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Brian Jackson edited subsection_The_Gamma__rm_act__.tex
almost 9 years ago
Commit id: e49f1bdbdc330a37e927e273c5a0efa2b23a2aa6
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\subsection*{The $\Gamma_{\rm act}$ Recovery Bias and Distortion}
\label{sec:the_gammaact_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.
...
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).