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The broad-band light curves of supernovae trace the temporal evolution of the radiative energy emitted by these objects. The apparent photometric uniformity of Type I supernovae (SNe I) has led to the adoption of standard templates to describe the light curves of these objects. Recent observations, however, have indicated that variations in the light curves of SNe I do occur. In order to investigate the differences in SNe I light curves, a quantitative description of the shape of the light curve is needed.
We have developed a least-squares fitting scheme for the broad band $UBV$ photometric data in which the observed light curves are approximated by a combination of a Gaussian curve for the peak and early decline phase and a line for the decline after $\sim$40 days past maximum. This purely empirical representation allows us to obtain objective measurements of a set of parameters describing the light curves of individual supernovae. For example, the fitting procedure yields the maximum magnitude, the time of maximum, the decline rates, and the width of the peak. In addition, an estimate of the observational errors is obtained.
Using this empirical representation, we have fitted all the photometric (and photographic) data available for SNe I light curves presented in Leibundgut et al. (1991, A\&AS, 89, 537). We discuss the decline parameter $\Delta$m$_{15}$, as defined by Phillips (1993, ApJ Letters, in press), and compare it to other quantities characterizing of the light curve shapes. We examine the late-time decline rates and find a wide range of values.
While not based on any particular physical model, the continuous representation of the data that we have used provides a convenient and quantitative means of characterizing SNe I light curves. Possible differences among the light curves of subtypes of SNe I can be investigated in an objective manner. Comparisons can be made not only between the light curves of various supernovae, but also between the light curves exhibited by the photometric data in different pass bands for a given individual supernova. This approach is clearly superior to the use of standard templates to describe SNe I light curves.
