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\subsection{Prior Constraints on Spin}  \label{subsec:prior_constraints}  Since spin is largely degenerate with mass ratio, and spin is expected to be small for BNS sources, it is interesting to ask how the mass constraints are affected by making stronger prior assumptions about the spin of NSs. First, we make the extreme assumption that NSs have negligible spin, as was done in \citet{Singer_2014} and \citet{Berry_2014}. Figure \ref{fig:mass_std} compares the distribution of (fractional) uncertainties in chirp-mass, mass-ratio and total-mass estimates for the spinning and non-spinning analyses. For the non-spinning analysis, the mean (median) fractional uncertainties in chirp mass, mass ratio and total mass are $0.0185\%$ ($0.0165\%$), $8.90\%$ ($8.79\%$) and $0.542\%$ ($0.491\%$) respectively,both  being a factor of $\sim3$--$4$ smaller than the uncertainties from a spinning analysis in the case of $\mathcal{M}_\mathrm{c}$ and $q$, and about an order of magnitude smaller for the total mass.