deletions | additions       diff --git a/section_Analysis_label_sec_cprops__.tex b/section_Analysis_label_sec_cprops__.tex  index cc5e07b..ceb0b34 100644  --- a/section_Analysis_label_sec_cprops__.tex  +++ b/section_Analysis_label_sec_cprops__.tex 
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The masked emission is then divided into individual molecular clouds using a seeded watershed algorithm, with individual clouds being defined by local maxima that are separated by at least 15 pc spatially or 2.6 km~s$^{-1}$ in velocity. Any pair of local maxima in the same contiguous region of the mask are also required to be at least $2\sigma(\alpha,\delta)$ above the saddle point of emission connecting those maxima. This cloud extract identifies 394 clouds across the face of the galaxy.  We determine the macroscopic properties of the GMCs in the system by calculating moments of the emission line data. To account for emission below the edge of the emission mask, the values of the moments are extrapolated as a function of pixel value to the 0 K brightness threshold (see Rosolowsky \& Leroy 2006) for details. threshold.  This extrapolation is necessary to avoid bias in low signal-to-noise data, but it can introduce substantial uncertainty (up to 50\% for clouds near the signal-to-noise cut). We calculate the CO luminosity of the molecular clouds ($L_{\mathrm{CO}}$) by integrating the emission associated with each cloud, with a quadratic extrapolation. The luminous mass is calculated by scaling by a single CO-to-H$_2$ conversion factor: \begin{equation}  M_{\mathrm{lum}} = \alpha_{\mathrm{CO}} L_{\mathrm{CO}},  \end{equation}  where $\alpha_{\mathrm{CO}}=4.35 M_{\odot}\mbox{ pc}^{-2}~\mathrm{(K~km~s^{-1})^{-1}}$. The velocity dispersion is the linearly-extrapolated, emission-weighted second moment of the velocity axis, corrected for the channel width. Similarly radius of the cloud is the root-mean-square of the linearly-extrapolated, emission-weighted second moments of the major and minor spatial axis of the emission. The radius is also corrected for the instrumental response by assuming an elliptical beam and subtracting its width in quadrature. See Rosolowsky \& Leroy (2006) \citet{Rosolowsky_2006}  for details. The algorithm corrects for the case where the beam and cloud position angles are not aligned. The virial mass of the cloud is calculated from the radius and line width of the molecular cloud: $M_{\mathrm{vir}} = 5 \sigma^2 R/G$. Comparing the virial and luminous masses gives insight to the dynamical nature of the molecular clouds identified in the data. The average surface density is calculated from the luminous mass $\Sigma = M_{\mathrm{lum}}/(\pi R^2)$. Typical uncertainties are 0.2 dex in the velocity dispersion and line width and 0.3 dex in the mass estimates (both virial and luminous), though these errors grow when the signal to noise approaches the $4\sigma$ threshold.