1) The specific intensity is defined from:
p( Fo ) = 2 p (I(cos (q))
And for q = p/4, then cos (p/4) = Ö2/2 and:
I = p( Fo ) / 2 p (Ö2/2) = p( Fo ) / p (Ö2)
Therefore:
I = (6.3 x 10 7 Jm-2 s-1) / p(Ö2)
I » 1.4 x 10 7 Jm-2 s-1
2) The effective temperature is obtained using:
p( Fo ) = s(Teff)4
So: Teff = [p( Fo ) / s] 1/4
Where s = 5.67 x 10-8 W m-2 K-4
Then:
Teff = [6.3 x 10 7 Jm-2 s-1/ 5.67 x 10-8 W m-2 K-4] 1/4
Teff » 5800 K
The boundary temperature is found from:
Teff = (2)1/4 To = 1.189 To
Or: To = Teff /1.189 = 5800K/ 1.189 » 4800 K
The boundary temperature differs because of being referenced to a different optical depth. The boundary temperature (To) approaches the value of the effective (or surface) temperature when t = 0, but this still exhibits a difference in layers so will not be exactly the same!
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