle
40
The model
large amounts of atomic data. In the following I will describe the data we have
used, and briefly why we have chosen to use those data instead of others.
The elements included in the model are H, He, C, N, O, Ne, Mg, Al, Si, S,
Ar, Ca, Fe and Ni. Table A1 of paper I lists the ions for which level population
calculations are performed, along with the number of levels included for each
ion, with the exception of Al, which was not included at the time of writing of
that article.
The ionization rates (collisional and autoionization) are computed according to Arnaud & Rothenflug (1985), except for Fe, where we use the method
suggested by Arnaud & Raymond (1992).
The recombination rates are evaluated as the sum of the radiative and dielectronic recombination coefficients, α = αr + αd . At the high temperatures discussed here especially dielectronic reombination is important. Details and references are given in the appendix of paper I.
The collisional and radiative rates for the excited levels are taken from version 4.2 of the Chianti database (Dere et al. 1997; Young et al. 2003) 1 , except
for the recombination to individual levels. The latest version of Chianti, version 5.2 (Landi et al. 2006), has been tested. This version includes new data
for Fe XVII–Fe XXIV, which are of interest for the X-ray emission which we
model. However, we find that the changes to the spectrum are to a great extent
washed out by the resolution of the instruments, while the larger amount of
data greatly increases both the required computer memory and the computational time. We have therefore chosen not to use this version in the calculations
reported here.
4.2.4
The code
As described above, the numerical code consists of two parts. Here follows a
short description of the structure of the code. This is also illustrated schematically in the flowchart in Fig. 4.1. The emission code takes as its input the
temperature and density, which are calculated from the hydrodynamical code,
or given explicitly as input parameters. I describe here the case where a complete model is run, with both parts included. At the start of a run two of the
parameters η , Vs and Trev are given, as well as the chemical composition and
configuration parameters specifying the maximum number of zones and the
spectral and density resolution. Initially the density structure is computed,
and from this the temperature, velocity and pressure in each zone are computed from Eqs. 3.2–3.4.
The emission code takes as its input the chemical composition, the temperature (Ti ) and density (ni ) of each zone, as well as atomic rates. In each zone
the ionization structure of each element is computed by letting the ionization
state in the previous zone evolve over the time needed for the gas to flow
1 CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), and the Universities
of Florence (Italy) and Cambridge (UK).
4.2 Modelling
Start
41
Input:
T0, n0,
composition
Emission code
i=0
Compute
Ti, ni
Hydrodynamic code
Yes
i=maxZones?
i=0
No
Compute
ionization balance and
level populations
Compute
emission and
cooling
i=i+1
Compute
size of shell
and flow time
No
End
Compute
spectrum
Yes
R = Rold?
Compute
total size, R, of
cooling region
Yes
Ti<Tlim,
i=maxZones
or
ti>texp?
No
Figure 4.1: The structure of the code
to this zone, and computing the equilibrium state corresponding to this time
and the temperature of the gas. For all ions that have non-negligible abundances, the level populations are solved and the emission computed according
to Eqs. 4.13–4.15. Now the size, ∆X , of each zone can be computed from
Eq. 4.16.
Since the cooling, Λ(Te ), is needed in order to compute the density and
temperature, which are themselves used for computing Λ(Te ), we need to use
an iterative procedure. Using tabulated cooling functions we make an initial
guess at Λ(Te ), from which we compute the density and temperature. Inserting
these in the emission routine we compute an improved Λ(Te ), and redo the
emission calculations. This is repeated until the change in the total size, X , of
the cooling region between two iterations is less than one percent.
4.2.5
Fitting observed spectra
When applying our model to observed X-ray spectra from supernovae we
use the spectral analysis package XSPEC, which is the most commonly used
tool for analysing X-ray spectra (Arnaud 1996). XSPEC includes response
matrices for most X-ray instruments, as well as a large number of spectral
models that can be used for fitting the observations. However, XSPEC does
not include models that are useful for cooling regions like the cases of interest
to us. Therefore we use the models described in this chapter, by importing
42
The model
them into XSPEC. There are two ways of including one’s own models in
XSPEC - either by including the code itself, and running it every time a fit
is made, or by including a pre-compiled table model, which is simply a grid
of models for different parameters, between which XSPEC can interpolate.
We have chosen to use the latter method, mainly because the code is too time
consuming to be run every time a fit is made. We have computed a number
of different table models, each for a given composition, and with the temperature as the interpolating parameter. The contribution to the spectrum from
each element has been included as a separate spectrum, and can be varieded
in the fitting. This will not give a self-consistent result, because the cooling
will not be correct, but it can give some idea about which abundances should
be varied. A new, improved model can then be computed based on this. We
have used this method in paper IV, where it is used for analyzing the X-ray
spectra of SN 1993J and SN 1998S.
43
5
Summary of the papers
5.1
Paper I
The main part of this work has been to develop the numerical model described
in chapter 4, which self-consistently models the X-ray emission from the interaction between supernovae and their surroundings. In paper I we describe
this model, and discuss its limitations. Our model differs from earlier models
in that full multi-level calculations are performed in order to obtain the line
emission as well as using updated atomic data. This gives a more realistic
solution both for the resulting spectrum, and for the cooling of the gas. The
fact that this cooling is used in the hydrodynamic equations to compute the
structure of the region means that the emission from each zone is determined
self-consistently, which has not been the case in earlier models.
When analyzing X-ray spectra it is common to use a single-temperature
model to fit the whole spectrum, or, if that is not sufficient, to combine several
single-temperature models. In neither of these cases can the spectrum of a
cooling shock be reproduced. In paper I we show that a single-temperature
spectrum with the same temperature as the shock overestimates the emission
at high energies and underestimates it at low energies as compared to the
spectrum from a cooling shock. Also, the relative strengths of emission lines
of different ionization stages differ from those in a cooling shock, and so the
elemental abundances will be misinterpreted. A comparison between these
spectra is shown in Fig. 5.1, where the differences described here are evident.
The code was originally intended mainly for radiative shocks, and in paper I we show that the reverse shock will be radiative for a long time (Fig. 5
of paper I). However, we also show that this depends strongly on the composition, the ejecta density gradient and the mass loss rate of the progenitor.
Paper I also discusses the effects of varying different parameters, in particular the shock temperature and the composition (Figs. 9 and 11 of paper I).
Fig. 9 shows that, although the line emission is strongest in the models with
a low shock temperature, even the high-temperature radiative shocks show
emission lines from low and intermediate ionization stages. This is a characteristic of a cooling shock, which a single-temperature model lacks.
My contribution to paper I has been the development of the code for the
emission from the reverse shock, as well as writing most of the text.
44
Summary of the papers
Figure 5.1: Comparison of the spectrum from a cooling shock with a shock temperature of 1 keV (thick line) with a single-temperature spectrum, with kT =1 keV (thin
line).
5.2
Paper II
Paper II discusses the radio and X-ray emission from Type IIP SNe. We find
that both the radio and X-ray observations indicate mass loss rates of a few
times 10−6 M yr−1 (for a wind velocity of 10 km s−1 ). This is consistent with
ordinary RSG winds, and there is no need for a short lived superwind phase,
as for the Type IIn SNe. My contribution to this paper was the computation
of the X-ray spectrum from the reverse shock, which is shown in Fig. 7 of the
paper. Although my model was originally intended for radiative shocks, the
emission code is also valid for an adiabatic shock, subject only to different
input parameters.
5.3
Paper III
Paper III discusses the optical emission from the collision between the supernova ejecta and the circumstellar ring in SN 1987A. High resolution optical
spectra obtained with UVES/VLT are analyzed. A number of high ionization
lines are observed with temperatures of up to ∼ 2×106 K, which indicates that
they originate in shocked gas. Spectral modelling shows that most of the emis-
5.4 Paper IV
45
sion comes from radiative shocks with velocities of 310–390 km s−1 . This is
consistent with the observed line widths of ∼ 350 km s−1 .
My contribution to paper III consists in modelling the emission, the results
of which are shown in Figs. 8–10 in the paper, as well as contributing to that
part of the text which deals with the model.
5.4
Paper IV
In paper IV we discuss the X-ray observations of SN 1993J and SN 1998S.
We argue that the lack of self-consistent models for a cooling shock in the original analysis led to questionable conclusions about the shock temperatures
and the composition of the gas. We re-analyze the spectra with our numerical
model, and discuss how well the observations are reproduced by a single radiative model, and by a combination of radiative and adiabatic models. We
use compositions based on realistic explosion models, and on the observed
abundances in the circumstellar ring of SN 1987A. We find that the spectra
are consistent with CNO-enriched abundances, and that the overabundance
of metals that was claimed for SN 1998S is not necessary. There is therefore
now a consistency between the X-ray spectrum and the optical observations,
showing evidence for CNO processing. In SN 1998S we find that the contribution from the circumstellar shock is appreciable, while this contribution is
not needed in SN 1993J. Instead, SN 1993J is best fit with a combination of an
adiabatic reverse shock and one radiative component at half the reverse shock
temperature. This spectrum is shown in Fig. 5.2, for a composition resembling
that of the circumstellar ring of SN 1987A.
My contribution to this paper has been the modelling, and writing most of
the initial text, except for the parts dealing with data extraction.
5.5
Corrections to the atomic data
One characteristic of the development of any numerical code is the presence
of errors, or bugs, in the program, which need to be found and fixed. A large
amount of the time spent on developing a code is actually spent on searching
for bugs, and a completely bug-free code is hard, or even impossible, to obtain.
Even after a code has been used a long time, a bug may turn up which affects
the results. So also in this case. During the preparation of paper IV, an error
was found in the reading of dielectronic recombination rates to the C-like,
O-like and F-like iso-electronic sequences. The result of this error was that
the ion densities of these ions, and consequently the strength of their emission lines, were underestimated. The largest effect was for the Fe XVI and
Fe XVII emission, and in particular the emission at 0.7-0.8 keV, for temperatures of kT ∼ 0.5 − 2.0 keV. This does not affect the results of paper II, where
46
Summary of the papers
CNO!enhanced, Rad T=0.75, 0.22keV, Adia comp T=1.4keV, nH(shell)=0.006, Chi2=1.6
0.1
0
!10
!20
sign(d!m)*!2
0
normalized counts/sec/keV
0.2
SN 1993J XMM!Newton
0.5
1
2
5
channel energy (keV)
Figure 5.2: Fit to the XMM spectrum of SN 1993J with an adiabatic shock at kTrev =
1.4 keV and a radiative shock at kTrev = 0.75 keV, both with a composition resembling
that of the circumstellar ring of SN 1987A.
the temperature was too high for these ions to be abundant, nor is it relevant
for paper III, where the temperature was too low. For paper I, the effect of
the error was that the strength of the emission lines of Fe XVI and Fe XVII,
and consequently the ratio of these lines to O VIII in Fig. 10 of paper I, was
underestimated. The effects on the spectrum for two temperatures is shown in
Fig. 5.3. The differences in the 0.3 keV model are negligible, but for the 1 keV
model the differences described above are noticeable. The main conclusions
of paper I are, however, unchanged.
5.5 Corrections to the atomic data
47
Figure 5.3: Spectra at Trev = 0.3 keV (left) and Trev = 1.0 keV (right), with wrong
Fe XVI and Fe XVII emission (thick line), as in paper I, and with correct emission
(thin line).
49
6
Future prospects
6.1
Multi-dimensional hydrodynamics
An obvious next step of my work would be to include multi-dimensional and
time-dependent hydrodynamics. As explosion models like the one in Fig. 2.5
show, the structure of the ejecta is far from simple, and neither is the structure
of the interaction region (see Fig. 3.5). A lot of work has been done in recent
years on developing multi-dimensional codes, but in none of these is the emission and cooling computed self-consistently. In my code, on the other hand,
the emission and cooling are computed self-consistently, but with a simplified one-dimensional hydrodynamic structure. Combining my code with existing multi-dimensional models would be a vast improvement on both models.
However, this will require large amounts of computer time and memory space,
as the ionization structure and level population will have to be computed over
a large spatial and temporal grid.
6.2
Supernova remnants
When the model has been adjusted to include multi-dimensional hydrodynamics, we will be able to apply it to older supernova remnants. Only a few supernovae show strong interaction at early times, and therefore the model is at
present applicable to only a limited number of all supernovae. Including more
complicated, time-dependent hydrodynamics, would enable us to calculate the
temporal evolution of the gas. First this will be applied to studying SN 1987A
in more detail. 20 years after the explosion SN 1987A is now undergoing a
transition to a supernova remnant, and in order to interpret the observations,
updated models for the shock emission are required. Combining my model
with multi-dimensional hydrodynamic codes will improve our ability to investigate the structure of the remnant and allow us to say something about
the mixing in the supernova and the evolution both of the progenitor and of
the newborn supernova remnant. Similar studies could also be conducted for
other young remnants like Cas A, Tycho and Kepler.
50
6.3
Future prospects
Other projects
In the future I also wish to extend the model to include the photoionized
post-shock and pre-shock regions to model the optical/UV emission. This
would give a more complete picture of the various aspects of the interaction
between supernovae and their surroundings. Other possible projects involve
radiative shocks in different environments. Although the model described
here has been developed for the radiative shocks surrounding supernovae, it
could in principle be used for any radiative shock, which occur in a number
of environments in the Universe. Examples include interacting winds,
Herbig-Haro objects, cooling flows in galaxies, gamma-ray bursts.
6.4
Future observational facilities
As mentioned earlier, good theoretical models are needed to keep up with
the rapid development of observational facilities. However, as the models improve, the observational facilities soon lag behind. The model described in
this thesis provides the ability to distinguish between the contribution of a
large number of atomic lines in a cooling plasma. However, for most supernovae (with the exception of SN 1987A) the X-ray observations do not have
the resolution that is necessary for this analysis. Therefore better observational capabilities are desirable. The planned ESA X-ray mission XEUS (Xray Evolving Universe Spectroscopy), which will be launched sometime after
2015, will provide 200 times the sensitivity and about 20 times the spectral
resolution of XMM-Newton. This will allow detailed spectroscopic studies,
even of faint sources. For the cases which we study, XEUS will be able to
resolve individual spectral lines, and thus determine the contributions from
different ionization stages in cooling shocks. By using my model to analyse
those spectra, we will be able to determine the temperatures and abundances
in the cooling region with much greater accuracy than previously.
51
Svensk sammanfattning
Föreliggande avhandling behandlar den växelverkan som uppstår mellan
vissa supernovor och den kringliggande gasen. Avhandlingen består av fyra
vetenskapliga artiklar, som här benämns artikel I–IV.
En supernova är det våldsamma slutet på vissa stjärnors liv. I en enorm explosion slungas stora delar av stjärnan ut i rymden, och under en kort tid lyser
den starkare än alla stjärnor i den galax i vilken den befinner sig. Det finns två
typer av supernovor. Den ena har sitt ursprung i en vit dvärgstjärna, den rest
som finns kvar när en relativt lätt stjärna dör. Om den samlar på sig mycket
gas från en närliggande stjärna, kan kärnprocesser åter tändas som resulterar i
en explosion som sliter sönder hela stjärnan. Den andra formen av supernova
uppstår när en massiv stjärnas kärna kollapsar, för att sedan explodera. De
senare är de supernovor som behandlas i denna avhandling.
En stjärna är en gigantisk kärnreaktor, där den ursprungliga gasen sakta omvandlas till tyngre grundämnen. All gas i universum var från början i form av
väte, helium, och mycket små delar av andra ämnen. I alla stjärnor omvandlas
väte till helium, och i alla förutom de allra lättaste stjärnorna omvandlas sedan
helium till kol och syre. I denna process frigörs energi, som lämnar stjärnan
i form av ljus. I mer massiva stjärnor, de som senare ska sluta som supernovor, omvandlas även kol och syre till tyngre grundämnen, ända upp till järn.
Tyngre ämnen än järn kan inte bildas utan att man tillför energi, så när en
tillräckligt stor kärna av järn har byggts upp i stjärnans centrum finns inget
mer som kan producera energi. Tyngdkraften tar över, och kärnan kollapsar.
Denna kollaps vänds till en explosion då den repulsiva kraften mellan partiklarna i atomkärnorna blivit tillräckligt stark, och den infallande gasen studsar
mot kärnan. Vid denna explosion frigörs gravitationsenergi, och denna energi
räcker även till att bilda tyngre grundämnen än järn. Samtidigt är det just explosionen som sprider ut dessa nybildade ämnen i rymden. Många av dessa
ämnen är de som bygger upp jorden vi lever på, och även våra kroppar. Supernovor är på så sätt en essentiell faktor för att liv ska kunna uppstå.
Under största delen av stjärnans liv är dess inre delar dolda för oss, och de
processer som äger rum där kan aldrig observeras direkt, utan enbart studeras
indirekt utifrån de effekter de har på det som händer i de yttra lagren. Mot
slutet av stjärnans liv ändrar sig både strukturen och kärnprocesserna alldeles
för fort för att informationen om detta ska hinna ut till de yttre lagren. Inget
syns därför på ytan när stjärnan är nära att dö. Det är följaktligen svårt att
genom direkta observationer ta reda om teorierna för stjärnutveckling stäm-
52
Svensk sammanfattning
mer. Vid explosionen blottläggs dock de inre delarna av stjärnan, och studier
av explosionen gör det möjligt att testa teorierna.
Vissa supernovor uppvisar en kraftig växelverkan med sin omgivning. När
stjärnans yttre lager med stor kraft slungas ut i rymden, bildas en chockvåg
som sveper upp den kringliggande gasen, som då värms upp till temperaturer
på ungefär en miljard grader. Det höga trycket gör att en ny chockvåg bildas,
som rör sig in i supernovan och sveper upp supernovagasen. Eftersom denna
chockvåg rör sig saktare än den första, blir temperaturen lägre, bara några
tiotals miljoner grader. Bakom dessa båda chocker bildas kopiösa mängder
röntgenstrålning. Framförallt vid den bakre (eller reversa) chocken, där temperaturen är lägre, bildas starka emissionslinjer. Denna kraftiga strålning kyler
gasen effektivt, och gör så att ett tunt, kallt skal med hög täthet bildas.
I denna avhandling studeras strålningen från den reversa chocken, och då
framförallt röntgenstrålningen. Den största delen av avhandlingsarbete har
bestått i att utveckla en numerisk modell som ger spektra från den reversa
chocken. Dessa kan sedan jämföras med observationer, och därigenom kan vi
dra slutsatser om bland annat den kemiska sammansättningen och temperaturen i gasen. I artikel I beskriver vi modellen och dess begränsningar, samt
ger exempel på användningsområden.
Vi har tillämpat denna modell på några supernovor som uppvisar stark
växelverkan. I artikel II studerar vi supernovor av Typ IIP. Dessa supernovor ger en bra möjlighet att bestämma massförlusten under sena stadier av
stjärnors liv, och i artikel II finner vi att både radio och röntgenobservationer
indikerar en massförlust på 10−6 M yr−1 för en hastighet av 10 km s−1 .
I artikel III studerar vi kollisionen mellan SN 1987A och den ring som
omger supernovan. SN 1987A var den mest magnifika supernovan på många
hundra år, och efter 20 år fortsätter den att fascinera. För ungefär 10 år sedan
hann gasen från explosionen i kapp delar av den inre av de tre ringar som
omger supernovan, och sedan dess har hela ringen gradvis lyst upp. Observationer med VLT-teleskopet i Chile visar emissionslinjer från olika jonisationsgrader, vilket indikerar att linjerna har bildats i gas med olika temperaturer. Detta tyder på att gasen är kylande. Vi finner också att gasen där linjerna
bildas rör sig med hastigheter mellan 310–390 km s−1 .
I artikel IV behandlas röntgenstrålningen från två Typ II supernovor,
SN 1993J och SN 1998S. Dessa supernovor visade tidigt tecken på
växelverkan med omgivningen. Vi diskuterar observationer som gjorts med
röntgenobservatorierna XMM-Newton (SN 1993J) och Chandra (SN 1993J
och SN 1998S). Dessa observationer har tidigare använts för att bestämma
den kemiska sammansättningen i supernovagasen. I artikel IV visar vi att
den analys som gjorts tidigare är tvivelaktig, och att den sammansättning
som bestämts inte är realistisk. Vi har beräknat spektra baserat på teoretiska
modeller för explosionen och den kemiska sammansättningen. Preliminära
resultat indikerar att en sammansättning baserat på teoretiska beräkningar
reproducerar de viktigaste emissionslinjerna i de observerade spektrana, och
53
att den oväntat höga metallhalt som föreslagits framförallt för SN 1998S
därför inte behövs.
55
Acknowledgements
There are a number of people whose assistance and support in one way or
another have been essential for the completion of this thesis.
First I wish to express my gratitude to my supervisor, Claes Fransson, who
first introduced me to the field of supernova research, and whose encouragement and vast knowledge has been a great source of inspiration to me.
I am sincerely grateful to Cecilia Kozma for all help and for the many fruitful discussions we have had over the years, and for thorough reading and many
comments on various versions of this manuscript.
I am also indebted to the late Roland Svensson, who first invited me to
Stockholm Observatory and encouraged me to come here. Thanks to all the
people at Stockholm Observatory, and especially all past and present graduate
students for making my time here so interesting. I am grateful to the people
in the supernova group, for many stimulating discussions. I also want to thank
Stefan Larsson and Linnea Hjalmarsdotter for helping me with XSPEC, and
Magnus Axelsson for advice on various formalities. Warm thanks to Lena
Olofsson, Ulla Engberg and Sandra Åberg for your assistance on all administrative issues and to Uno Wänn for willingly helping me with practical problems both big and small. Your help has been invaluable. Thanks to Robert
Cumming for discussions and very valuable comments on a late version of
this manuscript.
I would like to thank Poonam Chandra for the collaboration we have had
over the past months, and for working so hard when I needed to complete this
work.
Special thanks to Lena Gumaelius, Christer Nilsson, Magnus Näslund, and
all the others at the House of Science, for creating such a warm and encouraging atmosphere to work in.
I am deeply indebted to my husband, Raymond, for all support, for helping
me with programming and debugging, and for believing in me when I did not.
Thanks also to my parents for always supporting me, and to Marianne, Ingrid
and Andreas for providing distractions when I needed them the most, and for
making life so much fun.
Stockholm, 19th February 2007
57
Publications not included in this thesis
Nymark, T.K. & Fransson, C., 2005, in proceedings of “The X-ray Universe”,
ESA publications, p. 373
Nymark, T.K., 2005, in “Cosmic Explosions”, IAU Colloquium
192, eds. J.M. Marcaide, K.W. Weiler (Springer), CD-ROM p. 113
Nymark, T.K. & Fransson, C., 2002, in “From Twilight to Highlight: The Physics of Supernovae.”, eds. Hillebrandt, W. & Leibundgut, B.,
(Springer), p. 315–320.
Nymark, T.K., 1997, in ”White dwarfs”, eds. Isern, J., Hernanz, M.
and Garcia-Berro, E., Kluwer Academic Publishers
Nymark, T.K., 1996, Cand. Scient. thesis, University of Tromsø
Nymark, T.K. & Solheim, J.-E., 1995, Baltic Astronomy, Vol 4,
386–395
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