We investigate the vertical structure of neutrino dominated accretion disks by self-consistently considering the detailed microphysics , such as the neutrino transport , vertical hydrostatic equilibrium , the conservation of lepton number , as well as the balance between neutrino cooling , advection cooling and viscosity heating .
After obtaining the emitting spectra of neutrinos and antineutrinos by solving the one dimensional Boltzmann equation of neutrino and antineutrino transport in the disk , we calculate the neutrino/antineutrino luminosity and their annihilation luminosity .
We find that the total neutrino and antineutrino luminosity is about 10 ^ { 54 } ergs/s and their annihilation luminosity is about 5 \times 10 ^ { 51 } ergs/s with an extreme accretion rate 10 M _ { sun } /s and an alpha viscosity \alpha = 0.1 .
In addition , we find that the annihilation luminosity is sensitive to the accretion rate and will not exceed 10 ^ { 50 } ergs/s which is not sufficient to power the most fireball of GRBs , if the accretion rate is lower than 1 M _ { sun } /s .
Therefore , the effects of the spin of black hole or/and the magnetic field in the accretion flow might be introduced to power the central engine of GRBs .