Abstract
Abstract
Long gamma-ray bursts (lGRBs) are associated with jets in Type Ic broad-line supernovae. The collapsar model provides a theoretical framework for the jet formation from the core collapse of a massive star in such supernovae. The gamma-ray burst (GRB) can only be produced after a successful jet breakout from the star. Under this formalism the GRB duration (
t
90
) has been hypothesized to be the difference between the central engine activity duration (
t
eng
) and the jet breakout time (
t
bo
), that is
t
90
=
t
eng
−
t
bo
. This disallows
t
90
>
t
eng
and puts a lower bound on the successful lGRB jet central engine duration (
t
eng
>
t
bo
), however various numerical simulations have shown otherwise. This study considers a photospheric GRB emission from a relativistic jet punching out of a Wolf–Rayet-like star. We use the bolometric lightcurve generated to calculate the lGRB duration (
t
90
) for the varying engine durations. We find for a longer engine duration the lGRB lightcurve reflects the jet profile and
t
90
≈
t
eng
. While for a shorter engine duration, the
t
90
has a photospheric radius (
R
ph
) dependence. This can be modeled by the relation
t
90
=
t
eng
90
+
0.03
R
ph
c
, where c is the speed of light with a lower bound on
t
90
for a successful lGRB. This relation should be most relevant for possible low-luminous lGRBs originating from a collapsar with central engine duration comparable to the jet breakout time.