Analysis

\label{sec:cprops}

GMC properties

We characterize the properties of the extracted clouds in the CO data to assess whether we are identifying clouds that can be compared to GMCs seen in the Milky Way, or whether the emission structures in the M83 data are better described as Giant Molecular Associations (GMAs), which are larger scale structures of molecular gas \cite{Rand_1990}.

We identify molecular clouds in the the CO emission line data using the cprops algorithm \citep{Rosolowsky_2006}¹. We utilize their recommended algorithm for identifying GMCs in interferometer data described as follows. The algorithm first calculates a spatially and varying estimate of the noise in the map by calculating the rms (\(\sigma(\alpha,\delta)\)) of signal-free channels. Emission is then identified as those pixels in the (three-dimensional) data cube that are larger than \(4\sigma(\alpha,\delta)\) in two adjacent velocity channels. This emission mask is then extended to include all connected pixels which are larger than \(2\sigma(\alpha,\delta)\) in three adjacent channels. We test the masking algorithm by applying it to the negative data and we find no false positives are included, so the masking criteria are likely robust.

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. 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: \[M_{\mathrm{lum}} = \alpha_{\mathrm{CO}} L_{\mathrm{CO}},\] 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 \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.

We only include clouds in our final analysis with \(M>3\times 10^{5}~M_{\odot}\), corresponding formally to a \(50\sigma\) aggregate detection of a molecular cloud. This is a factor of \(\sim 8\) larger than the minimum mass that would be admitted by our masking procedure, but represents a conservative treatment of the spatial filtering artifacts in the center of the galaxy, which makes cloud identification less certain.