PX282 - C10a - radiative transfer equation

• combining all the sources of opacity:

where, ${\kappa }_{\lambda }={\kappa }_{b-b}+{\kappa }_{b-f}+{\kappa }_{f-f}+{\kappa }_{H^{-}}+{\kappa }_{e-s}$ factors in all the absorptions

defining the source function:

• therefore, the radiative transfer equation is:

• considering the balance between $I_{\lambda }$ and $S_{\lambda }$

  • if $I_{\lambda }>S_{\lambda }:\frac{d{I}_{\lambda }}{dz}<0$ , so, $I_{\lambda }$ decreases with $z$
  • if $I_{\lambda }<S_{\lambda }:\frac{d{I}_{\lambda }}{dz}>0$ , so, $I_{\lambda }$ increases with $z$

• thus, $I_{\lambda }$ converges to the source function

• the beam intensity approaches the local value of the source function ($S_{\lambda }$ may vary too quickly to reach)

• in $\tau$-space, the classic form of radiative transfer equation is obtained: