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Christopher edited Temperature [1].tex
almost 10 years ago
Commit id: 2f868fb9b19c8d0ac990dbf9be7030824282e315
deletions | additions
diff --git a/Temperature [1].tex b/Temperature [1].tex
index 5eadea5..369513f 100644
--- a/Temperature [1].tex
+++ b/Temperature [1].tex
...
\begin{equation} %\label{eqn:F(T_ex)}
F(T_{ex}) = 2.31 * 10^{14} \frac{T_{ex} + 0.92}{1 - e^{-5.53/t_{ex}}} \frac{1}{J(T_{ex}) - J(T_{bg})}
\end{equation}
and
assuming that the gas is a black body
\begin{equation} %\label{eqn:rayleigh jean}
T_B = \frac{B_v c^2}{2 v^2 k T}
\end{equation}
...
\begin{equation} %\label{eqn:J(T)}
J(T) = \frac{hv}{k(e ^ {\frac{hv}{kT}} - 1)}
\end{equation}
$M$ is the mass, $[{\rm H}_2/^{12}{\rm CO}]$ the mass ratio between $H_2$ and $^{12}CO$ (assumed to be $1/(8.6 * 10 ^{-5})$, $\mu_m$ the mean molecular mass of $H_2$, $A$ the area of emission (1 pixel), $T_{ex}$ the assumed temperature of excitation, $T_{bg}$ the background temperature (assumed to be 0K), $T_B$ the brightness
temperature(???), temperature, $\Delta v$ the velocity
resolution. resolution, k the Boltzman constant, $v$ the frequency of observation (115.3Ghz for $^{12}CO$, 110.2Ghz for $^{13}CO$).
(Bourke et al. 1997)
{\bf Every symbol here must be defined. What is v, what is alpha, A, etc? Explain it to yourself a year ago. If that you wouldn't understand, the reader probably won't either. State what this equation assumes. Also how do you get $T_B$ from the datacube I gave you? Give the equation you use. }