Pamela Freeman edited untitled.tex  about 8 years ago

Commit id: 34d058a013b411362398b46e20ea00a757afd1be

deletions | additions      

       

Analysis  We examined the GMC properties as in Solomon et al. (1987). M83 clouds exhibit similar relationships for velocity line width to radius, which confirms our assumption of the clouds being in virial equilibrium. As well, the virial mass to luminous mass and luminous mass to radius relationships are also consistent with previous findings. We then binned the clouds by equal surface area on the disk as in Adamo et al. (2015), and for each bin examined the cumulative mass function:  \begin{center} $N(>M)=\int^\infty_M \frac{dN}{dM}dM=\frac{\beta M_\odot}{\alpha+1}\left(\frac{M}{M_\odot}\right)^\alpha=\frac{N_max}{M_max}\left[\left(\frac{M}{M_max}\right)^{\alpha+1}-1\right]$ \end{center}  where N(>M) is the number of clouds above a certain mass M, β is a normalization constant and α is the index. The latter expression represents the truncated power law case where Mmax is the maximum mass we are looking for. Using the ‘powerlaw’ package in Python, each bin was fitted by two distributions: an ordinary power law and a truncated power law (example in Figure 1). The distributions were constrained by a minimum mass of 2496477 M_⨀ above which there is a stable fit for the whole galaxy. ‘Powerlaw’ also returned the index α for the power law that best described the data.  The nuclear clouds (0-0.45 kpc) are the only bin well represented by a truncated power law. Adamo et al. (2015) excluded this inner bin due to the high luminosity gradient and the more active star formation. The stellar clusters, in contrast, are well described by a truncation for the three outer bins [2]. The indices found for the GMCs are along the same magnitude as those found for GMCs in other nearby galaxies, but in relation to the stellar clusters in M83 the indices are larger and do not consistently increase outwards (Table 1) [1].  Table 1. The indices alpha for the fitted mass distributions of giant molecular clouds and stellar clusters (from Adamo et al. 2015) in different bins.  \begin{table}   \begin{tabular}{ c c c c c c }  Bin (kpc)      GMC index      Stellar cluster  index          0-0.45      -1.856      N/A          0.45-2.3      -2.695      -1.90          2.3-3.2      -3.294      -2.20          3.2-3.9      -2.839      -2.20          3.9-4.5      -2.708      -2.70 & Bin (kpc) & GMC index & Stellar cluster  index & 0-0.45 & -1.856 & N/A & 0.45-2.3 & -2.695 & -1.90 & 2.3-3.2 & -3.294 & -2.20 & 3.2-3.9 & -2.839 & -2.20 & 3.9-4.5 & -2.708 & -2.70 & & \\   Bin (kpc) & GMC index & Stellar cluster  index \\   0-0.45 & -1.856 & N/A \\   0.45-2.3 & -2.695 & -1.90 \\   2.3-3.2 & -3.294 & -2.20 \\   3.2-3.9 & -2.839 & -2.20 \\   3.9-4.5 & -2.708 & -2.70 \\   & & \\   & & \\   & & \\   & & \\   & & \\   \end{tabular}   \end{table}  [1] Y. Fukui, and A. Kawamura. Annu. Rev. Astro. Astro. 48, 547-580 (2010).  [2] A. Adamo, J.M.D. Kruijssen, N. Bastian, E. Silva-Villa, and J. Ryon. MNRAS, 452,   246-260 (2015).  [3] P.M. Solomon, A.R. Rivolo, J. Barrett, and A. Yahil. ApJ, 319, 730-741 (1987).