Gravitational Instability in Neutrino Dominated Accretion Disks

We revisit the vertical structure of neutrino-dominated accretion flows (NDAFs) in spherical coordinates under a boundary condition based on a mechanical equilibrium. The solutions show that the NDAF is significantly geometrically thick. The Toomre parameter is determined by the mass accretion rate and the viscosity parameter, which is defined as Q=c_S Ω/πGΣ, where c_S , Ω and Σ are the sound speed, angular velocity and surface density, respectively. According to the distribution of the Toomre parameter, the possible fragments of the disk may appear near the disk surface in the outer region. These possible outflows originating from the gravitational instability of the disk may account for the late-time flares in gamma-ray bursts.