from an infinitesimally thin, filled, uniformly radiating surface centered on the black hole. For regions in the disk at distances much larger than the radius of the annulus, this leads to the following expression for the total flux incident on one surface of the disk: $$\label{fd}
     F_{\rm d}(R,t)=(1-A) {{L_X(t)}\over {4{\pi}R}}
             \cdot{d\over dR}\left[{{H(t)}\over R}\right]^2,$$ where $A$ is the X-ray albedo.

In practice, this irradiation is computed to arise from a disk with the radius of the inner zone and from a height above the disk plane equal to the disk height, $H$, of the innermost computed zone. The latter is a function of time and is used to compute the rays for direct irradiation of the outer disk.

Equation (\[fd\]) is equivalent to that adopted by King et al. (1997, see their equation 6). It is smaller by a factor of $H/R$ than the prescription used by van Paradijs (1996) for neutron-star systems. For simplicity, we take the X-ray albedo to be $A$= 0.5. De Jong et al. (1996) have deduced an albedo of $\sim$ 90 % for low-mass X-ray binaries, but the specific choice of the albedo does not appreciably affect the disk structure, since shadowing suppresses direct irradiation (see 