deletions | additions       diff --git a/usepackage_fixltx2e_As_a_brief__.tex b/usepackage_fixltx2e_As_a_brief__.tex  index 8655305..5162629 100644  --- a/usepackage_fixltx2e_As_a_brief__.tex  +++ b/usepackage_fixltx2e_As_a_brief__.tex 
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\end{align*}  \end{flushleft}  where "$I$" refers to the intensity of light received from 13CO $^{13}$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 M51 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 $\delta v$).