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Pamela Freeman added subsection_Mass_distributions_We_then__.tex
about 8 years ago
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\subsection{Mass distributions}
We then binned the clouds by equal surface area on the disk as in \citet{Adamo_2015}, and for each bin examined the cumulative mass function:
\begin{equation}
N(>M)=\int^\infty_M \frac{dN}{dM}dM
\end{equation}
The {\sc powerlaw} fit function is
\begin{equation}
\frac{dN}{dM} = M^{\alpha} \exp\left(-\frac{M}{M_c}\right)
\end{equation}
where $N(>M)$ is the number of clouds above a certain mass $M$, and $\alpha$ is the index. The latter expression represents the truncated power law case where $M_c$ 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 5). The distributions were constrained by a minimum mass of 3*10$^5$ M$_\odot$ 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.
