Ben Farr edited results.tex  almost 9 years ago

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\subsection{Mass Estimates}\label{sec:mass}  To maximize sampling efficiency, model parameterizations are chosen to minimize degeneracies between parameters. To leading order, the post-Newtonian expansion of the waveform's phase evolution depends on the \emph{chirp mass}, $\mathcal{M}_\mathrm{c} = (m_1 m_2)^{3/5} (m_1 + m_2)^{-1/5}$, making it a \emph{very} well constrained parameterization of binary mass. The second mass parameter used is the mass ratio $q = m_2/m_1$, where $0 < q \leq 1$. Detectors are much less sensitive to the mass ratio, and strong degeneracies with spin make constraints on $q$ even worse \citep{Cutler_1994}. It is primarily the uncertainty in $q$ that governs the uncertainty in component masses $m_1$ and $m_2$.  Figure \ref{fig:mass_pdfs} shows the superimposed, one-dimensional marginal posterior PDFs and cumulative density functions (CDFs) for the chirp mass (centered on each mean) and mass ratio for all $250$ events. Also shown are As a representation of a typical event's posterior distribution, we show  the average  PDFs and CDFs averaged CDFs, where the average is taken  over all $250$posteriors, representing a typical event's  posterior distributions. PDFs and CDFs at each point.  Chirp-mass distributions are usually well approximated by normal distributions about the mean, while mass ratio estimates have broad support across most of the prior range. To trace individual parameter uncertainties across the population we use the fractional uncertainties $\sigma_{\{\mathcal{M}_\mathrm{c},\,q\}}/\{\langle\mathcal{M}_\mathrm{c}\rangle,~\langle q\rangle\}$, where $\sigma_x$ and $\langle x\rangle$ are the standard deviation and mean of the distributions respectively. The mean (median) fractional uncertainties in chirp mass and mass ratio for the simulated population are $0.0675\%$ ($0.0640\%$) and $28.7\%$ ($28.4\%$).