and Cosmology

8.3 High-Redshift Supernovae and the Cosmological Constant
seen in the bottom panel of Fig. 8.13. A scatter of only
σ = 0.15 mag around the Hubble relation remains. Figure
8.14 demonstrates the effect of this correction on
the light curves of several SNe Ia which initially appear
to have very different maximum luminosities and
widths. After correction they become nearly identical.
The left panel of Fig. 8.14 suggests that the light curves
of SN Ia can basically be described by a one-parameter
family of functions, and that this parameter can be deduced
from the shape, in particular the width, of the
light curves.
With this correction, SNe Ia become standardized
candles, i.e., by observing the light curves in several
bands their “corrected” maximum luminosity can be determined.
Since the observed flux of a source depends
on its luminosity and its luminosity distance D L , and the
latter also depends, besides redshift, on the cosmological
model, SNe Ia can be used for the determination of
cosmological parameters by measuring the luminosity
distance as a function of redshift. To apply this method,
it is necessary to detect and observe SNe Ia at appreciable
redshifts, where deviations from the linear Hubble
law become visible.
325
Fig. 8.13. The Hubble diagram for relatively nearby SNe Ia.
Plotted is the measured expansion velocity cz as a function of
the distance modulus for the individual supernovae. In the top
panel, it is assumed that all sources have the same luminosity.
If this was correct, all data points should be aligned along
the straight line, as follows from the Hubble law. Obviously,
the scatter is significant. In the bottom panel, the luminosities
have been corrected by means of the so-called MLCS method
in which the shape of the light curve and the colors of the SN
are used to “standardize” the luminosity (see text for more
explanations). By this the deviations from the Hubble law
become dramatically smaller – the dispersion is reduced from
0.42 mag to 0.15 mag
derived from the observed colors of the SN. The combined
analysis of these effects provides a possibility
for deducing an empirical correction to the maximum
luminosity from the observed light curves in several filters,
accounting both for the relation of the width of the
curve to the observed luminosity and for the extinction.
This correction was calibrated on a sample of SNe Ia
for which the distance to the host galaxies is very accurately
known. With this correction applied, the SNe Ia
follow the Hubble law much more closely, as can be
8.3.2 Observing SNe Ia at High Redshifts
An efficient strategy for the discovery of supernovae
at large distances has been developed, and two large
international teams have performed extensive searches
for SNe Ia at high redshifts in recent years. Two photometric
images of the same field, observed about four
weeks apart, are compared and searched for sources
which are not visible in the image taken first but which
are seen in the later one. Of these candidates, spectra
are then immediately taken to verify the nature of
the source as a SN Ia and to determine its redshift.
Subsequently, these sources become subject to extensive
photometric monitoring in order to obtain precise
light curves with a time coverage (sampling rate) as
complete as possible. For this observation strategy to
be feasible, the availability of observing time for both
spectroscopy and subsequent photometry needs to be
secured well before the search for candidates begins.
Hence, this kind of survey requires a very well-planned
strategy and coordination involving several telescopes.
Since SNe Ia at high redshift are very faint, the new 8-m