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fix kappa render
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arjunsavel committed Jul 25, 2024
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Expand Up @@ -109,7 +109,7 @@ depth, and $\alpha$ is the absorption coefficient. Setting $\tau = 1$, we have $
is the product of the opacity and the density of the gas: $ds = \frac{1}{\kappa_\lambda \rho}$. Therefore,$ds = \frac{1}{\kappa_\lambda \rho}$.
The density of the gas $\rho$ is the pressure divided by the product of the temperature and the gas constant:
$\rho = \frac{P}{k_B T \mu}$ for mean molecular weight $\mu$. This leads to the final equation for the column length:
$ds = \frac{k_BT\mu}{P\kappa_\lambda}$. For CO, the mean molecular weight is 28.01 g/mol. Plugging in, we arrive at $ds \approx 10^{34}$m (roughly $10^{17}$ parsecs) for $kappa_\lambda = 10^{-33} cm^2/g$, which is equivalent to roughly a cross-section of
$ds = \frac{k_BT\mu}{P\kappa_\lambda}$. For CO, the mean molecular weight is 28.01 g/mol. Plugging in, we arrive at $ds \approx 10^{34}$m (roughly $10^{17}$ parsecs) for $\kappa_\lambda = 10^{-33}$ $\rm cm^2/g$, which is equivalent to roughly a cross-section of
$\sigma_\lambda = 10^{-60} m^2$.

![Top panel: The original opacity function of CO [@rothman:2010] (solid lines) and its `cortecs` reconstruction (transparent lines) over a large
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