The basic equation for gas which is affected by the radiation is as follows:
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![$\displaystyle \frac{d \rho}{d t}+\rho\mbox{\boldmath${\nabla\cdot v}$}=0,$](img1733.png) |
(D.1) |
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![$\displaystyle \rho\frac{d \mbox{\boldmath${v}$}}{d t}=\rho\nabla\phi - \nabla \psi + \frac{\chi_{F0}}{c}\mbox{\boldmath${F}$}_0,$](img1734.png) |
(D.2) |
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![$\displaystyle \rho\frac{d \epsilon}{d t}+p\mbox{\boldmath${\nabla\cdot v}$}=h_{\rm CR}\rho
+c\chi_{E0}E_0-4\pi \chi_{P0}B,$](img1735.png) |
(D.3) |
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![$\displaystyle \nabla^2\psi=4\pi G \rho,$](img1736.png) |
(D.4) |
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![$\displaystyle \epsilon = \frac{p}{(\gamma-1)\rho},$](img1737.png) |
(D.5) |
where
,
, and
are the absorption coefficient,
the cosmic-ray heating rate perunit mass, and teh Planck function
.
In equation (D.2), the term
represents
the acceleration of gas due to the photon pressure.
In equation (D.3),
,
and
represent, respectively the heating due to the CR particles,
heating due to the absorption of radiation and cooling die to the emission.
The frequence-integrated radiation energy density and radiation flux are defined as
![$\displaystyle E_0=\int_0^\infty d\nu_0\int d\Omega I(\nu,\mbox{\boldmath${n}$}),$](img1745.png) |
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(D.6) |
![$\displaystyle \mbox{\boldmath${F}$}_0=\int_0^\infty d\nu_0\int d\Omega I(\nu,\mbox{\boldmath${n}$})\mbox{\boldmath${n}$},$](img1746.png) |
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(D.7) |
where
denotes the specific intensity of radiation at frequency
along the direction vector
.
These equation could be solved if the the radiation transfer is solved.
The frequency-averaged absorption coefficients are defined as follows:
While the equation for the radiation transfer is basically as follows:
![\begin{displaymath}
\frac{1}{c}\frac{\partial I(\nu,\mbox{\boldmath${r}$},\mbox{...
...$},\mbox{\boldmath${n}$})-S(\nu,\mbox{\boldmath${r}$})\right],
\end{displaymath}](img1751.png) |
(D.11) |
where
represent the source term.
Kohji Tomisaka
2009-12-10