Clumpy-gas relativistic radiation hydrodynamics: Formulation

Clumpy-gas radiation hydrodynamics, where a lot of clumps/cloudlets coexist with the tenuous ambient gas, is extended to the special relativistic regime as clumpy-gas relativistic radiation hydrodynamics. The formulation is performed under the macroscopic treatment, where a sheet-like stratus is moving at a relativistic speed over a luminous source with an infinite/finite extension, and receives an accelerating radiative force as well as a decelerating radiation drag force. Similar to the nonrelativistic case, cloudlets with a finite optical depth are generally less accelerated than the ambient gas, while the interactive force (ram pressure) between cloudlets and the tenuous gas works to decrease the gas velocity and increase the cloudlet one. The relativistic effect, as in a usual case, suppresses both the gas and cloudlet velocities, and is necessary to evaluate quantitatively the clumpy-gas outflows from a black hole accretion disk system. Due to the gravitational and radiation drag forces, furthermore, the clumpy-gas outflows have usually subrelativistic terminal velocities, which are often observed in active luminous objects. Similar to the nonrelativistic case, there are many simplifications, and there is still plenty of room for further developments.