<p>When adding a term to E-B approx it should lead to this for the astronomical flux.
<span class="math-container">$\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)+\frac{5}{18}\frac{d^2S}{d\tau ^2}_{\tau =\frac{2}{3}}$</span></p>
<p>S is the source function, tau is the optical density, F is the astronomical flux</p>
<p>usually the E-B approx is just <span class="math-container">$\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)$</span> now we want the second term also.</p>
<p>I don't know how to start or get here...</p>

CC BY-SA 4.0
2024-02-12T06:57:59.117Z
Only someone steeped in the subject would stand any chance of understanding this question. Could you give a bit of context and explain all the symbols?
ProfRob
CC BY-SA 4.0
2024-02-12T09:01:11.347Z
https://arxiv.org/abs/1711.07026 might be helpful
planetmaker
CC BY-SA 4.0
2024-02-12T11:42:55.810Z
And there is another completely different derivation: https://adsabs.harvard.edu/full/1965ZA.....61..237D (paper in German, but possibly one can follow its detailed mathematical derivation even without command of the language)
planetmaker
CC BY-SA 4.0
2024-02-12T19:47:33.653Z
Thank you for these
user54705
CC BY-SA 4.0
2024-02-13T14:50:03.793Z
Looks like a Taylor expansion around a minimum at $\tau = 2/3$.
ProfRob
<flux><radiative-transfer>
Eddington-Barbier approximation next term for flux
user54705
# Eddington-Barbier approximation next term for flux

(Asked by: username_0 on 2024-02-11)

When adding a term to E-B approx it should lead to this for the astronomical flux.
$\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)+\frac{5}{18}\frac{d^2S}{d\tau ^2}\_{\tau =\frac{2}{3}}$

S is the source function, tau is the optical density, F is the astronomical flux

usually the E-B approx is just $\frac{F}{\pi }\approx S\left(\tau =\frac{2}{3}\right)$ now we want the second term also.

I don't know how to start or get here...

**Tags:** flux, radiative-transfer

> **Comments:**
> **username_1**: Only someone steeped in the subject would stand any chance of understanding this question. Could you give a bit of context and explain all the symbols?  
> **username_2**: https://arxiv.org/abs/1711.07026 might be helpful  
> **username_2**: And there is another completely different derivation: https://adsabs.harvard.edu/full/1965ZA.....61..237D (paper in German, but possibly one can follow its detailed mathematical derivation even without command of the language)  
> **username_0**: Thank you for these  
> **username_1**: Looks like a Taylor expansion around a minimum at $\tau = 2/3$.  

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## 0 answers

