LAUSR

Abstract Type Ic supernovae can be classified as normal supernovae Ic, type Ic super-luminous supernovae, X-ray flash-connected supernovae, broad-line supernovae Ic, and gamma-ray burst-connected supernovae. Here we suggest an inner connection for all kinds of supernovae Ic which is based on whether a pair of jets are successfully launched: a normal supernovae Ic is a normal core collapsar without jets launched; a gamma-ray burst-associated supernovae Ic is a core collapsar with relativistic jets launched and successfully breaking out the envelope of the progenitor; an X-ray flash-associated supernovae Ic is a core collapsar with jets launched but can only develop a relativistic shock breakout; a broad-line supernovae Ic is an off-axis gamma-ray burst or an X-ray flash-associated supernova; and a type Ic super-luminous supernovae is close to the X-ray flash-connected supernovae Ic, but the shock breakout is not relativistic and most of the jet energy is deposited into the supernova component. Based on the luminosity-distance diagram, we derived the luminosity function of all different types of supernovae Ic as a whole. We also show that the normal supernovae Ic and gamma-ray burst-connected supernovae Ic have similar accumulative distributions.