Clumpy-gas radiation hydrodynamics: Self-shadowing and cumuly optical depth

Abstract Inhomogeneous cloudlets–gas mixtures, such as radiatively driven clumpy outflows, can be treated by clumpy-gas radiation hydrodynamics (CRHD), where a lot of clumps/cloudlets coexist with the tenuous ambient gas. In the cloudlets–gas two-component fluids, the radiation-received efficiency for cloudlets is smaller than that for the ambient gas, and cloudlets are generally less accelerated in winds/outflows. In the original formulation of CRHD, the cross-sectional area and/or the number density of cloudlets are implicitly assumed to be sufficiently small; in other words the cloudlet fluid is supposed to be “optically thin.” When the product of the cross-sectional area and the number density increases (i.e., the “optical depth” of the cloudlet fluid becomes large), the cloudlet fluid starts to shield the radiative flux, and self-shadowing takes place. Due to this self-shadowing, the radiative flux decreases exponentially in the “optically thick” cloudlet fluid. The essential roles of self-shadowing are reducing wind velocity, extinction of the central luminosity, and failure of the flow, in some cases. Self-shadowing may be significant when the mass-loss rate of cloudlets is sufficiently large and the flow is so dynamic that multiple scattering between cloudlets can be ignored. We introduce and define the “cumuly” optical depth for piled cloudlets, and find that inhomogeneity reduces the system optical depth like rainy days. In addition to other related topics, the Eddington luminosity of cloudlets–gas mixtures is redefined.