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Measuring\Omega and \Lambda with Type Ia Supernovae
J.C. Niemeyer
Max­Planck­Institut f¨ur Astrophysik
Karl­Schwarzschild­Strasse 1, D­85748 Garching, Germany
B. Leibundgut
European Southern Observatory
Karl­Schwarzschild­Strasse 2, D­85748 Garching, Germany
The explosive carbon incineration of white dwarfs produces very luminous events with no hydrogen in their
spectra ­ Type Ia supernovae (SNe Ia). These objects display a fairly uniform behavior which led to their
use as cosmological distance probes. The simple adoption of a unique peak luminosity (standard candle),
however, has recently been challenged by SN Ia samples with accurate relative distances. A dispersion of 0.6
magnitudes in maximum luminosity and a correlation of luminosity with the light curve shape have been
described (Phillips 1993, Hamuy et al. 1996). Local samples can be corrected by the proposed light curve
shape fitting which leaves only a small residual scatter (!0.2 mag; Hamuy et al. 1996, Riess et al. 1996).
The determination of
the\Omega and \Lambda through standard candles is based on very general cosmological
considerations (Carroll et al. 1992). With many supernovae observed accurateluy at large, but different,
redshifts the two parameters can be constrained simultaneously (Goobar & Perlmutter 1995). It has been
argued that this approach is preferable to the traditional decelaration parameter q 0 in the classical Hubble
diagram for standard candles (Perlmutter et al. 1997). The complication of the luminosity variations
has to be treated carefully for a trustable result. Only the combination of spectroscopy, to assure correct
classification and discriminate peculiar objects, and multi­filter light curves, for estimates of absorption,
can produce reliable determinations (Leibundgut & Spyromilio 1997, Schmidt 1997).
There are currently two groups searching and recording distant supernovae (Schmidt 1997, Leibundgut et
al. 1996, Perlmutter et al. 1997). Both find substantial numbers of SNe Ia (?15 per year) at z?0.3. The
classification is based on spectroscopy acquired with Keck and 4m­class telescopes around the world. Light
curves are measured for as many objects as possible.
Determination of the cosmic deceleration is observationally simpler than determining the Hubble constant,
since it is done through relative measurements. It is based on the comparison of the apparent brightness of
objects with known relative luminosity at largely different redshifts. The ability to find the luminosity of a
distant SN Ia relative to a nearby twin rests purely on observables (Schmidt 1997, Perlmutter et al. 1997).
Measuring the luminosity distance L as a function of redshift z, one can directly estimate the cosmological
density
parameter\Omega and the cosmological constant \Lambda by virtue of their different dependence on z in L
(Goobar & Perlmutter 1995).
A first measurement using SNe Ia has been presented by Perlmutter et al. (1997). Their determination
of\Omega and \Lambda is based on the analysis of 7 supernovae at redshifts z ? 0:35. The redshift range is not yet
sufficient for significant independent limits
on\Omega and \Lambda. With the additional assumption of a spatially flat
universe the cosmological constant can, however, be constraint to !0.7 (2oe).
References
Carroll, S. M., Press, W. H., & Turner, E. L. 1992, ARA&A, 30, 499
Goobar, A. & Perlmutter, S. 1995, ApJ, 450, 14
Hamuy, M., et al., 1996, AJ, 112, 2438
Leibundgut, B. & Spyromilio, J. 1997, in The Early Universe and the VLT, ed. J. Bergeron, New York;
Springer, in press
Leibundgut, B., et al. 1996, ApJ, 466, L21
Perlmutter, S., et al. 1997, ApJ, in press (preprint LBNL­39291)
Phillips, M. M. 1993, ApJ, 413, L105
Riess, A. G., Press, W. M., & Kirshner, R. P. 1996, ApJ, 473, 88
Schmidt, B. P., 1997, in Thermonuclear Supernovae, eds. P. Ruiz­Lapuente, R. Canal, J. Isern, Dordrecht:
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