Distributions of Galaxy Spectral Types in the Sloan Digital Sky Survey

We perform an objective classification of 170,000 galaxy spectra in the Sloan Digital Sky Survey (SDSS) using the Karhunen-Lo\`eve (KL) transform. With about one-sixth of the total set of galaxy spectra which will be obtained by the survey, we are able to carry out the most extensive analysis of its kind to date. The formalism proposed by Connolly and Szalay is adopted to correct for gappy regions in the spectra, and to derive eigenspectra and eigencoefficients. From this analysis, we show that this gap-correction formalism leads to a converging set of eigenspectra and KL-repaired spectra. Furthermore, KL eigenspectra of galaxies are found to be convergent not only as a function of iteration, but also as a function of the number of randomly selected galaxy spectra used in the analysis. From these data a set of ten eigenspectra of galaxy spectra are constructed, with rest-wavelength coverage 3450-8350 angstrom. The eigencoefficients describing these galaxies naturally place the spectra into several classes defined by the plane formed by the first three eigencoefficients of each spectrum. Spectral types, corresponding to different Hubble-types and galaxies with extreme emission lines, are identified for the 170,000 spectra and are shown to be complementary to existing spectral classifications. From a non-parametric classification technique, we find that the population of galaxies can be divided into three classes which correspond to early late- through to intermediate late-types galaxies. (Abridged)