Erik Rosolowsky edited subsection_Systematic_Effects_The_above__.tex  about 8 years ago

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The above analysis points to a good connection between cluster mass and cloud mass in M83. However, two systematic effects can potentially alter these results. Here we review the nature of the ALMA data and the effects of the cataloging algorithm to assess the nature of these uncertainties.  {\it Data Quality} -- The quality of ALMA data vastly exceeds nearly every other previous study of extragalactic molecular clouds, and the sensitivity and resolution of this study are excellent compared to the preceding work that frames this study. However, these results only use data drawn from the 12-m dishes on ALMA. As such, they are affected by spatial filtering of emission. The comparison of the surface density profiles to those of \citep{Lundgren_2004a} highlights that ALMA recovers between 50\% and 100\% at every radius. Futhermore, the data cube shows negative sidelobes around some of the bright sources, particularly in the center of the galaxy. Such effects are typical of in  extragalactic studies \citep{Rosolowsky_2006} \citep{Rosolowsky_2006}. However, this filtering is most likely filtering out a diffuse CO(1-0) emission component, highlighting the bright, compact structures in the data, namely the molecular clouds. Such an effect was seen in M51 where the interferometer data provided a good measurement of the GMC properties and most the filtered emission was associated with a diffuse, high-line-width emission component \cite{Pety_2013} and not molecular clouds. The excellent agreement of the cloud properties seen here with previous studies suggests that the analysis is doing an adequate job of recovering cloud properties. The maximum recovered scale for these data should be $\sim 10\times$ the beam scale or 200 pc, and the velocity gradient of the galaxy keeps emission in each channel confined spatially. Thus, we should get a relatively good measurement of cloud properties, of quality comparable to but exceeding previous work.  {\it Cloud Decomposition} -- The major systematic uncertainty in the analysis is the cloud decomposition algorithm. CPROPS is designed to provide a stable decomposition of ISM structure in the low signal-to-noise case, including the effects of interferometers. However, the algorithm does not have a large dynamic range in the scales of objects that it recovers. We have set the parameters to stabilize the cloud recovery on scales comparable to the prior cloud structures expected from Milky Way studies. Since the algorithm attempts to assign all emission in the data cube to molecular clouds that are well separated, the analysis will tend to join low mass clouds to neighboring high mass clouds. The combined object will be seen as a single, high-mass object. However, if the underlying mass distribution is steep (say a power law distribution with $\beta \sim -2$ and cloud are drawn randomly from the mass distribution, the high mass cloud will tend to be significantly more massive than the low mass cloud. The effect of such combination is to remove clouds from the low mass portion of the mass spectrum and add them to the high mass clouds. This will make the mass distribution appear artificially shallow at the low mass end. However, correctly separating the low mass clouds from their high mass neighbors would create an even sharper truncation in the distribution and it is unlikely to move significantly in value. However, higher resolution and sensitivity observations may serve to better constrain the index of the mass distribution below $M_{c,\mathrm{GMC}}$.   The blending effects will be particularly acute in the galaxy center where the separation between the clouds is comparable to the cloud size. We should therefore regard the clouds in the $R_g<0.45$~kpc bin as particularly suspect and not necessarily representing distinct physical entities. The average characteristics of the ISM in this area are still a useful measure of the changing internal conditions of the clouds. Thus, the mass distribution is suspect, but the ISM clearly has higher turbulent velocity dispersions, average densities, but not significantly different degrees of gravitational binding. However, in the outer disk of the galaxy, the clouds should be well separated and the mass distributions are closer to the true distributions. It is in this outer region where we can make a clearer association between the cloud masses and cluster masses, finding a link consistent with theoretical expectations.