Abstract
Two quantitative tests DIFF1 and DIFF2 for measuring goodness-of-fit between two locally-normalized supernova spectra are presented. Locally-normalized spectra are obtained by dividing a spectrum by the same spectrum smoothed over a wavelength interval relatively large compared to line features, but relatively small compared to continuum features. DIFF1 essentially measures the mean relative difference between the wave patterns of locally-normalized spectra and DIFF2 is DIFF1 minimized with respect to a relative logarithmic wavelength shift between the spectra: the shift is an artificial relative Doppler shift. Both DIFF1 and DIFF2 measure the similarity of spectra: DIFF1 puts more weight on overall physical similarity in spectrum formation; DIFF2, just on the similarity of the line patterns in the spectra because the shift compensates for some physical distinction in the supernovae. Both tests are useful in ordering supernovae into empirical groupings for further analysis. We present some examples of locally-normalized spectra for Type IIb supernova SN 1993J with some analysis of these spectra. The spectra include two HST spectra that have not been published before. We also give an example of fitted locally-normalized spectra and, as an example of the utility of DIFF1 and DIFF2, some preliminary statistical results for hydrogen-deficient core-collapse (HDCC) supernova spectra. This paper makes use of and refers to material to found at the first author's online supernova spectrum database SUSPEND (SUpernovae Spectra PENDing further analysis, http://www.nhn.ou.edu/~jeffery/astro/sne/spectra/spectra.html).