<p>I have an important problem and maybe some of you can help me with the following question:</p>
<p>I have a mathematical expression for the total scattered flux in Jansky and the total linear polarized flux (also in Jansky) for one dust particle that is around 0.1 astronomical units away from the star. How can I extend this equation to a circle of 360 particles so I get a ring around the star, where each dust particle is located at one degree around the star?</p>
<p>The equation for the total scattered flux is:
<span class="math-container">$F_{\text{sca}}=L_{*}(\lambda)\cdot\pi\cdot Q_{\text{sca}}(a)\cdot \frac{\pi\cdot a^2}{4\cdot \pi \cdot r^2}\cdot \frac{S_{11}}{d^2 \cdot \frac{4\cdot \pi^2\cdot C_{\text{sca}}}{\lambda^2} }$</span></p>
<p>The equation for the total scattered linear polarized flux is:</p>
<p><span class="math-container">$F_{\text{polarized}}=L_{*}(\lambda)\cdot\pi\cdot Q_{\text{sca}}(a)\cdot \frac{\pi\cdot a^2}{4\cdot \pi \cdot r^2}\cdot \frac{S_{12}}{d^2 \cdot \frac{4\cdot \pi^2\cdot C_{\text{sca}}}{\lambda^2} }$</span></p>
<p>With <span class="math-container">$L_{*}(\lambda)$</span> as the luminosity of the star, <span class="math-container">$Q_{\text{sca}}$</span> is the scattering efficiency, <span class="math-container">$C_{\text{sca}}$</span> is the scattering cross section , <span class="math-container">$a$</span> is the radius of the dust particle, <span class="math-container">$r$</span> is the distance from the dust to the star, <span class="math-container">$d$</span> is the distance from the star to the observer, <span class="math-container">$\lambda$</span> is the corresponding wavelength of the star and <span class="math-container">$S_{11}$</span> and <span class="math-container">$S_{12}$</span> are Müller Matrix elements for the corresponding scattering process.
I have all this parameters for a single dust grain and now my question is how to extend these equations on a ring of 360 dust particles around the star.</p>
<p>Best wishes, Lyapunov</p>

CC BY-SA 4.0
2022-03-18T16:58:11.337Z
Yes, please give your equation.
WarpPrime
CC BY-SA 4.0
2022-03-18T22:10:48.003Z
@Lyapunov *Welcome to Stack Exchange!* Please add as much information to your question as you can. Potential answer authors may hesitate to second guess your question only to find out later that what you need is something different. Add everything you can, starting with the expression itself. If you can't use [MathJax](https://math.meta.stackexchange.com/q/5020/284619) yet, at least add a screenshot of the equation *and a link to its original source* and someone can help you with the formatting.
uhoh
<mathematics><flux><particles><disk><polarization>
Total scattered flux and polarization for a ring of dust particles close to a star
Lyapunov
# Total scattered flux and polarization for a ring of dust particles close to a star

(Asked by: username_0 on 2022-03-18)

I have an important problem and maybe some of you can help me with the following question:

I have a mathematical expression for the total scattered flux in Jansky and the total linear polarized flux (also in Jansky) for one dust particle that is around 0.1 astronomical units away from the star. How can I extend this equation to a circle of 360 particles so I get a ring around the star, where each dust particle is located at one degree around the star?

The equation for the total scattered flux is:
$F\_{\text{sca}}=L\_{\*}(\lambda)\cdot\pi\cdot Q\_{\text{sca}}(a)\cdot \frac{\pi\cdot a^2}{4\cdot \pi \cdot r^2}\cdot \frac{S\_{11}}{d^2 \cdot \frac{4\cdot \pi^2\cdot C\_{\text{sca}}}{\lambda^2} }$

The equation for the total scattered linear polarized flux is:

$F\_{\text{polarized}}=L\_{\*}(\lambda)\cdot\pi\cdot Q\_{\text{sca}}(a)\cdot \frac{\pi\cdot a^2}{4\cdot \pi \cdot r^2}\cdot \frac{S\_{12}}{d^2 \cdot \frac{4\cdot \pi^2\cdot C\_{\text{sca}}}{\lambda^2} }$

With $L\_{\*}(\lambda)$ as the luminosity of the star, $Q\_{\text{sca}}$ is the scattering efficiency, $C\_{\text{sca}}$ is the scattering cross section , $a$ is the radius of the dust particle, $r$ is the distance from the dust to the star, $d$ is the distance from the star to the observer, $\lambda$ is the corresponding wavelength of the star and $S\_{11}$ and $S\_{12}$ are Müller Matrix elements for the corresponding scattering process.
I have all this parameters for a single dust grain and now my question is how to extend these equations on a ring of 360 dust particles around the star.

Best wishes, username_0

**Tags:** mathematics, flux, particles, disk, polarization

> **Comments:**
> **username_1**: Yes, please give your equation.  
> **username_2**: @username_0 *Welcome to Stack Exchange!* Please add as much information to your question as you can. Potential answer authors may hesitate to second guess your question only to find out later that what you need is something different. Add everything you can, starting with the expression itself. If you can't use [MathJax](https://math.meta.stackexchange.com/q/5020/284619) yet, at least add a screenshot of the equation *and a link to its original source* and someone can help you with the formatting.  

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## 0 answers

