# Total scattered flux and polarization for a ring of dust particles close to a star

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, Lyapunov

• Yes, please give your equation. Commented Mar 18, 2022 at 16:58
• @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 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
Commented Mar 18, 2022 at 22:10