... | ... | @@ -62,8 +62,7 @@ $`\begin{array}{lll} |
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where $`Q^+`$ is the viscous heating and $Q^-$ is the radiative cooling.
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the stress tensor in the 2 dimensional case is:
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$`Q^+ = 2\Sigma \nu (D_{RR}^2+D_{\theta \theta}^2
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+{1\over 2}D_{R\theta}^2-
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$`Q^+ = 2\Sigma \nu (D_{RR}^2+D_{\theta \theta}^2+D_{R\theta}^2-
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{1\over 3}(\nabla \cdot \vec v)^2)`$
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in the hypothesis the the gas has only Keplerian speed (no radial velocity and
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... | ... | @@ -73,7 +72,6 @@ $`Q^+ = \Sigma \nu D_{R\theta}^2 = {9\over 8}\Sigma \nu \Omega_K^2`$ |
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this simple prescription can also be implemented in a 2 dimensional disk.
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If we assume that the disk's two surfaces can radiate as Plank functions with temperature $`T_{eff}`$ then the radiative cooling rate is: $`Q^-=2\sigma_{SB}T_{eff}^4`$
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If we assume that the disk's two surfaces can radiate as Plank functions with temperature $`T_{eff}`$ then the radiative cooling rate is: $`Q^-=2\sigma_{SB}T^4/\tau_{eff}`$
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where the effective temperature is $`T_{eff} = {T\over \tau_{eff}}`$
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with $\tau_{eff} = 0.5\Sigma k$ where $`k`$ is the disk opacity. |