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minor fixes to estimated Draine opacities.
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08-short-projects/project-3/project3_description_mcrt.md

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@@ -135,9 +135,9 @@ There is NO gradual energy loss - it's all or nothing! As $N \to \infty$, this s
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- **Dust density:** $\rho_{\text{dust}} = \rho_{\text{gas}} \times f_{D/G} = 3.84 \times 10^{-23}$ g/cm$^3$
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**Dust Model:** [Draine (2003a,b)](https://ui.adsabs.harvard.edu/abs/2003ApJ...598.1017D/abstract) Milky Way dust with $R_V = 5.5$
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**Dust Model:** [Draine (2003a,b)](https://ui.adsabs.harvard.edu/abs/2003ApJ...598.1017D/abstract) Milky Way dust with $R_V = 5.5$. All data here: <https://www.astro.princeton.edu/~draine/dust/dustmix.html>
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- Data file: [kext_albedo_WD_MW_5.5B_30](https://www.astro.princeton.edu/~draine/dust/extcurvs/kext_albedo_WD_MW_5.5B_30)
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- Data file: [kext_albedo_WD_MW_5.5A_30_D03](https://www.astro.princeton.edu/~draine/dust/extcurvs/kext_albedo_WD_MW_5.5A_30_D03.all)
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**Note on units:** Use CGS units as your default throughout this project.
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@@ -277,9 +277,9 @@ where $\Delta s$ is the distance to the next cell boundary or interaction point.
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| Band | $\langle\kappa\rangle$ (cm$^2$/g) | Why This Value? |
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|------|--------------------------------|-----------------|
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| B | 35,000-36,000 | Peak dust extinction near 220 nm |
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| V | 30,000-31,000 | Still strong extinction |
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| K | 3,400-3,500 | Wavelength $\gg$ grain size |
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| B | $\sim \times 10^4$ | Peak dust extinction near 220 nm |
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| V | $\sim 7.3 \times 10^3$ | Still strong extinction |
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| K | $\sim 1.5 \times 10^3$ | Wavelength $\gg$ grain size |
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These apply to dust mass, not gas mass!
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@@ -437,8 +437,8 @@ If your results seem wrong:
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Validate your opacity calculations from the Draine data:
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- X-axis: Wavelength (0.3-3 $\mu$m, log scale)
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- Y-axis: Mass absorption coefficient $\kappa$ (cm$^2$/g, log scale)
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- X-axis: Wavelength
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- Y-axis: Mass absorption coefficient $\kappa$
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- Show the Draine opacity curve for $R_V = 5.5$
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- Overlay vertical shaded bands for B, V, and K filters
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- Include points (`plt.scatter`) or horizontal lines (`plt.axhline`) showing calculated band-averaged opacities

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