In this relation, 0O = j>(v=v0) is determined by the requirement that the profile be normalized to unity:

Our solution to equation (6.18) will assume, for simplicity, that all quantities are spatially constant. We obtain J by starting with the exact solution of the radiative transfer equation for Iv (Appendix C). We then evaluate the specific intensity at the center of the sphere in Figure 6.4. Equations (C.3) and (C.8) together imply

Here we have set the optical thickness avAs in equation (B.3) equal to Arv/2 and have again applied the Rayleigh-Jeans approximation. Since Iv at the center is isotropic, Jv = Iv. To obtain J , we use Equations (6.19) and (6.20). Writing Atu in (6.21) as At0v)/$Q, we find

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