Toward an inner connection of SNe Ic, SLSNe Ic, XRF connected SNe, SNe Ic-BL, and GRB connected SNe

Type Ic supernovae (SNe) can be classified as: normal SNe Ic, type Ic super-luminous SNe (SLSNe Ic), X-ray flash (XRF) connected SNe, broad-line SNe Ic (SN Ic-BL), and gamma-ray burst (GRB) connected SNe. Here we suggest an inner connection for all kinds of SNe Ic based on a pair of jets being successfully launched: a normal SN Ic is a normal core collapsar without jets launched; a GRB associated SN Ic is a core collapsar with relativistic jets launched and successfully breaking out the envelope of the progenitor; an XRF associated SN Ic is a core collapsar with jets launched but can only develop a relativistic shock breakout; an SN Ic-BL is an off-axis GRB or XRF associated supernova; and an SLSN Ic is close to the XRF-SN 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 SNe Ic as a whole. We also show that the normal SNe Ic and GRB connected SNe Ic have similar accumulative distributions.