Theoretically expected natures of a supernova driven by a wind/jet are discussed .
Approximate analytical formulations are derived to clarify basic physical processes involved in the wind/jet-driven explosions , and it is shown that the explosion properties are characterized by the energy injection rate ( \dot { E } _ { iso } ) and the mass injection rate ( \dot { M } _ { iso } ) .
To explain observations of SN 1998bw associated with Gamma-Ray Burst ( GRB ) 980425 , the following conditions are required : \dot { E } _ { iso } \dot { M } _ { iso } \ga 10 ^ { 51 } erg M _ { \odot } s ^ { -2 } and \dot { E } _ { iso } \ga 2 \times 10 ^ { 52 } erg s ^ { -1 } ( if the wind Lorentz factor \Gamma _ { w } \sim 1 ) or \dot { E } _ { iso } \ga 7 \times 10 ^ { 52 } erg s ^ { -1 } ( if \Gamma _ { w } \gg 1 ) .
In SN 1998bw , ^ { 56 } Ni ( \sim 0.4 M _ { \odot } ) is probably produced in the shocked stellar mantle , not in the wind .
The expected natures of SNe , e.g. , ejected ^ { 56 } Ni masses and ejecta masses , vary depending on \dot { E } _ { iso } and \dot { M } _ { iso } .
The sequence of the SN properties from high \dot { E } _ { iso } and \dot { M } _ { iso } to low \dot { E } _ { iso } and \dot { M } _ { iso } is the following : SN 1998bw-like – intermediate case – low mass ejecta ( \la 1 M _ { \odot } ) where ^ { 56 } Ni is from the wind – whole collapse .
This diversity may explain the diversity of supernovae associated with GRBs .
Our result can be used to constrain natures of the wind/jet , which is linked to the central engine of GRBs , by studying properties of the associated supernovae .