A Novel Relationship Between Gamma Ray Burst Duration and Photospheric Radius

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.