Collapsar accretion and the gamma-ray burst X-ray light curve

We present axisymmetric hydrodynamical simulations of the long-term accretion of a rotating gamma-ray burst progenitor star, a "collapsar," onto the central compact object, which we take to be a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in two spatial dimensions and with an explicit shear viscosity. The evolution of the central accretion rate exhibits phases reminiscent of the long GRB [gamma]-ray and X-ray light curve, which lends support to the proposal by Kumar et al. (2008a,b) that the luminosity is modulated by the central accretion rate. In the first "prompt" phase, the black hole acquires most of its final mass through supersonic quasiradial accretion occurring at a steady rate of [scientific symbols]. After a few tens of seconds, an accretion shock sweeps outward through the star. The formation and outward expansion of the accretion shock is accompanied with a sudden and rapid power-law decline in the central accretion rate Ṁ [proportional to] t⁻²̇⁸, which resembles the L[subscript x] [proportional to] t⁻³ decline observed in the X-ray light curves. The collapsed, shock-heated stellar envelope settles into a thick, low-mass equatorial disk embedded within a massive, pressure-supported atmosphere. After a few hundred seconds, the inflow of low-angular-momentum material in the axial funnel reverses into an outflow from the thick disk. Meanwhile, the rapid decline of the accretion rate slows down, which is potentially suggestive of the "plateau" phase in the X-ray light curve. We complement our adiabatic simulations with an analytical model that takes into account the cooling by neutrino emission and estimate that the duration of the prompt phase can be ~ 20 s. The model suggests that the steep decline in GRB X-ray light curves is triggered by the circularization of the infalling stellar envelope at radii where the virial temperature is below 10¹⁰ K, such that neutrino cooling is inefficient and an outward expansion of the accretion shock becomes imminent; GRBs with longer prompt [gamma]-ray emission should have more slowly rotating envelopes.