Constraining Physical Properties of Type IIn Supernovae through Rise Times and Peak Luminosities

We investigate the diversity in the wind density, supernova ejecta energy, and ejecta mass in Type IIn supernovae based on their rise times and peak luminosities. We show that the wind density and supernova ejecta properties can be estimated independently if both the rise time and peak luminosity are observed. The peak luminosity is mostly determined by the supernova properties and the rise time can be used to estimate the wind density. We find that the ejecta energy of Type IIn supernovae needs to vary by factors of 0.2-5 from the average if their ejecta mass is similar. The diversity in the observed rise times indicates that their wind density varies by factors of 0.2-2 from the average. We show that Type IIn superluminous supernovae should have not only large wind density but also large ejecta energy and/or small ejecta mass to explain their large luminosities and the rise times at the same time. We also note that the shock breakout does not necessarily occur in the wind even if it is optically thick, except for the case of superluminous supernovae, and we analyze the observational data both with and without assuming that the shock breakout occurs in the dense wind of Type IIn supernovae.