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Supernovae and Cosmology
Bruno Leibundgut
European Southern Observatory
KarlíSchwarzschildíStrasse 2, Dí85748 Garching
Germany
Email: bleibundgut@eso.org
Abstract
The extreme luminosity and their fairly unique temporal behaviour
have made supernovae a superb tool to measure distances in the unií
verse. As complex astrophysical events they provide interesting insights
into explosion physics, explosive nucleosynthesis, hydrodynamics of the
explosion and radiation transport. They are an end product of stellar
evolution and provide clues to the stellar composition. Since they can be
observed at large distances they have become critical probes to further
explore astrophysical e#ects, like dust properties in external galaxies and
the star formation history of galaxies. Some of the astrophysics interferes
with the cosmological applications of supernovae. The local velocity field,
distorted by the gravitational attraction of the local large scale structure,
and the reddening law appear at the moment the major limitations in the
accuracy with which cosmological parameters can be determined. These
absorption e#ects can introduce a secondary bias into the observations of
the distant supernovae, which needs to be carefully evaluated. Supernovae
have been used for the measurement of the Hubble constant, i.e. the curí
rent expansion rate of the universe, and the accelerated cosmic expansion
directly inferred from the apparent faintness of the distant supernovae.
1 Introduction
The energetic display of a supernova marks the transition from a bound star to
the recycling of material into the gas pool of a galaxy or beyond. The progenitor
star at explosion could still have an active nuclear furnace operating or could
be a degenerate end product of stellar evolution. The corresponding results also
take di#erent forms: a compact ``stellar'' remnant, a neutron star or a black
hole as the result of a collapse of the stellar core, or no compact remnant, when
the star is incinerated by a nuclear explosion. In all cases, the expelled material
will interact with its environment and produce a supernova remnant. One of
the main topic of interest is how the di#erent physical processes lead to the
observed displays. As further exposed in the following, some of the uncertainties
in our understanding of the supernova physics limits their use in cosmological
applications.
Supernovae shaped today's universe in many di#erent ways. They are the
main mechanism to create heavy elements, especially the ones only created
in explosive nucleosynthesis. They are also responsible for the return of these
newly created elements into the baryonic cycle of dust, gas and stars. The energy
input into the interstellar material can be so significant that star formation can
be triggered or suppressed. For smaller galaxies, supernovae most likely shape
1

their appearances. Cosmic ray acceleration is most probably done in the shock
of supernova remnants and the collapse of massive stellar cores are the main
source of neutrinos beyond the Big Bang.
Supernovae appear in very di#erent displays. In fact, a clear definition of
a supernova does not exist. There is a classification scheme, which dates back
to Walter Baade, Fritz Zwicky and Robert Minkowski (Baade & Zwicky 1934,
Minkowski 1941, 1964). For a modern version with detailed definitions see
Filippenko (1997). A supernova in the following will be the event when a star
ejects most of its material in a violent explosion and ceases to exist as a stellar
entity. Note that this is a physical description, while the observations we obtain
are often not able to definitely ascertain that the above condition is fulfilled.
Nevertheless, a supernova by definition cannot be recurrent. It marks the end
of the existence of a star as an individual object. One should note that this
definition includes #-ray bursts together with the more traditional supernova
classes.
Due to their luminosity supernovae have been a favourite for cosmological
applications. They are also markers of star formation and could be amongst the
earliest objects we may be able to observe in the early universe.
This article first presents a brief history of supernovae. It will then comment
on the current classification scheme and its use to understand the explosion
physics and the radiation hydrodynamics, which takes place in these explosions.
Supernovae as cosmological distance indicators will be examined first before we
will move on to a discussion of the Hubble constant and the expansion history
of the universe as derived from supernovae. The latter is currently concentrated
on Type Ia supernovae (SNe Ia hereafter), which have been the most successful
in measuring distances half way across the universe.
The literature on supernovae and their cosmological applications has literally
exploded in the past decade. There are the classic papers, which will be mení
tioned in this review, but also many associated interpretations. Overviews have
been presented in recent monographs on supernovae and gammaíray bursts (e.g.
Niemeyer & Truran 2000, Hillebrandt & Leibundgut 2003, Weiler 2003, HØoflich
et al. 2004, Marcaide & Weiler 2005, Turatto et al. 2005). Supernova physics
is reviewed in Filippenko (1997), Hillebrandt & Niemeyer (2000), Leibundgut
(2000) and Woosley & Bloom (2007). Several reviews of the supernova cosmolí
ogy have been published as well (Branch 1998, Riess 2000, Leibundgut 2001,
Perlmutter & Schmidt 2003).
1.1 Some early history
The appearance of new stars, ''stellae novae'' from their Latin designation, has
always intrigued astronomers as documented in the ancient Chinese and Koí
rean records (see Clark & Stephenson (1977) and Murdin & Murdin (1978) for
reviews of the historic supernovae in the Milky Way observed over the last two
millennia).
The first to suggest that there are two classes of novae was Lundmark (1925),
who proposed an 'upper class' about 10 magnitudes brighter than the 'lower
2

class' of novae. The latter would correspond to the well known Galactic novae.
He based his proposal mostly on the observation of the (super)nova 'S Aní
dromeda' observed in 1885 (designated SN 1885A in modern nomenclature),
which appeared that much brighter than a sample of about two dozen regular
novae in the Andromeda galaxy. Lundmark later seemingly was the first to
suggest the name 'superínova' (Lundmark 1932).
It was Walter Baade who made the connection between the historical suí
pernovae and the observed emission nebulae at their positions, thus identifyí
ing the remnants of the explosions. The most prominent object is of course
the Crab Nebular (Messier 1), the leftover from the supernova in 1054 (Baade
1942, Mayall & Oort 1942). With extensive observations of bright supernovae
Minkowski (1941) introduced two subclasses. Zwicky (1965) refined the classií
fication scheme for supernovae further. However, for several decades only two
main classes were maintained until in the early 1980s it became clear that at
least one further subclass needed to be added. The classification scheme has
now expanded again with the introduction of several subclasses to further disí
tinguish between di#erent observed displays. Some proposals mix spectroscopic
definitions with the light curve appearance, while others even introduced theoí
retical arguments into the classification. The reason for a classification scheme
should remain simple and it should not be mixed with theoretical ideas. While
di#erent behaviour clearly indicates di#erent physics, the classification as used
in the past was primarily to quickly plan observing strategies and give an iní
dication what type of event was observed. This still is often the case for the
projects, which make use of SNe Ia for cosmology, as the spectroscopy time
needs to be used as e#ciently as possible.
2 Supernova classification
The modern classification of supernovae is based on the spectroscopy at maxí
imum light (e.g. Filippenko 1997, Turatto et al. 2003 í see also Fig. 1). The
distinction is done through the presence (or absence) of hydrogen lines in the
optical spectra near maximum brightness leading to the classes of Type II suí
pernovae (or Type I supernovae). The hydrogenídeficient supernovae are furí
ther subdivided into groups which display prominent absorption near 6150 Ú A
attributed to a transition in singly ionised silicon (Si II in astronomical notaí
tion) for the Type Ia supernovae and others which show sodium and oxygen
absorption lines, designated Type Ib/c supernovae (Fig. 1). The separation of
these two subclasses happened during the early 1980s, when it became clear
that there was a subset of Type I supernovae that showed very red colours, a
spectral evolution, which appeared accelerated, and showed lines of intermedií
ate elements at late phases (Wheeler & Levreault 1985, Uomoto & Kirshner
1985, Panagia et al. 1986, Filippenko & Sargent 1986). The presence/absence
of helium lines is used as a separation into the Type Ib/Type Ic supernovae,
respectively. The exact physical interpretation of this separation remains relaí
tively weak. An evolutionary sequence for the separation of these coreícollapse
3

supernovae has been proposed, in which the appearance is determined by the
amount of hydrogen envelope remaining on the star at the time of explosion.
Regular stars with a thick hydrogen layer would explode as SNe II, while the
ones which lost this hydrogen layer, e.g. due to a strong stellar wind or interací
tion with a binary companion, would become SNe Ib. Should the helium layer
be eroded as well, then a SN Ic is observed. Moreover, there is one 'crossíover'
class of Type IIb supernovae, with the prominent example of SN 1993J. These
events typically start out as hydrogenídisplaying supernovae (hence SN II) beí
fore the hydrogen lines disappear and the objects start to resemble Type Ib/c
supernovae. They represent the major link showing that the SNe Ib/c are coreí
collapse supernovae. Figure 1 also lists some prominent examples for each SN
class.
A physical picture for this classification scheme has emerged. The Type
Ia supernovae are coming from thermonuclear explosions of stars, which have
shed hydrogen and helium during their progenitor evolution. Hence no traces
of these elements are observed in these explosions. All other supernovae most
likely come from the core collapse in massive stars or in some cases more exotic
phenomena, like pair instability (e.g. Heger et al. 2003). The signature for these
events are their oxygen and calcium rich spectra at late phases.
It is notable that gravity is the ultimate reason for both types of explosions.
In the cores of massive stars the hydrostatic equilibrium is maintained by burní
ing to higher and higher elements at increasing temperatures. By the time the
core has burnt its fuel to iron no further exothermic reactions are possible and
the stellar core collapses under the weight of the outer layers of the star. The
collapse is only stopped when the material reaches nuclear densities where elecí
trons and protons merge and create neutrons. At this stage the protoíneutron
star provides a hard surface. The neutrinos created in this process emerge
mostly without interacting, but even a tiny amount of energy deposited by the
neutrinos in the envelope can turn the implosion into an explosion. The exact
mechanism has not been fully explored, but at least small stars (8 -- 10 M# ) can
now be made to explode moderately by the modellers (Kitaura et al. 2006).
Hypernovae have been added to the list of supernovae and they repreí
sent the high energy end (at least in their kinematics) with the large expaní
sion velocities observed in these objects. The connection of gamma--ray burst
with supernovae has now been generally accepted with the observations of
SN 2003dh/GRB030329 (Stanek et al. 2003, Matheson et al. 2003, Hjorth et
al. 2003). It should be noted that already SN 1998bw/GRB980425 showed all
the signatures of a supernova (Galama et al. 1998, Patat et al. 2001). Hyí
pernovae are characterised by the absence of hydrogen and helium and very
high expansion velocities observed in their spectra (Mazzali et al. 2002, 2003,
Woosley & Bloom 2007). In some cases no gammaíray burst is observed, like for
SN 2002ap. The amount of nickel synthesised in these explosions is substantial
(up to about 0.5 M# ; Sollerman et al. 2002). The kinetic energies inferred from
the line widths are also substantially larger than the ones of regular SNe II.
In many aspects they appear to be similar to the SNe Ib/c with high kinetic
energy.
4

Figure 1: Classification scheme for supernovae. The presence or absence of
specific absorption features in the maximumílight spectrum is used to separate
the supernovae into di#erent classes. The SNe Ia are the only ones which are
thought to come from the thermonuclear explosion of a white dwarf. All others
are powered by the core collapse in a massive star. Prominent examples of the
various classes are indicated.
5

In the case of the thermonuclear supernovae the electronídegenerate white
dwarf has to cope with an increasing amount of material piled onto it by a
companion star, and hence increases the pressure and temperature in the core.
Again, it is the gravitational force which sets o# the explosion, in this case the
explosive carbon and oxygen burning, which disrupts the star. A comparison
of the binding energy of a neutron star or the binding energy of a solar mass of
iron give a clear indication of how much energy is released in these explosions.
Some objects cannot be clearly classified into one or the other class. Prime
examples are SN 2002ic and SN 2006gy, which both have been interpreted as
possibly a thermonuclear explosion or a coreícollapse. While SN 2002ic has
all the traits of a thermonuclear supernova it also displayed a strong hydrogen
Balmer H# emission line (Hamuy et al. 2003). This latter fact has led to an
investigation whether SN 2002ic could not be a coreícollapse supernova (Benetti
et al. 2006). SN 2006gy is a very energetic supernova clearly showing strong
H# emission, but a very slow light curve. One interpretation argues for possibly
the first observation of a pairíinstability supernova (Smith et al. 2007), while
another study finds that this could be a thermonuclear supernova within a dense
circumstellar shell (Ofek et al. 2007). Such cases show the di#culty to uniquely
map the classification scheme into the physical interpretation of the events.
3 Coreícollapse supernovae
The richness in appearance of the coreícollapse supernovae is due to their varied
progenitor histories. Spectra observed near maximum light show H# in these
events, but with a wide variety (e.g. Filippenko 1997, Leibundgut 2005). The
typical light curves of SNe II display a long plateau of about 100 days after
the maximum. The most prominent and best observed case after SN 1987A is
SN 1999em (Hamuy 2001, Leonard et al. 2001, Elmhamdi et al. 2003). SN 1987A
taught us a lot about core collapse supernovae (for reviews see Arnett et al. 1989,
McCray 1993, Leibundgut & Suntze# 2003, McCray 2005). While SN 1987A
displayed a strong P Cygni line of H#, it is almost not visible in SN 1993J. The
latter lost this line in its evolution completely and only after about one year
did H# reemerge in the nebular spectrum (Filippenko et al. 1994). The case
of SN 1988Z is di#erent again. In this case, the hydrogen is excited in circumí
stellar material shocked by the supernova ejecta. The emission is dominated by
the shock energy and not recombination or radioactive decay as in most other
supernovae.
This special case of supernovae interacting early on with their dense circumí
stellar environment is discussed in Chevalier & Fransson (2003) and Leibundgut
(1994). They typically have very slow light curves and spectra that show emisí
sion lines but very little absorption. The best studied cases so far are SN 1986J
(Leibundgut et al. 1991), SN 1988Z (Turatto et al. 1993), SN 1995N (Fransson
et al. 2002) and SN 1998S (Fassia et al. 2000). All of these objects are strong raí
dio emitters (reviews on the radio emission are available from Weiler & Sramek
1988 and Weiler et al. 2002). The radio observations in particular allow to trace
6

the massíloss history of the progenitor star with interesting conclusions on their
final evolution. These objects often can be observed for many years. The poster
child for a shock interacting with circumstellar material is of course SN 1987A,
which recently transitioned from a teenager into a maturing supernova remnant
(McCray 1993, 2005, Fransson et al. 2007).
Extreme examples of this class of supernovae demonstrate their diversity.
Examples are the GRBs (reviews in Weiler 2003 and Woosley & Bloom 2007),
the recent, very energetic SN 2006gy (Ofek et al. 2007, Smith et al. 2007), the
very faint objects like SN 1987A and the Type Ib/c events, which are presumably
stripped of their envelopes either by massive stellar winds or mass loss to a
companion star. All these di#erent appearances are a signature of the variety
the evolution of massive stars leading to di#erent configurations at the time of
explosion.
Several proposals have been made how coreícollapse supernovae could be
used as distance indicators. They will be discussed in ç5.1.1.
4 Type Ia supernovae
Although thermonuclear supernovae have simpler underlying physics than the
coreícollapse supernovae, there still remain formidable hurdles to fully underí
stand them (Hillebrandt & Niemeyer 2000). The observational material that has
been assembled in the last decade is considerable and many nearby supernovae
are now observed with exquisite detail. The last few years have seen dramatic
progress in recognising peculiar events and also determining specific characterí
istics. The situation a few years ago is described in Leibundgut (2000). Since
then the peculiar SN 2000cx (Li et al. 2001, Candia et al. 2003) and SN 2002cx
(Li et al. 2003) have been observed. A truly particular case has been discovered
in SN 2002ic (Hamuy et al. 2003), which displayed a strong, broadílined H#
emission after about 90 days past the maximum. This supernova displayed the
signatures of a bright SN Ia with what looked like residual H# emission from
the host galaxy. The spectral sequence later showed that the hydrogen emission
is intrinsic to the supernova and indicates that this explosion occurred inside a
dense hydrogen cocoon. Such events throw a dark shadow over the light curve
vs. luminosity relations that have been used in the past to normalise the peak
luminosity (Phillips 1993, Hamuy et al. 1995, Riess et al. 1996a, 1998, Perlmutí
ter et al. 1997, Phillips et al. 1999, Goldhaber et al. 2001, Wang et al. 2003a,
2006, Guy et al. 2005, 2007, Prieto et al. 2006, Jha et al. 2007) necessary to
derive accurate cosmological distances. The di#erences for individual objects
highlight the fact that not all SNe Ia are identical and provide us with a tool to
further investigate the true nature of these explosions.
The main observables of supernovae remain the optical and nearíinfrared
light curves and spectral evolution (e.g. Leibundgut 2000). Spectroípolarimetry
in the optical has matured significantly over the past decade and several SNe Ia
have significantly polarised light and also remarkable evolutions (Kasen et al.
2003, Wang et al. 2003b, Leonard et al. 2005, Wang et al. 2007). Very few obserí
7

vations at wavelengths outside the optical and nearíinfrared window have been
obtained. Only two events have so far been observed in the thermal infrared,
SN 2003hv and SN 2005df (Gerardy et al. 2007). The detection of emission lines
of nickel and cobalt over 100 days after explosion indicates a surprisingly large
amount of stable nickel in the ejecta. Also, prominent lines of argon ([Ar II]
#6.985²m) with a doubleíhorned profile are detected. The observations hint at
a stratified composition of the ejecta, which cannot be explained well with the
current models. So far not a single SN Ia has been detected at radio wavelengths
(Panagia et al. 2006) and only one Xíray detection of a peculiar event has been
reported (SN 2005ke, Immler et al. 2006).
Many optical and nearíinfrared light curves have become available. Large
collections of light curves are available from the CalÒan/Tololo and the Carnegie
projects (http://csp1.lco.cl/#cspuser1/PUB/CSP.html: Hamuy et al. 1995,
Phillips et al. 1999, 2006, 2007, Krisciunas et al. 2001, 2003, 2004a,b,c, 2006,
2007), the CfA group (http://www.cfa.harvard.edu/supernova/: Riess et al.
1996a, 1999a, Jha et al. 2006a), the Berkeley group (Filippenko et al. 1992a,b,
Li et al. 2001, 2003) and the more recent European Supernova Consortium
(http://www.mpaígarching.mpg.de/#rtn/: Pignata et al. 2004, Kotak et al.
2005, EliasíRosa et al. 2006, Pastorello et al. 2007a,b, Stanishev et al. 2007,
Garavini et al. 2007a).
Most of the very early photometric observations have been provided by these
projects (SN 2001el: Krisciunas et al. 2003, 2007; SN 2002bo: Benetti et al. 2004,
Krisciunas et al. 2004c; SN 2003du: Leonard et al. 2005, Stanishev et al. 2007;
SN 2004eo: Hamuy et al. 2006, Pastorello et al. 2007a; SN 2005cf: Pastorello et
al. 2007b) and the available data have more than doubled in the past five years
(Conley et al. 2006a). The rise time appears to be roughly 18 days, with some
uncertainty whether there is a correlation with the light curve decline rate as
well (e.g. Riess et al. 1999b, Contardo et al. 2000).
Overall, the following picture has emerged for SN Ia explosions. The emisí
sion of SNe Ia is powered by the stored energy in radioíactive decays from 56 Ni
through 56 Co to 56 Fe (Colgate & McKee 1969, Clayton 1974; see Kuchner et
al. 1994 for an observational proof of this mechanism for SNe Ia). This reí
lease is moderated by the optical depth in the ejecta (Arnett 1982, HØoflich et
al. 1993, Pinto & Eastman 2000). Using Arnett's rule (Arnett 1982) one can
derive the nickel mass from the observed luminosity at peak light (Arnett et al.
1985, Branch 1992, Vacca & Leibundgut 1996, Contardo et al. 2000, Stritzinger
& Leibundgut 2005, Stritzinger et al. 2006). Not all Type Ia SNe produce the
same amount of 56 Ni in the explosions (e.g. Cappellaro et al. 1997, Contardo et
al. 2000, Stritzinger et al. 2006). Some objects are clearly subluminous, a sigí
nature that very little radioactive nickel is produced (most recent examples are
SN 2002cx, SN 2003gq, SN 2005P and SN 2005hk; Jha et al. 2006b, Phillips et al.
2007). It has been speculated that they are deflagration explosions rather than
delayed detonations. The derivation of the nickel mass based on Arnett's rule
has been tested from explosion models, hydrodynamics and radiation transport
calculations and has been shown to be reliable (Blinnikov et al. 2006).
The interpretation of the light curves has seen a revival in the past few years
8

with attempts to explain the behaviour of the infrared light curves, in which a
second maximum is observed (e.g. Elias et al. 1985, Meikle 2000, Krisciunas et
al. 2003). The most convincing explanation is due to a temperature sensitivity
of the emissivity between singly and doubly ionised ironípeak elements (Kasen
2006). Depending on the temperature decrease in the ejecta, the energy is
released rapidly in the nearíinfrared and the secondary maximum is more or less
pronounced. A similar argument for a temperature dependence in the SN Ia
spectra had been made by Nugent et al. (1995) a decade earlier based on line
ratios of Ca II and Si II.
Further dependencies on the amount of nickel synthesised in the explosion,
the mixing within the ejecta and the progenitor metallicity exist (Kasen 2006).
At the same time, these model calculations also predict a very narrow distrií
bution of the nearíIR peak luminosity (based on Chandrasekharímass models
and a unique density structure of the ejecta), as it is observed (Krisciunas et al.
2004a). There are now hopes that the light curve width vs. luminosity relation
of SNe Ia might be understood through a detailed exploration of the parameter
space provided by current explosion models(Kasen & Woosley 2007).
At late times, the photometry and spectroscopy has been followed for several
objects. Especially the addition of the infrared has provided new insights (Spyí
romilio et al. 2004, Sollerman et al. 2004, Stritzinger & Sollerman 2007). SNe Ia
have IR light curves, which after the peak phase are nearly flat for several huní
dred days until the IR catastrophe sets in and the ejecta cool enough so that the
energy is radiated in fineístructure lines in the thermal infrared rather than in
the optical or the nearíinfrared (Fransson et al. 1996). As a consequence the IR
contribution to the bolometric flux increases dramatically 300 days after the exí
plosion. Derivations based simply on the V light curve (as sometimes employed
in the past) are hence unreliable at these late phases. Also, the emerging flux is
less than what is predicted assuming Arnett's rule to determine the nickel mass
from the peak luminosity. This is a clear sign of #-ray leakage from the ejecta
and a signature of lowímass progenitor stars. The late decline rate of the light
curves has been used by Stritzinger et al. (2006) to crudely determine ejecta
masses from the bolometric light curves. The deviation of the decline rate from
the expected decay rate of 56 Co is a signature of the losses due to the decreasí
ing column density in the ejecta. Using a very simple model of the conversion
of the #-ray energy into the optical/IR wavelengths the derived ejecta masses
all are well below the canonical Chandrasekharímass of the explosion models
(Stritzinger et al. 2006). The reason for this discrepancy remains unclear, but
could be due to asymmetries, i.e. dependencies on the viewing angle or a model
that does not capture the relevant physics.
Another signature of variations in the explosions are spectroípolarimetric
measurements which show that certain elements in the supernova ejecta are not
distributed spherically (Wang et al. 2003b, Leonard et al. 2005, Chornock et al.
2006, Chornock & Filippenko 2007). A synopsis of the current situation is given
by Wang et al. (2007). It appears that there is only a small asymmetry in the
overall shape of the ejecta as the continuum polarisation appears generally low
and in most cases below the detection limits. However, some stronger lines show
9

a marked evolution in their polarisation indicating that the material is not evenly
distributed throughout the ejecta and also giving clues on the possibly uneven
burning process. There even appears to be a correlation between the degree
of clumpiness and the luminosity of the supernovae with smaller polarisations
observed for more luminous supernovae (Wang et al. 2007).
The spectroscopic evolution has also obtained a lot of attention in the past
decade. Apart from some objects, which display truly di#erent spectra (in
particular the cases of SNe 1999aa (Garavini et al. 2004), 1999ac (Garavini et
al. 2005, Phillips et al. 2006), 2000cx (Li et al. 2001), 2002cx (Li et al. 2003,
Sollerman et al. 2004, Jha et al. 2006b), 2002ic (Hamuy et al. 2003, Kotak et al.
2004), and 2005hk (Jha et al. 2006b, Phillips et al. 2007) should be mentioned
here), the general spectral evolution is characterised by di#erent velocities at
which the line absorptions are observed. Detailed analyses of the velocity shifts
go back to Branch et al. (1988) and it is now established that most SNe Ia show
highívelocity components in their spectra (Hatano et al. 2000, Mazzali et al.
2005). Observational trends appear to emerge in the way the velocities within
the supernova ejecta evolve (Benetti et al. 2005), but the interpretation of these
correlations are not clear yet. It is noteworthy that the distant objects appear
to follow the general spectral evolution of their nearby counterparts and there is
no obvious sign of di#erences in the spectral appearance of SNe Ia (Blondin et
al. 2006, Garavini et al. 2007b). The interpretation of the spectra has now also
been expanded to reconstruct the element distribution in the ejecta through the
spectral evolution (Fisher et al. 1999, Stehle et al. 2005), which gives a direct
input to the explosion models. Also, spectral calculations based on noníspherical
ejecta are leading to new explanations for the luminosity and expansion velocity
variations in SNe Ia (Kasen et al. 2006, Sim 2007, Sim et al. 2007).
The ideas on the explosion models have evolved only little in the past few
years. The favourite mechanisms are the delayed detonation, in which an early
deflagration (burning slower than the local sound speed) turns into a detonation
(burning front moves supersonically) in the out layers (Khokhlov 1991, RØopke
& Niemeyer 2007, RØopke et al. 2007), and pure deflagrations (see Hillebrandt
& Niemeyer 2000 for a review of these models). Deflagrations in general are
regarded as not providing enough energy for the brilliant displays of SNe Ia,
however, in a few cases would a simple deflagration provide su#cient energy for
a SN Ia (Blinnikov et al. 2006, Jha et al. 2006b, Phillips et al. 2007). There has
been a lot of activity in extending the calculations into full threeídimensional
simulations to explore the e#ects of asymmetries (Reineke et al. 2002, Gamezo
et al. 2003, 2004, 2005, RØopke & Hillebrandt 2005, RØopke et al. 2006). The
simulations are now also incorporating o#ícentre ignitions and other aspects,
which could lead to noníuniform explosions (Sim et al. 2007).
Despite these advances, it remains to be understood, why SNe Ia can be calí
ibrated with rather simple methods to provide accurate cosmological distances.
10

5 Cosmology with Supernovae
Cosmology with supernovae has developed over the second half of the last cení
tury. Various methods were devised to use supernovae to determine cosmological
parameters ranging from simple standard candle paradigms to physical explaí
nations of the supernova explosions and subsequent derivation of distances. The
simplest use has been the determination of luminosity distances, i.e. the comí
parison of the observed flux to the total emitted radiation. A more elaborate
method is the comparison of the angular diameter, through the measurement of
the radial velocity of the expanding atmosphere, and the observed brightness. A
critical assumption here is the sphericity of the explosion and the corresponding
connection of the ejecta velocity and the luminosity, which has to be achieved
through detailed emission models of the supernova explosion.
The classical parameters of observational cosmology, which govern the exí
pansion of the universe in FriedmanníRobertsoníWalker models, the Hubble
constant H 0 and the deceleration parameter q 0 , can be determined with accuí
rate (luminosity) distances (Sandage 1961, 1988, Weinberg 1972, Peebles 1993,
Peacock 1999). There is a rich literature on the Hubble constant and Type
Ia supernovae (see Branch & Tammann 1992, Branch 1998, Leibundgut 2001,
Perlmutter & Schmidt 2003 for reviews). The deceleration parameter has been
replaced by more modern formulations specifically including the cosmological
constant or some variants thereof (Carroll et al. 1992) and is generally referred
to as 'Dark Energy.' Detailed theoretical descriptions are given in other articles
of this issue.
5.1 The Hubble constant
5.1.1 Coreícollapse supernovae
Following early work by Baade (1926), originally done for Cepheid stars, the
expanding photosphere method (EPM; Kirshner & Kwan 1974, Schmidt et al.
1994, Eastman et al. 1996, Hamuy et al. 2001, Hamuy & Pinto 2002, Dessart &
Hillier 2005) has been applied to several supernovae. The most comprehensive
data sample has been assembled by Hamuy (2001). A critical test has become
the distance to SN 1999em, which was determined through EPM (Leonard et
al. 2001, Hamuy et al. 2002, Elmhamdi et al. 2003, Baron et al. 2004, Dessart
& Hillier 2006) and which also has a Cepheid distance available (Leonard et al.
2003). The discrepancy in the distance determinations towards SN 1999em can
be attributed to the fact that the correction factor for the dilution of the black
body flux in EPM are strongly model dependent and need to be calculated for
each supernova individually (Baron et al. 2004, Dessart & Hillier 2005).
Recently, Mario Hamuy has realised that the expansion velocity and the
luminosity during the plateau phase correlate and that Type II SNe may be calí
ibrated to become quite good distance indicators (Hamuy & Pinto 2002). The
distance accuracy achieved this way can be better than 20%. These determií
nations are based on the physical understanding of the plateau phase of SNe II
11

and are linked to physics of the supernova atmosphere. This means that they
are independent of the distance ladder, which is the basis for the SNe Ia (see
ç5.1.2). Typical values for the Hubble constant from SNe II are in the range of
65 to 75 km s -1 Mpc -1 (Hamuy 2003).
A first attempt to derive the Hubble diagram with distant (up to z#0.3)
SNe II using data assembled by the CFHT SN Legacy Survey has also been
made recently (Nugent et al. 2006). Potentially, this method can independently
check on the cosmic expansion history.
5.1.2 Type Ia supernovae
The best way to show that objects provide good relative luminosity distances is
to plot them in a Hubble diagram. Originally, this diagram was using recession
velocity vs. apparent magnitude (Hubble 1936, Sandage 1961). The underlying
assumptions are that the Hubble law holds, i.e. the local expansion is linear,
and that the objects are all of the same luminosity, i.e. standard candles, so that
the apparent brightness directly reflects distance. Early versions of this Hubble
diagram of SNe Ia showed that the peak magnitudes tracked the Hubble line
fairly well (Kowal 1968, Tammann & Leibundgut 1978, Leibundgut & Pinto
1992), but considerable scatter was still present.
There are essentially three quantities that can be derived from such a Hubí
ble diagram in the nearby universe: the slope of the expansion line, the scatter
around the expansion line and the value of the local Hubble constant from the
intercept at zero redshift (e.g Tammann & Leibundgut 1978, Leibundgut &
Pinto 1992, Branch & Tammann 1992, Riess et al. 1996a, Branch 1998). The
slope gives an indication of the local expansion field and for a linear expansion
in an isotropic universe has a fixed value. The scatter around the expansion line
provides a measure of the accuracy of the relative, in contrast to an absolute,
distance determination, individual deviations from the smooth cosmological exí
pansion and the measurement errors. The intercept of the line, finally, together
with an estimate of the absolute (normalised) luminosity provides absolute disí
tances and hence the Hubble constant. Recent Hubble diagrams of SNe Ia have
been published by Tonry et al. (2003), Knop et al. (2003), Barris et al. (2004),
Riess et al. (2004a,b), Astier et al. (2006), WoodíVasey et al. (2007), Riess et
al. (2007) and Jha et al. (2007). It should be noted that SNe Ia may be nearly
standard candles in the nearíinfrared (Krisciunas et al. 2004a). The first signifií
cant IR sample shows very small scatter without prior correction for light curve
shape.
Modern versions of this diagram have exchanged the recession velocity with
the redshift, often corrected to the CMB rest frame and the distance modulus
instead of the simple observed apparent peak brightness. It has become clear
that SNe Ia are not simple standard candles (see ç4, an extensive discussion is
given in Leibundgut 2004). Hence, the distance has to be determined for each
event individually, e.g. through the maximum luminosity vs. light curve width
relation discussed in ç4. Another option is to normalise the peak luminosities
and to plot a 'corrected' apparent peak brightness, a method employed by the
12

Supernova Cosmology Project (e.g. Perlmutter et al. 1997, 1999, Knop et al.
2003). This approach is masking the importance of the light curve correction
and also the importance of the absorption corrections.
The scatter of the normalised SNe Ia around the linear expansion line is less
than 0.2 magnitudes or 10% in distance (Phillips et al. 1999, Jha et al. 1999,
Tonry et al. 2003, Riess et al. 2004b, Jha et al. 2007; Fig. 2). Independent
of our ignorance of the exact explosion mechanism or the radiation transport
in the explosions this proves that SNe Ia can reliably be used as a (relative)
distance indicator in the local universe and makes them empirically calibrated.
This situation is very much comparable to the Cepheid stars, where the periodí
luminosity relation is based on empirical data from objects in the Magellanic
Clouds.
Figure 2: Hubble diagram of nearby Type Ia supernovae. The distances are
derived from light curve shape corrected luminosities (data from Jha et al. 2007).
Fits to di#erent velocity ranges are shown. The red line is a fit to all SNe Ia
with v>3000 km s -1 (extrapolated to lower velocities as a dashed line), the
green line for the sample restricted to 3000 km s -1 blue line for events with v>8000 km s -1 .
Fig. 2 displays the most recent, homogeneously treated sample of nearby
SNe Ia from Jha et al. (2007). The upper panel displays the regular Hubble
diagram with distance vs. recession velocity corrected to the rest frame of the
cosmic microwave background, while the lower panel shows the data with the
expansion field removed. This allows to appreciate the accuracy of the relative
13

distances derived by the supernovae and also provides a better demonstration
of the various cosmological models. This will become even clearer for the full
Hubble diagram discussed below (Fig. 3). The distance modulus (m - M)
combines the observed magnitude with the observed flux F through
m = -2.5 log(F ) + const
and the absolute luminosity L of an object at the distance of 10pc
M = -2.5 log(L) + const
and is determined for each supernova individually. The distance modulus deí
scribes the observed flux ratio of two objects at di#erent distances according to
the usual 1/D 2 law, which defines the cosmological luminosity distance and the
observed flux with distance and emitted energy through
F = L
4#D 2 .
For a linear cosmic expansion following Hubble's law
D = v
H 0
one expects that the distance moduli and the recession velocities are connected
through
(m -M) = 5 log(v) - 5 log(H 0 ) + 25
where the velocity is measured in km s -1 , the distance in Mpc and the Hubble
constant H 0 has units of km s -1 Mpc -1 .
It is obvious in Fig. 2 that below a recession velocity of about 3000 km s -1
the supernovae do not trace the smooth Hubble expansion, but the Hubble
flow is heavily disturbed by motions due to the local matter distribution, often
referred to as 'peculiar velocities.' These supernovae are regularly excluded
from the cosmological studies. The slope above 3000 km s -1 is slightly larger,
i.e. 5.22 ‘ 0.05, than the expected value for the linear expansion in the local
universe, which could be an indication of evolution.
We demonstrate in Fig. 2 the e#ect of a possible change in the universal
expansion rate at some distance from us. The lower panel shows the fits to data
with v > 3000 km s -1 , a fit to the data in the range 3000 < v < 8000 km s -1
and the data with v > 8000 km s -1 , where we force the fit for a linear expansion.
The upper value was taken to be close to the reported outer edge of a possible
'Hubble bubble' (Zehavi et al. 1998, Jha et al. 2007) where the expansion inside
is faster than outside and hence the true Hubble constant would be lower than
what is determined locally. Indeed, there appears to be a shift by about 0.07
magnitudes (about 4% change in H 0 ) for the objects outside 8000 km s -1 .
Another interpretation traces this change to an evolution in the intrinsic colours
of SNe Ia (Conley et al. 2007).
14

By fitting the intercept of the expansion line a combination of the Hubble
constant and the absolute luminosity is determined. Hence, for the derivation
of the Hubble constant the (normalised) luminosity of the SNe Ia has to be
known. The most direct way to achieve this is through the distance ladder and
in particular the calibration of nearby SNe Ia by Cepheids (for the most recent
results see Saha et al. 1999, Freedman et al. 2001, Sandage et al. 2006). The
main discrepancy for the published values of the Hubble constant from SNe Ia
is coming from the di#erent interpretations of the Cepheids and application of
the light curve shape correction. Ironically, the SNe Ia provide the best disí
tance indicator beyond the Cepheid range and have replaced many rungs in the
distance ladder making the Magellanic Clouds the last rung before cosmological
distances. We do not quote a value for the Hubble constant here. The interested
reader is referred to the papers mentioned above.
A di#erent way to establish the Hubble constant with SNe Ia is through
models. Originally tried by Arnett (1982) and Arnett et al. (1985) this has
been further attempted by Leibundgut & Pinto (1992) and most recently by
Stritzinger & Leibundgut (2005). In this case the absolute luminosity is derived
from the amount of nickel produced in the explosion models and the derived
luminosity, e.g. through Arnett's rule or direct radiation hydrodynamics calí
culations. Due to the range of observed SN Ia properties it is not possible to
derive a value for the Hubble constant itself, but at least an interesting lower
limit of H 0 > 50 km s -1 (3#) could be derived by matching the faintest obí
served SNe with the largest imaginable nickel mass (#1 M# ) for the models.
Overall, a slight inconsistency between the predications of the current modí
els and the observations could be found. By adopting a Hubble constant of
#70 km s -1 Mpc -1 one can derive a predicted range of nickel masses in the
explosions (0.5M# < M Ni < 1.0M# ; Stritzinger & Leibundgut 2005).
5.2 The expansion history of the universe
Exploring the cosmic expansion rate over the history of the universe tells us
about the changing contributions of the di#erent matter/energy components of
the universe (see the article by Linder). The supernovae provide an important
information by mapping out the expansion history over a significant lookback
time (out to a redshift of z#1.5, corresponding to a lookback time of about 2/3
of the age of the universe, or over 9 billion years for the concordance model and
H 0 = 70 km s -1 Mpc -1 ). It should be stressed that for the expansion history
only relative distances are need to be measured. The SN Ia Hubble diagram
of nearby objects (Fig. 2) gives ample empirical confidence that this can be
achieved reliably.
The published distances of highíz supernovae are typically based on an
adopted Hubble constant. Several theoretical papers in the recent past have
made the mistake to include the Hubble constant as a free parameter in their
fits. While this is okay to check that the marginalisation actually works corí
rectly, claims that a specific value for the Hubble constant has been found are
incorrect. The original papers all state very clearly what Hubble constant has
15

been adopted for the study and people who use those data should be aware of
this assumption.
The proposal to use supernovae to measure the cosmic deceleration goes
back to Olin Wilson (1939) and was elaborated further by Tammann (1978)
and Colgate (1979). one prediction made by these early visionaries was that
time dilation would a#ect the observed light curves. This could finally be shown
convincingly with the first distant SN Ia, SN 1995K, by Leibundgut et al. (1996)
and was further confirmed on a large sample by Goldhaber et al. (1997, 2001).
In the meantime this test has been performed following the detailed spectral
evolution (Riess et al. 1997, Foley et al. 2005, Hook et al. 2005, Blondin et al.
2006, 2007). The predictions of a universal expansion have been confirmed in
all cases ruling out alternative theories of ``tired light.''
Proposals to use SNe Ia to measure the expansion history of the universe go
back into the late 1980s. The main goal at the time was to determine the mean
matter
density# M to check the cosmological models. The first observational atí
tempts were frustrated by lack of 'grasp,' i.e. the di#culty to cover large enough
area on the sky to su#cient depths frequently enough. A search with the Daní
ish 1.5m telescope on La Silla monitoring several fields once per month yielded
only two distant SNe after two years. The followíup spectroscopy was di#cult
to organise in a time before observatories were fully connected to the Internet
and the information had to be transmitted through fax and telex, a particular
problem for finding charts. The spectroscopic capabilities of the available 4m
telescopes were marginal for the faintness of the objects (NœrgaardíNielsen et
al. 1989, Hansen et al. 1989, Schmidt et al. 1998, Riess et al. 1998). A large
project to search for distant SNe Ia was initiated in the early 1990s in Berkeley
(Perlmutter et al. 1991) and yielded first results on seven objects (several withí
out spectroscopy and insu#cient colour coverage Perlmutter et al. 1995). As
a result the inferred cosmology was not correct (Perlmutter et al. 1997). The
following years saw the emergence of vastly improved search techniques, the
advent of 8m and 10m telescopes --- greatly improving the quality of the specí
troscopic confirmations, refined analysis methods taking many contaminating
e#ects into account and the delivery of a surprise. With the proof of concept
from the early searches the new projects, the Supernova Cosmology Project
(Perlmutter et al. 1995, 1997, 1998, 1999, Knop et al. 2003, Hook et al. 2005)
and the Highíz Supernova Search Team (Schmidt et al. 1998, Leibundgut et
al. 1996, Riess et al. 1997, 1998, Garnavich et al. 1998a,b, Riess et al. 2000,
Coil et al. 2000, Tonry et al. 2003, Williams et al. 2003, Barris et al. 2004,
Clocchiatti et al. 2006), started to provide astonishing evidence that the distant
SNe Ia appeared fainter than predicted in a massless, empty universe. Early
criticism of these results concentrated on di#culties with photometric accuracy
of the faint sources, the treatment of the dust absorption in the host galaxy
of the supernova, possible secular evolution of the supernovae over time, uní
certainties in the normalisation of the peak luminosity of the SNe Ia and the,
at the time still fairly small, sample size of distant objects, which could lead
to sample biases or Malmquist e#ects (see Leibundgut 2001 for a summary of
these early problems). Exotic possibilities, like unusual dust properties (Aguirre
16

1999a,b) were proposed or di#culties with the normalisation pointed out (Drell
et al. 2000, Leibundgut 2000). Many of these di#culties have been addressed
in the meantime. Also, the importance of the nearby SN Ia sample should not
be underestimated. The reason that Riess et al. (1998) could find a signal for
accelerated expansion with only 10 distant SNe Ia was largely due to the fact
that an extensive, controlled, local sample of SNe Ia was at hand.
In the past few years the CanadaíFranceíHawaii Telescope CFHT Superí
nova Legacy Survey (SNLS; http://www.cfht.hawaii.edu/SNLS/) and the
ESSENCE project (http://www.ctio.noao.edu/wproject/) have been colí
lecting data of distant supernovae to measure the value of a constant equaí
tion of state parameter # to 7% and 10% accuracy, respectively. The SNLS
monitors four fields with the MegaCam instrument at the CFHT continuously,
while ESSENCE uses the MosaicII camera with the CTIO 4m telescope during
three months each year. The ultimate goals of these fiveíyear projects are >700
SNe Ia for SNLS and >200 SNe Ia for ESSENCE. All supernovae must have a
positive spectral classification to be included.
The SNLS has published cosmological results of their first year of obserí
vations based on 71 distant SNe Ia (Astier et al. 2006). The selection of the
candidates and the spectroscopy of this project are described in Sullivan et al.
(2006a), Lidman et al. (2005) and Howell et al. (2005). Other important reí
sults based on this extensive data set are a determination of the SN Ia rise time
(Conley et al. 2006a), as well as the supernova rates and their connection to star
formation in the host galaxy (Sullivan et al. 2006b, Neill et al. 2006). Further,
this project obtained observations of a peculiar SN Ia possibly emerging from
a superíChandrasekharímass progenitor (Howell et al. 2006) and made a first
measurement of distances at z > 0.1 of SNe II (Nugent et al. 2006).
The ESSENCE project is presented in Miknaitis et al. (2007) and the cosmoí
logical results based on the first three years including 60 SNe Ia are discussed in
WoodíVasey et al. (2007). All corresponding spectroscopy has been published
(Matheson et al. 2005, Blondin et al. 2006, 2007). A first detailed description
of photometry of a subset of the ESSENCE events observed with the Hubble
Space Telescope (HST) pointed out some potential selection e#ects in the samí
ple (Krisciunas et al. 2005). An evaluation of exotic proposals for dark energy
when compared to the available SN Ia data was made in Davis et al. (2007).
A separate project including many ESSENCE members is the higheríz SN
search with HST. The targets for this study have been SNe with z>1 (Strolger
et al. 2004). These highíz supernovae have shown that the universe indeed
was decelerating at z>1 and the acceleration phase has started only during
the second half of the universal history (Riess et al. 2004a,b, 2007). The most
recent data sample allowed Riess et al. (2007) to map out the change of the
Hubble parameter over redshifts for the first time ever directly showing that
the universal expansion rate has changed over time. This project also yielded
important results on the evolution of the SN Ia rate as a function of redshift
(DahlÒen et al. 2004). However, the inference of long lead time before a SN Ia
explosion has been disputed (FØorster et al. 2006).
Other ongoing projects are the continuation of the Supernova Cosmology
17

Project (http://panisse.lbl.gov/ACSclustersearch/) to find supernovae in
distant clusters with z>1. The goal is to observe SNe Ia in elliptical galaxies
as the problem with the extinction in the host galaxy is strongly reduced. A
first exploration of this method had been done by Sullivan et al. (2003). The
claim has been made that SNe Ia in elliptical galaxies provide a cleaner sample.
Possible problems with this approach is the lack of a good comparison sample of
local supernovae. Data for a first object have recently been published exploring
new groundíbased observational methods, in particular adaptive optics imaging
(Melbourne et al. 2007).
The extension of the Sloan Digital Sky Survey for a threeíyear supernova
search is ongoing (http://sdssdp47.fnal.gov/sdsssn/sdsssn.html). The
goal is to find 200 SNe Ia at 0.1 cessful with many spectroscopically confirmed SNe Ia. An impressive mosaic
is available from the above Web page and has been published in National Geí
ographic Magazine. The local supernova searches have been described in ç4.
One should add here the SN Factory (http://snfactory.lbl.gov/), which is
specifically set up to provide a large sample of nearby SNe Ia for the comparií
son with the highíz sample. So far only few events from this project has been
published (Aldering et al. 2006, Thomas et al. 2007), all of peculiar nature.
The cosmological signal imprinted on the supernova data is modulated by
several unwanted technical and astrophysical e#ects. At the basis is accurate
photometry (Stubbs & Tonry 2006). While this sounds like a trivial statement,
it has become di#cult to free the measurement from all the e#ects of Earth's
atmosphere to the percent level required for the SN light curves. Improveí
ments in the instrumental characterisations are made continuously (Miknaitis
et al. 2007), but one of the limiting e#ects are the implementation of the varií
ous filter pass bands at the telescope, which has to be known accurately to be
able to combine observations from di#erent telescopes (Davis et al. 2006). For
nearby supernovae this led to the introduction of an empirical correction (often
referred to as Sícorrection) of data sets from di#erent telescopes (Stritzinger
et al. 2002). As a consequence recent projects concentrate on single instruí
ments (CFHT/MegaCam for the SNLS and CTIO Blanco telescope/MosaicII
for ESSENCE) for the photometry to avoid this problem. Nevertheless, it still
remains di#cult to combine SNLS and ESSENCE data for a joint analysis as
done in WoodíVasey et al. (2007), Riess et al. (2007), Davis et al. (2007) and
various other publications.
Since the supernovae have to be corrected for foreground extinction the
colour needs to be measured as accurately as possible. Any uncertainty in this
respect is multiplied by the absorption correction. The uncertainty of the colour
measurement also has a direct influence on the Kícorrection (Hamuy et al. 1993,
Kim et al. 1996, Nugent et al. 2002, Hsia et al. 2007). The observed photometry
has to be translated into the supernova rest frame and hence any redshift of
the spectrum needs to be taken into account (see Jha et al. 2007 for a detailed
description of this problem and a current implementation). The Kícorrections
are timeídependent and need to be calculated for the correct phase as well as
the correct intrinsic colour. This intimately connects the Kícorrections with the
18

absorption correction and modern versions of lightícurve fitting programmes for
distant supernovae merge this evaluation. The light curve fitting methods and
calibration are critical to the supernovae cosmology and it should be emphasised
that depending on which methods are used, the derived distances can change
-- sometimes in a systematic way. WoodíVasey et al. (2007) have performed
a detailed analysis of the SNLS/SALT fitter (Guy et al. 2005) and MLCS2k2
(Riess et al. 2004b, 2007, Jha et al. 2007) and confirmed that consistent cosmoí
logical results are derived by the two methods on the same data sets, but small
di#erences remain.
Detailed spectroscopy certainly would help, but the signal achieved with the
current telescopes is still limited and in many cases the supernova spectrum is
contaminated by host galaxy light. Methods to separate the SN spectrum from
the galaxy are either to try a deconvolution (Blondin et al. 2005) or subtract a
scaled galaxy spectrum (Sainton 2004, Howell et al. 2005). The spectroscopy is
also essential to distinguish SNe Ia from luminous SNe Ib/c as the two classes
stem from distinct explosion mechanisms and confusion could lead to wrong
conclusions, when the objects are not separated correctly (Homeier 2005, Tautí
enberger et al. 2006).
Astrophysical e#ects, which can influence the cosmological interpretation
of supernova data include absorption in the Milky Way and in the host galaxy,
gravitational lensing, evolution of the supernovae as a function of age of the unií
verse, e.g. due to di#erent metallicity, selection biases due to limiting sampling
of the intrinsic supernova distribution and e#ects from a local underdensity,
which would mean that the local expansion rate is lower than the global one
('Hubble bubble').
Several of these are well under control. Gravitational lensing does not appear
to be a major issue for the redshifts considered so far. The highest redshift
supernovae may be a#ected by lensing individually, but the overall e#ect should
be minimal (Wambsganss et al. 1997, Holz & Wald 1998, Amanullah et al. 2003,
Gunnarsson et al. 2006, JØonsson et al. 2006, 2007). The absorption due to dust
in our own Milky Way is also fairly easily corrected. The e#ect is somewhat
alleviated by the redshift and the diminished influence of dust absorption at
redder wavelengths. Evolution of the supernova peak luminosity could mimic a
cosmological e#ect, but the available data do not indicate any significant changes
between the local and distant SN Ia samples. Within the achievable accuracy
the distant supernovae appear the same spectroscopically (Hook et al. 2005,
Lidman et al. 2005, Matheson et al. 2005, Blondin et al. 2006, Riess et al. 2007)
and also their light curve behaviour appears rather similar to the local sample
(Astier et al. 2006, WoodíVasey et al. 2007). The e#ect of the metallicity of the
progenitor star is predicted to be insignificant (RØopke & Hillebrandt 2004).
Our deductions on cosmology and dark energy could be severely hampered
by the limited accuracy with which we know the local expansion field (see ç5.1.2,
Hui & Greene 2006, Cooray & Caldwell 2006, Jha et al. 2007), selection biases
which skew the observed distribution from the intrinsic one (Leibundgut 2001,
WoodíVasey et al. 2007), and our lack of a good understanding of the dust
properties in the host galaxies (EliasíRosa et al. 2006, Astier et al. 2006, Woodí
19

Vasey et al. 2007).
As already shown in ç5.1.2 the local expansion field is not smooth and local
flows are distorting our ability to set the zeroípoint for the expansion rate.
This leads to a systematic uncertainty, which needs to be overcome, if more
accurate determination of cosmological parameters will be attempted. The e#ect
is of the order of about 6 to 8% overall (Jha et al. 2007, WoodíVasey et al.
2007). Larger nearby supernova samples are required to evaluate the reality
of a Hubble bubble. Another possibility is to improve our knowledge of the
density distribution in the local universe (as attempted over a decade ago, e.g.
Bertschinger et al. 1990, Blakeslee et al. 1999) for a better understanding of the
local disruption of the smooth universal expansion. With very large samples of
nearby supernovae one could attempt to map this density field as well, but that
will likely require several thousand supernovae.
The problem can of course also be inverted and the SNe Ia be used to
determine the local velocity field compared to the CMB. This has been done
with early samples by Riess et al. (1995) and more recently by Haugbœlle et al.
(2007) who find a quadrupole in the velocity distribution.
Ideally one would like to use distance limited supernova samples. With a hyí
pothetical standard candle, which has a narrow luminosity function, one would
hope that a flux limited sample would also be volume limited. There are seví
eral reasons why the available distant supernova samples are not volume limited.
First, the SNe Ia are not standard candles and their luminosity function is spaní
ning almost a factor of 10 from the brightest to the faintest events. Even though
the most extreme cases are not included the most distant supernovae are also
the most luminous ones (Krisciunas et al. 2005). Second, supernova searches all
use a certain frequency, with which the search fields are monitored. This means
that a supernova is discovered during its rise and depending on the distance
and the weather conditions objects will be lost (Miknaitis et al. 2007). Finally,
dust absorption in the host galaxy will dim some events, hence make them too
faint to be discovered and remove them from the sample. A priori this would
seem not such a problem, but it turns out that for more distant objects this
becomes progressively more important and together with the limited sampling
frequency creates a systematic bias. WoodíVasey et al. (2007) have simulated
this e#ect in detail for the ESSENCE data set and found a considerable bias
(nearly 0.3 magnitudes in distance modulus at z=0.6), if the default absorption
prior was used. They introduced separate, redshift dependent priors for the
ESSENE data to correct for the fact that more SNe Ia go undetected at higher
redshift and larger host galaxy absorption. The classical Malmquist bias is here
mixed together with the assumption on the intrinsic colours of the supernovae
and the absorption in their host galaxies.
The unknown reddening law in external galaxies is a further uncertainty,
which systematically limits our ability to determine cosmological parameters.
Light scattering depends on the physical size of the dust particles. So far the
local absorption law has been assumed for all supernovae, but it has been shown
that for many heavily extincted SNe Ia a di#erent reddening law seems to apply
(Riess et al. 1996b, Krisciunas et al. 2000, EliasíRosa et al. 2006, Astier et al.
20

2006). The curious fact is that with the regular colour dependence a colour
excess, i.e. an apparent redder colour due to the interstellar dust scattering, is
rather large for bluer bands. The canonical value for the solar neighbourhood
is about 3.1 for the visual V band. For many SNe Ia this value appears to be
reduced to somewhere between 2 and 3. This has also the curious e#ect that
the absorption correction for some supernovae is reduced and the scatter in the
distances reduced. However, once the reddening law is a free parameter it can
be assumed that it will be vary for di#erent sight lines through distant galaxies.
This will introduce a random scatter, which will be very di#cult to overcome.
For the ESSENCE supernovae, these combined colour e#ects constitute the
largest uncertainty (about 10% overall; WoodíVasey et al. 2007).
These last uncertainties will not easily be remedied by larger samples. They
present fundamental shortcomings of our understanding of some of the critical
items in supernova cosmology. They are not directly related to the supernova
physics itself, but are an expression of the fact that the universe is filled with
clumped matter, dark and baryonic, which distorts our position as a fair obí
server of the universe and a#ects the light we observe of these distant objects.
Overcoming these systematic di#culties will be key to further improve the ací
curacy with which we can determine the cosmological parameters.
Figure 3 displays the latest data set, which is a combination of the largest
nearby SN Ia sample from Jha et al. (2007), the ESSENCE data (WoodíVasey et
al. 2007) and the published SNLS (Astier et al. 2006). The data are remarkably
consistent with the concordance model
of# M = 0.3
and# # = 0.7.
The SNe Ia are further used to determine the integral of the equation of
state parameter # over the observed redshift range (z<1.7). All experiments
find a consistent value of # = -1 within the uncertainties. Currently these are
of about 13% statistical and 13% systematic for ESSENCE (WoodíVasey et al.
2007) and 9% statistical and 5% systematic for SNLS (Astier et al. 2006). These
values are unfortunately not directly comparable as di#erent assumptions went
into the calculations of the errors. Nevertheless, all results so far are consistent
(within 1 #) with a cosmological constant. An important ingredient in this
derivation is the matter density, which in most recent studies has been taken
from the baryonic acoustic oscillation measurements of Eisenstein et al. (2006)
or Cole et al. (2005). The accuracy of the derivation of # strongly depends on
how well the matter
density# M can be constrained. Sometimes a flat geometry
of the universe is also assumed.
Attempts have been made to derive constraints on a possible time depení
dence of # using the supernova data. One should caution these enterprises as
they are based on data, which are most likely not accurate enough to warrant
such analyses. Most published attempts demonstrate this fairly clearly as the
parameters become essentially unconstrained (Riess et al. 2004b, WoodíVasey
et al. 2007, Riess et al. 2007). Several theoretical papers have further ignored
the systematic uncertainties in the data and may have derived spurious results.
One other interesting application of the Hubble diagram of SNe Ia is the
attempt to constrain any change of Newton's gravitational constant G. The
21

Figure 3: Hubble diagram of Type Ia supernovae. The distances are derived
from light curve shape corrected luminosities (data from Davis et al. 2007). The
red line is for an empty
universe(# #
=# M = 0), the blue line for an Einsteiníde
Sitter
model(# # =
0,# M = 1). The concordance
model(# # =
0.7,# M = 0.3)
is shown as the green line fitting the data best. The bottom panel shows all
distances relative to the empty universe model. The data for the individual
supernovae is plotted as shaded point, while the binned data are shown in black.
current limits exclude changes larger than | ×
G
G | < 2.9 § 10 -11 year -1 (GaztaÔnaga
et al. 2002, LorÒeníAguilar et al. 2003, GarcÒÐaíBerro et al. 2007).
6 Outlook and future projects
SNe Ia are amongst the most promising candidates to further improve our view
of the cosmos. They appear prominently in the recent studies on how dark
energy could be further constrained (Albrecht et al. 2006, Peacock et al. 2006).
Together with other probes of the deep universe the SNe Ia should help us to
characterise dark energy and possibly discover its nature.
Several projects have been proposed. The next surveys require new iní
strumentation, in particular wideífield cameras and dedicated telescopes. The
SNLS has already shown the way forward with its allocation of several huní
dred nights on a single telescope. The next step is the Dark Energy Surí
vey (http://www.darkenergysurvey.org/) planned with the CTIO Blanco
4m telescope. For this project a new camera is being built for this telescope.
22

The goal is to observe 2000 SNe Ia with 0.3 like the Large Synoptic Survey Telescope (LSST; http://www.lsst.org) or
The Panoramic Survey Telescope & Rapid Response System (PaníSTARRS;
http://panístarrs.ifa.hawaii.edu/public) will find thousands of superí
novae. It will become impractical to obtain spectroscopy for all these objects
for the classification and statistical approaches using the observed light curve
shapes and the colours are being developed (e.g. Barris & Tonry 2004, Riess et
al. 2004b, Sullivan et al. 2006a, Conley et al. 2006b, Kuznetsova & Connolly
2007). However, it still needs to be demonstrated that such large samples will
allow us to improve the cosmological parameters.
An important extension of the current supernova work is towards higher
redshifts. The sample of known SNe Ia at z>1 is very small still (Riess et al.
2007) and these events help significantly to constrain the cosmological models
and also to check for systematic e#ects in the supernovae. All these very disí
tant SNe Ia have been found by HST and its large area Advanced Camera for
Surveys ACS. This is one reason why future space projects aim at wide field
imaging. The synergy with weak lensing studies are obvious and strong scií
ence drivers for these missions have been developed. The best know proposal
is the SuperNova Acceleration Probe (SNAP; http://snap.lnbl.gov), which
has stimulated many interesting studies of what could be achieved by such a
data set. Currently the SNAP satellite could reach SNe Ia out to z#1.5. Three
missions have been selected for a study as a Joint Dark Energy Mission (JDEM)
between NASA and the US Department of Energy. They are the Advanced Dark
Energy Physics Telescope (ADEPT), the Dark Energy Space Telescope (Desí
tiny; http://destiny.asu.edu) and SNAP. All of them employ the supernova
Hubble diagram in addition to weak lensing surveys to further characterise dark
energy.
To overcome the di#culties with the optical colours it has been suggested
to construct a supernova Hubble diagram in the near infrared. At these waveí
lengths the SNe Ia are showing very small scatter in their peak luminosity and
promise to approach the standard candle concept better than at the blue waveí
lengths employed so far (Krisciunas et al. 2004a). The di#culty so far has been
that due to the redshift the rest frame nearíinfrared wavelengths are pushed to
wavelengths were not enough sensitivity is available. With the future JWST
and its infrared capabilities it will be possible to compile a Hubble diagram of
distant SNe Ia in the near infrared. This will present a critical test of the current
results and may significantly improve the distance accuracy as several limiting
e#ects, like light curve shape and reddening corrections can be avoided. A first
attempt of a Hubble diagram in the I pass band has been made by Nobili et al.
(2005).
An independent test of the cosmology will come from an extended Hubble
diagram of type II supernovae. These distances are based on completely di#erent
physical assumptions. Work in this direction has started (Nugent et al. 2006).
Further improvements will come from a better understanding of the exploí
sions themselves. The question whether the distant SNe Ia are identical to the
ones observed locally has not been fully addressed. The currently available obí
23

servational resources do not allow us to obtain data of the required quality to
compare, e.g., the spectral evolution of the distant supernovae. With a secured
model for the explosion, it will become easier to explore possible systematic
di#erences of supernovae coming from younger progenitor systems than older
ones. There have been discussions of di#erences between supernovae coming
from presumably di#erent parent populations, e.g. SNe Ia in spiral galaxies and
elliptical galaxies, which might be from slightly di#erent progenitor systems,
but it is too early to draw conclusions. The key to solving this question lies
with observations of local SNe Ia. These objects can be observed with su#cient
detail that we can explore the di#erent explosion models and possible progenitor
channels, which lead to the explosions.
7 Conclusions
Supernovae have been one of the main reasons, why we now consider a dark
energy component for the universe. These explosive events have proved to be
ideally suited for cosmological distance measurements. Their variability, often
regarded as detrimental by placing severe observational constraints, has turned
into an advantage. The brightness evolution allows us to identify these cosmic
light houses, and, with su#cient knowledge of their intrinsic properties, we can
correct for various astrophysical e#ects, which could compromise the cosmologí
ical deductions.
Understanding the physics of the explosions remains a prime task. Coreí
collapse supernovae have a relatively simple radiation transport and can be
used to derive fairly accurate distances in the local universe. Coreícollapse suí
pernovae are fascinating events, which also tell us about the stellar evolution
of massive stars, how they shape their environments through winds and how
companions can change their surface evolution, while the stellar core evolves
towards the collapse. Since at least some #-ray bursts also show signatures of
supernovae, it is important to understand this supernova class better. Through
a modified expanding photosphere method they will continue to provide further
constraints on the Hubble constant. The physical nature of this measurement is
very attractive as it bypasses the usual distance ladder. By expanding to higher
redshifts an independent confirmation of the accelerated expansion will become
possible. This method is observationally and theoretically expensive requiring
multiíband photometry and spectroscopy at several epochs and tailored simuí
lations of the spectra to match the observations. Nevertheless, the e#ort should
be continued as it appears at the moment to be the only distance measurement
to individual events to complement the thermonuclear supernovae.
Thermonuclear supernovae have spectacularly changed our view of the unií
verse. Empirically calibrated they have proved to be excellent distance indicaí
tors. The fact that many questions regarding the exact explosion mechanism
and the as yet uncertain progenitor systems remain has not hindered their use
for cosmology. There is significant progress in both areas. At the moment a
consensus on these questions, however, still remains to be found. The past
24

decade has seen SNe Ia take centre stage for the derivation of cosmological paí
rameters. While they have been a favourite for the determination of the Hubble
constant for several decades, the di#cult calibration of their absolute luminosity
at maximum has hampered their ability to determine an accurate value free of
systematics. With the exquisite capability of SNe Ia to deliver relative distances
the problem of the Hubble constant rests with an accurate calibration through
other distance indicators, e.g. Cepheid stars.
A beautiful confirmation of general relativity as the basis for the cosmoí
logical model is the demonstration of time dilation in the light curves and the
spectral evolution of SNe Ia. SNe Ia discovered the accelerated cosmic expaní
sion and hence provided support for an additional energy component of the
universe. They now supply strong evidence for a cosmological constant. The
most recent supernova surveys, based on over one hundred events, have not
shown any significant deviations from an integrated equation of state parameí
ter #=-1. One should, however, caution against any attempts to overíinterpret
the current data. Exploring a timeívariable # should be done with the current
limitations of the data in mind. The accuracy required to significantly constrain
#(t) is probably beyond what is currently available.
Several systematic e#ects are still of concern for this determination. The
statistical uncertainties have reached the level of these systematics and simply
increasing the sample size beyond what will be become available through SNLS
and ESSENCE (several hundred SNe Ia beyond z>0.3) will not improve on the
result any longer. Detailed understanding of the various astrophysical e#ects,
which have to be treated to extract the cosmological signal, has now become
imperative. The physical nature of the light curve shape vs. peak luminosity
relation, the intrinsic colour variations among SNe Ia, the influence of dust
absorption in the host galaxies, evolutionary trends in SNe Ia as a function of
redshift and the selection biases of the searches need to be examined carefully.
The limitations in accurately determining the local expansion rate are now also
becoming a significant weakness. The latter is an obvious demonstration of the
importance of the local SNe Ia. They provide the zeroípoint against which the
distant supernovae are compared for the cosmology.
It is hence clear that an improved local sample of SNe Ia will provide seví
eral avenues for future improvements on the determination of the dark energy
parameters. In addition, supernovae projects extending to higher redshifts and
into the infrared hold great promise to overcome the systematic problems ení
countered at the moment.
Supernovae are one of the prime candidates to describe the characteristics
of dark energy. With the lack of a clear theoretical contender for this unknown
component, observations exploring the e#ects of dark energy are decisive and
hopefully will lead us eventually to understand the properties of dark energy.
Acknowledgements I am grateful for continuous discussions with colí
leagues of the Highíz Supernova Search Team, the Higheríz Team and the
ESSENCE Team as well as with team members of the Supernova Cosmology
Project and the Supernova Legacy Survey. This research was supported by the
DFG cluster of excellence 'Origin and Structure of the Universe' (www.universeí
25

cluster.de) and the DFG TransRegio TR33 'The Dark Universe.'
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