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The contribution of a differential surface element to the flux is d F (u) = I (u)u dudp (3.2.25)

with the intensity distribution (here, for the linear limb-darkening law)

I(u) = D(u,)I0 = (1 - x + x cos y)I0, I0 = 1, (3.2.26)

where I0 is the normal emergent intensity; for spherical stars this is the normal emergent intensity at disk center. Observing the (spherical star) relation u sin y = —,

the differential du and r can be eliminated using du = R cos ydy. (3.2.28)

It then follows that r2n rn/2 2

F = / dF(y, <), dF(y, <) := DA cos yI0R sin y cos ydyd<,

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