This is the second paper of a series in which we present new measurements of the observed rates of supernovae (SNe) in the local Universe, determined from the Lick Observatory Supernova Search (LOSS). In this paper, a complete SN sample is constructed, and the observed (uncorrected for host-galaxy extinction) luminosity functions (LFs) of SNe are derived. These LFs solve two issues that have plagued previous rate calculations for nearby SNe: the luminosity distribution of SNe and the host-galaxy extinction. We select a volumelimited sample of 175 SNe, collect photometry for every object and fit a family of light curves to constrain the peak magnitudes and light-curve shapes. The volume-limited LFs show that they are not well represented by a Gaussian distribution. There are notable differences in the LFs for galaxies of different Hubble types (especially for SNe Ia). We derive the observed fractions for the different subclasses in a complete SN sample, and find significant fractions of SNe II-L (10 per cent), IIb (12 per cent) and IIn (9 per cent) in the SN II sample. Furthermore, we derive the LFs and the observed fractions of different SN subclasses in a magnitude-limited survey with different observation intervals, and find that the LFs are enhanced at the highluminosity end and appear more 'standard' with smaller scatter, and that the LFs and fractions of SNe do not change significantly when the observation interval is shorter than 10 d. We also discuss the LFs in different galaxy sizes and inclinations, and for different SN subclasses. Some notable results are that there is not a strong correlation between the SN LFs and the host-galaxy size, but there might be a preference for SNe IIn to occur in small, late-type spiral galaxies. The LFs in different inclination bins do not provide strong evidence for extreme extinction in highly inclined galaxies, though the sample is still small. The LFs of different SN subclasses show significant differences. We also find that SNe Ibc and IIb come from more luminous galaxies than SNe II-P, while SNe IIn come from less luminous galaxies, suggesting a possible metallicity effect. The limitations and applications of our LFs are also discussed.

This is the third paper of a series in which we present new measurements of the observed rates of supernovae (SNe) in the local Universe, determined from the Lick Observatory Supernova Search (LOSS). We have considered a sample of ∼1000 SNe and used an optimal subsample of 726 SNe (274 SNe Ia, 116 SNe Ibc and 324 SNe II) to determine our rates. We study the trend of the rates as a function of a few quantities available for our galaxy sample, such as luminosity in the B and K bands, stellar mass and morphological class. We discuss different choices (SN samples, input SN luminosity functions, inclination correction factors) and their effect on the rates and their uncertainties. A comparison between our SN rates and the published measurements shows that they are consistent with each other to within the uncertainties when the rate calculations are done in the same manner. Nevertheless, our data demonstrate that the rates cannot be adequately described by a single parameter using either galaxy Hubble types or B − K colours. A secondary parameter in galaxy 'size', expressed by luminosity or stellar mass, is needed to adequately describe the rates in the rate-size relation: the galaxies of smaller sizes have higher SN rates per unit mass or per unit luminosity. The trends of the SN rates in galaxies of different Hubble types and colours are discussed. We examine possible causes for the rate-size relation. Physically, such a relation for the core-collapse SNe is probably linked to the correlation between the specific star-formation rate and the galaxy sizes, but it is not clear whether the same link can be established for SNe Ia. We discuss the two-component ('tardy' and 'prompt') model for SN Ia rates, and find that the SN Ia rates in young stellar populations might have a strong correlation with the core-collapse SN rates. We derive volumetric rates for the different SN types [e.g. for SNe Ia, a rate of (0.301 ± 0.062) × 10 −4 SN Mpc −3 yr −1 at redshift 0] and compare them to the measurements at different redshifts. Finally, we estimate the SN rate for the Milky Way Galaxy to be 2.84 ± 0.60 SNe per century (with a systematic uncertainty of a factor of ∼2), consistent with published SN rates based on several different techniques.

This is the first paper of a series in which we present new measurements of the observed rates of supernovae (SNe) in the local Universe, determined from the Lick Observatory Supernova Search. We have obtained 2.3 million observations of 14 882 sample galaxies over an interval of 11 years (1998 March to 2008. We considered 1036 SNe detected in our sample and used an optimal subsample of 726 SNe (274 Type Ia SNe, 116 Type Ibc SNe and Type II 324 SNe) to determine our SN rates. This is the largest and most homogeneous set of nearby SNe ever assembled for this purpose, and ours is the first local SN rate analysis based on CCD imaging and modern image-subtraction techniques. In this paper, we lay the foundation of the study. We derive the recipe for the control-time calculation for SNe with a known luminosity function and provide details on the construction of the galaxy and SN samples used in the calculations. Compared with a complete volume-limited galaxy sample, our sample has a deficit of low-luminosity galaxies but still provides enough statistics for a reliable rate calculation. There is a strong Malmquist bias, so the average size (luminosity or mass) of the galaxies increases monotonically with distance, and this trend is used to showcase a correlation between SN rates and galaxy sizes. Very few core-collapse SNe are found in early-type galaxies, providing strong constraints on the amount of recent star formation within these galaxies. The small average observation interval (∼9 d) of our survey ensures that our control-time calculations can tolerate a reasonable amount of uncertainty in the luminosity functions of SNe. We perform Monte Carlo simulations to determine the limiting magnitude of each image and the SN detection efficiency as a function of galaxy Hubble type. The limiting magnitude and the detection efficiency, together with the luminosity function derived from a complete sample of very nearby SNe in Paper II, will be used to calculate the control time and the SN rates in Paper III.