Brian Jackson edited subsection_The_Gamma__rm_act__.tex  almost 9 years ago

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\subsection*{The $\Gamma_{\rm act}$ Recovery Bias and Distortion}  \label{sec:the_gammaact_recovery_bias_and_distortion}  Now turning to $\Gamma$-values, a bias similar to that above favors recovery of devils with larger $\Gamma_{\rm act}$-values, and by analogy, we can cast this recovery bias in terms of relative areas, suppressing the term involving pressure:  \begin{equation}  f_{P_{\rm act}} \equiv \left( \dfrac{\Gamma_{\rm act}}{\Gamma_{\rm max}} \right)^2. 

\begin{equation}\label{eqn:n-Gammaobs_from_uniform-n-Gammaact}  n(\Gamma_{\rm obs}) = 4k\ \Gamma_{\rm max}^{-2}\ \left( \Gamma_{\rm obs} - \Gamma_{\rm min} \right) \Gamma_{\rm obs}.  \end{equation}  Figure \ref{fig:n-Gammaobs_from_uniform-n-Gammaact} illustrates this result (using linear axes since the curves are not as steep as in the previous figures).