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We present axisymmetric hydrodynamical simulations of the long-term accretionof a rotating GRB progenitor star, a "collapsar," onto the central compactobject. The simulations were carried out with the adaptive mesh refinement codeFLASH in two spatial dimensions and with an explicit shear viscosity. Theevolution of the central accretion rate exhibits phases reminiscent of the longGRB gamma-ray and X-ray light curve, which lends support to the proposal thatthe luminosity is modulated by the central accretion rate. After a few tens ofseconds, an accretion shock sweeps outward through the star. The formation andoutward expansion of the accretion shock is accompanied with a sudden and rapidpower-law decline in the central accretion rate Mdot ~ t^{-2.8}, whichresembles the L_X ~ t^{-3} decline observed in the X-ray light curves. Thecollapsed, shock-heated stellar envelope settles into a thick, low-massequatorial disk embedded within a massive, pressure-supported atmosphere. Aftera few hundred seconds, the inflow of low-angular-momentum material in the axialfunnel reverses into an outflow from the surface of the thick disk. Meanwhile,the rapid decline of the accretion rate slows down, or even settles a in steadystate with Mdot ~ 5x10^{-5} Msun/s, which resembles the "plateau" phase in theX-ray light curve. While the duration of the "prompt" phase depends on theresolution in our simulations, we provide an analytical model taking intoaccount neutrino losses that estimates the duration to be ~20 s. The modelsuggests that the steep decline in GRB X-ray light curves is triggered by thecircularization of the infalling stellar envelope at radii where the virialtemperature is below ~10^{10} K, such that neutrino cooling shuts off and anoutward expansion of the accretion shock becomes imminent.

Collapsar Accretion and the Gamma-Ray Burst X-Ray Light Curve