this is for holding javascript data
Joseph Nofech edited Text_Here__.tex
almost 8 years ago
Commit id: 9ea511884f0dc03684e3b04570eaedadffc96c50
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Text Here \usepackage{fixltx2e}
The Structure Function describes the average of the square of the difference in intensity between the light received from one position (from a source moving at a certain speed toward or away from the observer) and light received from another position (from a source that may be moving at a different speed).\\
For a slightly less ugly description, the Structure Function is as follows:\\
\begin{flushleft}
\begin{align*}
S_2 &= \left< \left[ I(\vec{r},v) - I(\vec{r}+\delta \vec{r},v+\delta v) \right]^2 \right>\\
&= S_{2(signal)} + S_{2(noise)}
\end{align*}
\end{flushleft}
where "$I$" refers to the intensity of light received from $^{13}$CO $(___???___)$ emissions, "$\vec r$" refers to the position of the source, and "$v$" refers to the radial velocity at which the source is moving.\\ \\
What we care about is the $S_{2(signal)}$. This is found simply by calculating $S_2$ from noise only, and subtracting it from $S_2$ overall.\\
The above image displays (from left to right) the $T_{max}$ map of the region of M33 that we're looking at (at speeds from $______$ to $______$), a 2D map of $S_{2(signal)}$ where $\delta v=0$, and a 1D plot of azimuthally-averaged $S_{2(signal)}$ versus radius (for various values of $\delta v$).
