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Due to their extreme luminosities at maximum light, type~Ia supernovae (SNe~Ia) have long been considered among the most attractive cosmological standard candles. Although nearly all work to date has been devoted to attempts to use these objects to determine the local rate of expansion of the universe ($H_{o}$), SNe~Ia also provide one of the few direct techniques for measuring the deceleration parameter $q_{o}$. However, in a recent study of nine well-observed events based largely on data obtained at CTIO, Phillips (1993, ApJ, 413, L105) found clear evidence for a significant intrinsic dispersion in SNe Ia absolute magnitudes amounting to $\sim$0.8 mag in $B$, $\sim$0.7 mag in $V$, and $\sim$0.5 mag in $I$. Such a range in peak luminosity could introduce a subtantial Malmquist bias into searches for distant ($z \leq$ 0.3) SNe~Ia which, if uncorrected, could lead to an erroneous value of q$_{o}$.
In this paper we present the Hubble diagram for 13 SNe~Ia discovered and observed in the course of the Cal\'an/Tololo Supernova Survey. This sample, which covers the redshift range 0.01 $\leq z \leq$ 0.1, provides unequivocal evidence for an intrinsic spread in the peak luminosities of type~Ia events. The data also confirm Phillips' conclusion that the maximum-light luminosity is strongly correlated with the initial decline rate of the $B$ light curve. Interestingly, the most luminous SNe in our sample all occurred in spiral galaxies, which is true for Phillips' sample of nearby SNe~Ia as well. This is opposite to what one would expect if dust extinction were important. These findings are consistent with recent speculations that the progenitors of SNe~Ia are white dwarfs covering a range of masses, and also suggest that the brightest events may be found in galaxies which are still actively forming stars. The implications for the use of SNe~Ia to measure $q_{o}$ are briefly discussed.
This research has been supported by Grant 92/0312 from Fondo Nacional de Ciencias y Tecnolog\'{\i}a (FONDECYT-Chile).
