Stella Offner edited Temperature [1].tex  almost 10 years ago

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\subsection{Derivation of Mass, Momentum and Energy}  We used the following formulae to determine the mass of the outflow. outflow:  \begin{equation} %\label{eqn:Mass from temp}  M(v, \alpha, \delta) = [{\rm H}_2/^{12}{\rm CO}] \mu_m A(\alpha, \delta) F (T_{ex}) T_B(v, \alpha, \delta) \delta),  \Delta v \end{equation}  Where where  \begin{equation} %\label{eqn:F(T_ex)}  F(T_{ex}) = 2.31 x 10^{14} \frac{T_{ex} + 0.92}{1 - e^{-5.53/t_{ex}}} \frac{1}{J(T_{ex}) - J(T_{bg})}  \end{equation}  and   \begin{equation} %\label{eqn:J(T)}  J(T) = \frac{hv}{k(e ^ {\frac{hv}{kT}} - 1)}  \end{equation}  (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. }  {\bf need to add a couple sentences on how you derive the momentum and energy: To "To  obtain the momentum...} momentum..."}  {\bf Before discussing excitation temperature, need a general paragraph on the basic trends, i.e. what does the raw simulation show, what are the general trends with time.} time. I can write this if you want.}  \section{Results} 

{\bf Figure \ref{texcit} illustrates the impact of the assumed excitation temperature on the mass estimate.} We found that there was a systematic bias to overestimate the mass of the outflow. We attribute this to errors in assuming a single temperature of excitation. We examined the simulation data and found that there was significant temperature variation in the data cube and slight temperature variation over time. We followed the same protocol as observers and assumed a single temperature of excitation for each image. However we used a different temperature for each time. These temperatures are shown in Table \ref{tab_texcit}.  {\bf See how I added the table number and caption below. Do this for the other tables. Also explain how you get this temperature. I think you did:}  \begin{equation}  \bar T = \frac{ \Sigma \rho_i T_i } \frac{\Sigma \rho_i}  \end{equation}  {\bf update accordingly.}  \begin{center}  \begin{tabular}{c | c}  \tablecaption{Average Temperature \label{tab_texcit}}