Using radiation hydrodynamics simulations in a local stratified shearing box with realistic equations of state and opacities , we explored the outcome of self-gravity at 50 AU in a protoplanetary disc irradiated by the central star .
We found that gravito-turbulence is sustained for a finite range of the surface density , from \sim 80 to \sim 250 gcm ^ { -2 } .
The disk is laminar below the range while fragments above it . 
In the range of gravito-turbulence , the Toomre parameter decreases monotonically from \sim 1 to \sim 0.7 as the surface density increases while an effective cooling time is almost constant at \sim { \color { black } 4 } in terms of the inverse of the orbital frequency .
The turbulent motions are supersonic at all heights , which dissipates through both shock waves and compressional heating .
The compressional motions , occurring near the midplane , create upward flows , which not only contribute to supporting the disc but also to transporting the dissipated energy to the disc surfaces .
The irradiation does not affect much the gravito-turbulence near the midplane unless the grazing angle is larger than 0.32 .
We also show that a simple cooling function with a constant cooling time does not approximate the realistic cooling .