Changes between Version 11 and Version 12 of u/erica/scratch3


Ignore:
Timestamp:
04/03/16 16:10:51 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/scratch3

    v11 v12  
    8787From this equation, it is clear that h is the scale-height. Thus, by writing R as:
    8888
    89 [[latex($R \approx |-\frac{\tau_R}{h \rho}| \approx \frac{\tau_R}{h \rho}$)]]
     89[[latex($R \approx |-\frac{1}{h \kappa_R\rho}| \approx \frac{1}{h \kappa_R\rho}$)]]
    9090
    9191we can set h to be the distance between the sink and box side (h=L), and imagine it as the scale height for the radiation.
     
    9595[[latex($\kappa_R=0.23~\frac{cm^2}{g}$)]]
    9696
    97 for 10 K gas.
     97for 10 K gas. Recall that opacity ([[latex($\kappa$)]]) is related to the absorption coefficient ([[latex($\alpha$)]]) by,
     98
     99[[latex($\kappa \rho=\alpha (cm^{-1})$)]]
     100
     101(where the absorption coefficient reduces the intensity of the ray by [[latex($dI_\nu=-\alpha_\nu I_\nu ds$)]])
    98102
    99103This implies that the optical depth is,
     
    101105[[latex($\tau_R\approx4.3~\frac{g}{cm^2}$)]]
    102106
     107
     108Recall that optical depth, opacity, and mean free path are related by,
     109
     110[[latex($$)]]