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Cosmic Deceleration measured with Type Ia Supernovae a;b
B. Leibundgut and J. Spyromilio
European Southern Observatory, Karl­Schwarzschild­Strasse 2
D­85748 Garching, Germany
With the observations of distant type Ia supernovae cosmological parameters can be measured
with an unprecedented accuracy. It is found that the distant supernovae appear dimmer
than expected in an empty universe indicating contributions by the vacuum energy density.
Systematic errors are the largest uncertainties at the moment. Evolution, extinction, weak
lensing, and sample discrepancies are the most important ones. All these systematics can
in principle be tested observationally. The current data sample also indicates an age of the
universe which is consistent with the oldest stellar components of the Galaxy.
1 Introduction
Type Ia Supernovae (SNe Ia) have proven to be excellent distance indicators when treated
suitably 1;2 . They have several virtues that come with standard candles, even though they
are not pure standard candles themselves. Combined with the high luminosity of the objects,
which makes them detectable out to redshifts near 1, they can be used to measure cosmological
distances and provide a determination of the deceleration of the universe 3;4 . The light curve
shape corrections, however, are purely empirical and have changed considerably since their first
application. Attempts to explain the empirical correlation between the peak luminosity and the
decline rate of SNe Ia after maximum are still controversial.
With samples of nearby (z ! 0:1) and distant (z ? 0:3) supernovae we can measure the
curvature of the universe and any possible contributions of a vacuum energy density based on
luminosity distances. The deceleration can be determined by comparing the distant supernovae
a 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, M. Phillips, D. Reiss, A.
Riess, B. Schmidt, R. Schommer, C. Smith, C. Stubbs, N. Suntzeff, J. Tonry, and P. Woudt.
b To appear in Fundamental Parameters in Cosmology, Rencontres de Moriond 1998, Paris: Editions Frontieres

with the local sample 4;5 . Two experiments are trying to make use of SNe Ia to achieve a
determination of the deceleration 6;7;8;9;10;11 . We report here the recent results obtained by the
High­z SN Search Team.
2 Type Ia supernovae as distance indicators
The light curves and spectral evolution show distinct variations among individual events. In par­
ticular the near­infrared light curves show a second maximum for many, but not all, SNe Ia 12 .
The strength of the second maximum changes considerably and is also distinguishable in bolo­
metric light curves 13 .
A generally accepted theory of SN Ia explosions has not emerged yet. For more than a
decade explosion models with a subsonic burning front have been favored 14;15 , but the physics
which sustains such a burning front without turning it into a detonation is not understood. New
models which explode a white dwarf through He detonation at the surface 16;17 , rather than the
direct explosive carbon burning inside, cannot be distinguished by the current observations 18 .
The exact trigger of the explosion and the reaction of the white dwarf is not constrained by
observations and many models have been proposed. 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 provided by 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 13 . The bolometric light curves display the characteristic
shoulder of the near­infrared light curves and the total energy changes from event to event.
Despite the lack of understanding of the explosion physics, observational trends have been
found to account for the light curve and luminosity variations. The correlation between lumi­
nosity and light curve decline is well established 1 ;2 . The rest­frame colors are good indicators of
reddening towards a supernova and extinction corrections can be applied. In this sense, SNe Ia
appear to be an ordered set and can empirically be used as distance indicators.
3
\Omega M
and\Omega \Lambda from SNe Ia
The determination of the cosmological energy density rests on the measurement of objects distant
enough so that the curvature of the universe becomes significant. SNe Ia discovered at redshifts
larger than 0.3 are very well suited for such an investigation.
Garnavich et al. 9 and Riess et al. 11 report the results from samples which include about 30
SNe Ia in the local sample and 10 objects at redshifts z – 0:3. With the exception of the
most distant object, SN 1997ck at z = 0:97, all objects have been classified by a spectrum and
detailed light curves in at least two filters are available, which allows us to apply the light curve
corrections, either template fitting and the \Deltam 15 analysis 1 ;19 or MLCS 2 . The color information
is essential to obtain an estimate of the extinction towards the supernova. The local sample
is used to determine the correlations between light curve shape and luminosity which are then
applied to the distant supernovae.
Of fundamental importance are systematic effects which can alter the result. Several tech­
nical 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 independently in several applications 10 ;11 .
Other uncertainties are introduced by the light curve shape correction, extinction, 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 achromatic and static. The systematic influence of weak lensing, however, is
expected to be very small 20 .

.4 .6 .8 1
­.2
0
.2
.4
.6
.8
1
redshift
dm (0.4,0.6)
(1,0)
(0,1)
(0,0)
Figure 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.
A luminosity shift between SNe Ia in early and late type galaxies has been observed. 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 samples in elliptical and spiral galaxies can be reduced to 0.05 magnitudes 10 . 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 21 .
Extinction can be detected through the color of the supernovae. Very few distant objects appear
reddened 9;11 . 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 follow­up observations are
taken. Thus, the absorption in the distant sample is likely to be less on average than in the
nearby sample.
Of paramount importance is the concordance of the nearby and the distant supernova sample.
Any systematic shift between the two would result in a distortion of the derived cosmological
parameters. Contamination by objects which are not SNe Ia has to be avoided. The spectroscopy
and the light curves provide ample information to make such a distinction, but there is at least
one case where a luminous SN Ic could not be excluded 11 . No classification of SN 1997ck, with
no observed supernova spectrum and only one filter light curve, is available. The light curve is,
however, consistent with a SN Ia at the observed galaxy redshift 9;5 . An obvious systematic effect
would be different average luminosities of the two samples. To first order, this can be tested
by comparing the light curve shapes. For our sample of 10 distant and 27 nearby supernovae
the average \Delta of the MLCS method 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 weighted
mean \Deltam 15 for the local sample is 1.296, while the distant sample has 1.184 on average. This
difference translates into a zero­point offset of 0.09 magnitudes using the second order treatment
proposed by Phillips et al. 19 The local sample is on average less luminous than the distant one.
Figure 1 displays the magnitude difference of the observed supernovae from an Einstein­
de Sitter
Universe(\Omega M =
1;\Omega \Lambda = 0). Many objects 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 10 distant supernovae appear to be too dim even for an empty universe. The magnitude
offset is 0:11 \Sigma 0:03 magnitudes. However, the RMS of the distribution is 0.19 magnitudes.
Excluding SN 1997ck does not change the values.

An analysis based on probability density functions finds that no solution for a positive matter
density(\Omega M ? 0) exists, if \Lambda = 0 at a ? 2:5oe significance from both methods 11 . This confirms
the preliminary result presented by Garnavich et al. 9 and is also in accordance with the one
reported by Perlmutter et al. 7 Due to the rather limited range of redshifts an exact value for
\Omega M
and\Omega \Lambda cannot be derived yet without further constraints.
4 Conclusions
The analysis of our distant set with two slightly different methods resulted in a signature of a
positive cosmological constant barring undetected systematic errors. A universe with negligible
\Lambda is (statistically) 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 parameter q 0 is negative 11 which
indicates an accelerated expansion over the time span sampled by our observations (5 Gyr).
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 accu­
rately. Riess et al. 11 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. The magnitude offset
from an empty universe model is very small (¸0.1 mag) and even small systematic effect are
important. Evolution, 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.
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