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Cosmological Parameters as measured by
Type Ia Supernovae
Bruno Leibundgut 1 , Brian Schmidt 2 , Jason Spyromilio 1 , Mark Phillips 3
1 European Southern Observatory, Karl­Schwarzschild­Strasse 2,
D­85748 Garching, Germany
2 Mount Stromlo and Siding Springs Observatory, Private Bag,
Weston Creek P. O. 2611 Australia
3 Cerro Tololo Inter­American Observatory, Casilla 603, La Serena, Chile
Abstract. Supernovae are among the most important cosmological distance indica­
tors. Through the application of distance independent correction methods to the peak
luminosity, it has become possible to determine very accurate luminosity distances.
Type Ia supernovae have been used extensively to measure the current Hubble con­
stant, H0 . More recently, they have been employed to determine the deceleration of
the universe. From a first sample of distant supernovae strong indications of a non­
vanishing cosmological constant \Lambda emerge. A careful analysis of the systematic effects
does not change this result. The distant supernovae also indicate a dynamic age which
is consistent with age determinations of the oldest stellar components of the Galaxy.
1 Introduction
The ability of Type Ia supernovae (SNe Ia) to measure cosmological distances
is largely based on empirical evidence. Samples of nearby SNe Ia display a very
narrow scatter around the expected linear expansion of the local universe (Kowal
1968, Tammann& Leibundgut 1990) and can be further improved by application
of distance independent corrections like for light curve shape (Hamuy et al.
1996a, Riess et al. 1996). The dispersion of the nearby sample decreases to
around 0.15 magnitude after an additional correction for absorption. Attempts
to explain the empirical correlation between the peak luminosity and the decline
rate of SNe Ia after maximum are, however, still controversial (H¨oflich et al.
1996, Eastman 1997).
With such a modified standard candle it is possible to derive accurate values
of the few parameters which govern the expansion in a homogeneous, isotropic
universe (e.g. Leibundgut & Pinto 1992, Goobar & Perlmutter 1995). Samples of
SNe Ia out to redshifts of z = 0:1 combined with a measurement of the absolute
luminosity yield values for the Hubble constant (Hamuy et al. 1996a, Riess et
al. 1996, Reiss et al. 1998).
1
--- We report results by the High­z Supernovae Search Team. Members of the team are
P. Challis, A. Clocchiatti, A. Diercks, A. Filippenko, P. Garnavich, R. Gilliland, C.
Hogan, S. Jha, R. Kirshner, D. Reiss, A. Riess, R. Schommer, C. Smith, C. Stubbs,
N. Suntzeff, J. Tonry, and P. Woudt.

2 Bruno Leibundgut, Brian Schmidt, Jason Spyromilio, Mark Phillips
With a sample of distant supernovae (z ? 0:3) we can measure the curvature
of the universe and any possible contributions of a cosmological constant. This
is a geometric measure of the universe. The deceleration can be determined by
comparing the distant supernovae with the local sample (Goobar & Perlmutter
1995, Leibundgut 1998). Two experiments are trying to make use of SNe Ia to
achieve a determination of the deceleration (Perlmutter et al. 1995, 1997, 1998;
Leibundgut et al. 1996, Garnavich et al. 1998, Schmidt et al. 1998, Riess et al.
1998). The current status of the two searches is summarized in section 3.
Yet supernovae are not true standard candles. The light curves and spectral
evolution show distinct variations among individual events (Phillips et al. 1987,
1992, Filippenko et al. 1992a, 1992b, Leibundgut et al. 1993). In particular the
near­infrared light curves show a second maximum for many, but not all, SNe Ia
(Elias et al. 1985, Frogel et al. 1987, Suntzeff 1996). The strength of the second
maximum changes considerably and is also distinguishable in bolometric light
curves (Vacca & Leibundgut 1996, Contardo et al. 1998).
2 Brief overview over SNe Ia
A generally accepted theory of SN Ia explosions has not yet emerged. For more
than a decade explosion models with a subsonic burning front have been fa­
vored (Nomoto et al. 1984, Woosley & Weaver 1986), but the physics which sus­
tains such a burning front without turning into a detonation is not understood.
New models which explode a white dwarf through He detonation at the surface
(Arnett & Livne 1994, Woosley & Weaver 1994), rather than the direct explo­
sive carbon burning inside, cannot be distinguished by the current observations
(Branch et al. 1995). The exact trigger of the explosion and the reaction of the
white dwarf is not constrained and many models have been proposed (e.g. H¨oflich
& Khokhlov 1996). The radiation transport is largely unsolved. The supernova
radiation is not thermalized in the ejecta and the observed pseudo­continuum
is dominated by line radiation. A simple way to see this is the fact that the
occurrence of maximum in the observed filter light curves does not indicate a
cooling shell, but rather a very complex redistribution of the emission (Contardo
et al. 1998). The bolometric light curves display the characteristic shoulder of
the near­infrared light curves and the total energy changes from event to event.
With this theoretical background it is difficult to support the standard can­
dle picture. The observations have shown a significant variety of appearance.
Nonetheless, most variations appear to correlate strongly so that the light curve
decline (Hamuy et al. 1996a, Riess et al. 1996), the strength of the Ca ii and
Si ii lines (Nugent et al. 1995), as well as the colors near maximum (Riess et al.
1998, Phillips et al. 1998) provide distance independent indicators of the intrin­
sic luminosity of SNe Ia. In this sense, SNe Ia appear to be an ordered set and
can empirically be used as modified standard candles.

Cosmological Parameters as measured by Type Ia Supernovae 3
3 The Hubble constant as derived from SNe Ia
The derivation of the Hubble constant from standard candles is in principle
very simple. With knowledge of the absolute magnitude the linear relation of
redshift and apparent magnitude provides the Hubble constant (Tammann &
Leibundgut 1990, Leibundgut & Pinto 1992). The recent programs to determine
distances to nearby galaxies which contained SNe Ia (Saha et al. 1997) provide a
fairly accurate determination of the luminosity of SNe Ia. Differences arise in the
treatment of the relative absorption of the Cepheid sample and the supernova,
and corrections to the supernova light curves themselves. The small scatter of
the measured peak luminosity of a sample of 7 nearby SNe Ia (Saha et al. 1997)
is further indication of the standard behavior of these objects.
The distribution of SNe Ia in the Hubble diagram then yields a value of the
Hubble constant. The controversy of the previous decades is finally subsiding
and values of 55 ! H 0 ! 70 km s \Gamma1 Mpc \Gamma1 are generally found (Hamuy et al.
1996a, Riess et al. 1996, Saha et al. 1997). This provides a measurement of H 0 to
15%. The differences are mainly in the treatment of the supernova light curves.
It has to be noted that the light curve correction in general changes the value of
H 0 by about 10% simply because the nearby SN sample with Cepheid distances
and the set of SNe Ia in the Hubble flow have a zero­point difference of this
order (Hamuy et al. 1996a, Leibundgut 1998). Other points of discussion are the
exact selection of the nearby sample which, although distance limited, suffers
from partially inadequate historical records of supernova photometry. These two
effects combine to the differences in the reported values. With more Cepheid
distances towards supernovae and better observed light curves the discrepancy
will disappear.
4 Distant
supernovae:\Omega M
and\Omega \Lambda
The determination of the cosmological energy density rests on the measurement
of objects distant enough so that the curvature of the universe becomes signif­
icant. SNe Ia discovered at redshifts larger than about 0.3 are very well suited
for such an investigation. Two groups aggressively pursue this experiment (Perl­
mutter et al. 1995, 1997, 1998, Leibundgut et al. 1996, Garnavich et al. 1998,
Schmidt et al. 1998, Riess et al. 1998). The cosmological frame work has been
layed out by Carroll et al. (1992) and Goobar & Perlmutter (1995).
Supernovae are now regularly found at large redshifts. So far, there is no
indication that their light curves and spectra differ from nearby objects. Many
SNe Ia have been classified and the light curves are being analyzed. The results
very strongly favor a positive value
for\Omega \Lambda (Riess et al. 1998).
Of fundamental importance are systematic effects which can alter the result.
Several technical steps lead to the luminosity distances. Accurate photometry of
faint sources on a spatially variable background, phase­dependent K­corrections,
and light curve determinations have to be applied. All of these corrections have
been tested thoroughly and independently in several applications (Schmidt et
al. 1998, Riess et al. 1998).

4 Bruno Leibundgut, Brian Schmidt, Jason Spyromilio, Mark Phillips
Other uncertainties are introduced by the light curve shape correction, extinc­
tion, possible evolution between the distant and the nearby supernovae, sample
selection, and (de­)magnification due to gravitational lensing. A careful analysis
can test for all effects with the exception of gravitational lensing which is achro­
matic and static. The systematic influence of weak lensing, however, is expected
to be very small (Wambsganss et al. 1997). Should the supernovae be lensed
significantly the scatter in the Hubble diagram would be increased, which is not
observed (Riess et al. 1998).
A luminosity shift between SNe Ia in early and late type galaxies has been
observed (Hamuy et al. 1996b). This has been attributed to the different ages,
masses, or metalicities of the progenitor population. The light curve corrections
can successfully neutralize the offset and the luminosity difference between sam­
ples in elliptical and spiral galaxies can be reduced to 0.05 magnitudes (Schmidt
et al. 1998). This is an indication of what has to be expected for a comparison
between the nearby and the distant sample. A critical parameter appears to be
the C/O composition of the progenitor white dwarf (H¨oflich et al. 1998). Ex­
tinction can be detected through the color of the supernovae. Very few distant
objects appear reddened (Garnavich et al. 1998, Riess et al. 1998). There is a
bias which favors discovery of unabsorbed objects due to the luminosity and
also the selection of objects well separated from the host galaxy. The latter is
not a true selection by the search, but rather is applied when decisions on the
follow up observations are taken. Thus, the absorption in the distant sample is
likely to be less on average than in the nearby sample. Another important issue
is the concordance of the nearby and the distant sample. Any systematic shift
between the two would result in a distortion of the derived cosmological param­
eters. An obvious systematic effect would be different average luminosities of the
two samples. This can be tested by comparing the light curve shapes of the two
samples. For our sample of 10 distant and 27 nearby supernovae the average \Delta
of the MLCS method (Riess et al. 1996) is ­0.126 and ­0.147 for the nearby and
the distant sample, respectively. The systematic offset is thus 0.02 magnitudes,
which is negligible. The same investigation for the analysis with \Deltam 15 yields
values which are slightly different. The mean \Deltam 15 for the local sample is 1.223,
while the distant sample has 1.173 on average. This difference translates into
a zero­point offset of 0.04 (0.03) magnitudes for B (V ) using the second order
treatment proposed by Phillips et al. (1998). The weighted mean value becomes
somewhat larger: 0.09 (0.08) magnitudes for B (V ). The local sample is on av­
erage less luminous than the distant one. This is also exemplified by Fig. 10 in
Riess et al. (1998). Figure 1 displays the magnitude difference of the observed
supernovae from an Einstein­de Sitter Universe
(\Omega M =
1;\Omega \Lambda = 0). Most ob­
jects clearly lie above the line for an empty universe (0,0) and thus indicate a
contribution of the vacuum energy to the energy density of the universe.
The comparison of 14 distant z?0.16 supernovae has shown that they appear
to be too dim for an empty universe. No solution for a positive matter density
(\Omega M ? 0) is found if \Lambda = 0 at a ? 2:5oe significance (Riess et al. 1998). Due
to the rather limited range of redshifts an exact value
for\Omega M
and\Omega \Lambda cannot

Cosmological Parameters as measured by Type Ia Supernovae 5
.4 .6 .8 1
­.2
0
.2
.4
.6
.8
1
redshift
dm (0.4,0.6)
(1,0)
(0,1)
(0,0)
Fig. 1. Magnitude difference from an Einstein­de Sitter Universe
(\Omega M =
1;\Omega \Lambda = 0).
The empty case
(\Omega M =
0;\Omega \Lambda = 0) and a mixed model with
(\Omega M =
0:4;\Omega \Lambda = 0:6) are
also indicated. The observed ffim for the supernovae are based on B and V light curves.
SN 1997ck is shown as an open symbol as no color information nor a spectrum for this
supernova are available.
be derived yet without further constraints. This confirms the preliminary result
presented by Garnavich et al. (1998) and is also in accordance with the one
reported by Perlmutter et al. (1998).
5 Conclusions
The analysis of our distant set with two slightly different analysis methods re­
sulted in a clear signature of a positive cosmological constant. A universe with
negligible \Lambda is excluded at the 2.5 oe level, as no solution with a positive matter
density is found. The effect is so strong that the value of the deceleration pa­
rameter q 0 is negative which indicates an accelerated expansion over the time
span sampled by our observations (5 Gyr; Riess et al. 1998).
The dynamic age shows a dependency very similar to the uncertainty regions
determined by the supernovae. It is thus possible to restrict the dynamic age of
the universe quite accurately. Riess et al. (1998) find values in the range of 13
to 15 Gyr which is consistent with most age determination of the oldest stellar
components.
Essential issues remain the systematic uncertainties of the experiment. Evo­
lution, extinction and sample selection are the most important contributors. The
only checks for evolution are extensive observations of distant objects to detect
any differences with nearby supernovae. A spectroscopic sequence with good
signal would allow us to investigate small differences in the ejecta. There are
clear signatures in the R and I light curves of SNe Ia which can be observed for
objects with z ! 0:4.

6 Bruno Leibundgut, Brian Schmidt, Jason Spyromilio, Mark Phillips
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