Nearby supernova rates from the Lick Observatory Supernova Search - II. The observed luminosity functions and fractions of supernovae in a complete sample

This is the second paper of a series in which we present new measurements of\nthe observed rates of supernovae (SNe) in the local Universe, determined from\nthe Lick Observatory Supernova Search (LOSS). In this paper, a complete SN\nsample is constructed, and the observed (uncorrected for host-galaxy\nextinction) luminosity functions (LFs) of SNe are derived. These LFs solve two\nissues that have plagued previous rate calculations for nearby SNe: the\nluminosity distribution of SNe and the host-galaxy extinction. We select a\nvolume-limited sample of 175 SNe, collect photometry for every object, and fit\na family of light curves to constrain the peak magnitudes and light-curve\nshapes. The volume-limited LFs show that they are not well represented by a\nGaussian distribution. There are notable differences in the LFs for galaxies of\ndifferent Hubble types (especially for SNe Ia). We derive the observed\nfractions for the different subclasses in a complete SN sample, and find\nsignificant fractions of SNe II-L (10%), IIb (12%), and IIn (9%) in the SN II\nsample. Furthermore, we derive the LFs and the observed fractions of different\nSN subclasses in a magnitude-limited survey with different observation\nintervals, and find that the LFs are enhanced at the high-luminosity end and\nappear more "standard" with smaller scatter, and that the LFs and fractions of\nSNe do not change significantly when the observation interval is shorter than\n10 days. We also discuss the LFs in different galaxy sizes and inclinations,\nand for different SN subclasses. Some notable results are ... (abridged).\n