deletions | additions       diff --git a/spinning followup.tex b/spinning followup.tex  index fb4886e..06bc03d 100644  --- a/spinning followup.tex  +++ b/spinning followup.tex 
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The simulated population of BNS systems contains slowly spinning NSs, with masses between $1.2~\mathrm{M}_\odot$ and $1.6~\mathrm{M}_\odot$ and spin magnitudes $\chi < 0.05$. This choice was motivated by the characteristics of NSs found thus far in Galactic BNS systems expected to merge within a Hubble time through GW emission. However, neutron stars \emph{outside} of BNS systems have been observed with spins as high as $\chi = 0.4$ \citep{Hessels_2006,Brown_2012}, and depending on the neutron-star equation of state (EOS) could theoretically have spins as high as $\chi \lesssim 0.7$ \citep{Lo_2011} without breaking up. For these reasons, the prior assumptions used for Bayesian inference of source parameters are more broad than the spin range of the simulated source population.  To simulate a real analysis scenario where the class of compact binary and the NS EOS are not known, we use uniform priors in component masses between $0.6~\mathrm{M}_\odot$ and $5.0~\mathrm{M}_\odot$ to avoid any prior constraints on mass posteriors, and our standard black hole spin prior: uniform in spin magnitudes $\chi_{1,\,2} \sim U(0, 1)$ and isotropic in spin orientation. Prior distributions for the location and orientation of the binary match that of the simulated population, i.e.\ isotropically oriented and uniform in volume (out to a maximum distance of $218.9~\mathrm{Mpc}$, safely outside the detection horizon, which is $\sim137~\mathrm{Mpc}$ for a $1.6~\mathrm{M}_\odot$--$1.6~\mathrm{M}_\odot$ binary).\footnote{The mean (median) true distance for the set of $250$ events is $52.1~\mathrm{Mpc}$ ($47.8~\mathrm{Mpc}$), and the maximum is $124.8~\mathrm{Mpc}$.} Choosing any particular upper bound for spin magnitude would require either assuming hard constraints on NS spin-up, which are based upon observations with hard-to-quantify selection effects, or making assumptions regarding the unknown EOS of NSs. For these reasons we choose not to rule out compact objects with high spin a priori by using an upper limit of $\chi < 1$, encompassing all allowed NS and black hole (BH) BH  spins. In section \ref{subsec:prior_constraints} we look at more constraining spin priors, and particularly how such choices can affect mass estimates. We describe parameter-estimation accuracy using several different quantities, depending upon the parameter of interest.  \begin{itemize} 
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\end{itemize}    To check that differences between our spinning and non-spinning analyses were a consequence of the inclusion of spin and not because of a difference between waveform approximants, we also ran SpinTaylorT4 analyses with spins fixed to $\chi_{1,~2}=0$. There were no significant differences in parameter estimation between the non-spinning TaylorF2 and zero-spin SpinTaylorT4 results for any of the quantities we examined.\footnote{Using as an example the chirp mass, the most precisely inferred parameter, we can compare the effects of switch from a non-spinning to a spinning analysis to those from switching waveform approximants by comparing the difference the posterior means $\langle \mathcal{M}_\mathrm{c}\rangle$. The difference between means from the SpinTaylorT4 analyses with and without spin, is an order of magnitude greater than the difference between the zero-spin SpinTaylorT4 and TaylorF2 analyses: defining the log-ratio $\xi = \log_{10}(|\langle \mathcal{M}_\mathrm{c}\rangle^\mathrm{S} - \mathcal{M}_\mathrm{c}\rangle^0|/|\langle \mathcal{M}_\mathrm{c}\rangle^\mathrm{NS} - \mathcal{M}_\mathrm{c}\rangle^0|)$, where the superscripts $\mathrm{S}$, $0$ and $\mathrm{NS}$ indicates results of the fully spinning SpinTaylorT4, the zero-spin SpinTaylorT4 and the non-spinning TaylorF2 analyses respectively, the mean (median) value of $\xi$ is $0.90$ ($1.03$), and $92.8\%$ of events have $\xi > 0$ (indicating that the shift in the mean from introducing spin is larger than the shift from switching approximants).} Therefore, we only use the TaylorF2 results to illustrate the effects of neglecting spin.