deletions | additions       diff --git a/Consistent_with_the_discussion_above__.tex b/Consistent_with_the_discussion_above__.tex  deleted file mode 100644  index 7e813a8..0000000  --- a/Consistent_with_the_discussion_above__.tex  +++ /dev/null 
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Consistent with the discussion above, the figure indicates a bias to recover the deepest and widest profiles.  To relate the two-dimensional number density $n(\Gamma_{\rm act}, P_{\rm act})$ to $n(\Gamma_{\rm obs}, P_{\rm obs})$ in the case that $\Gamma_{\rm act}$ and $P_{\rm act}$ are uncoupled, we can break it into the product of two one-dimensional densities, i.e. $n(\Gamma_{\rm act}, P_{\rm act}) = n(\Gamma_{\rm act}) \times n(P_{\rm act})$ and perform the same integrations as in the previous sections over $\Gamma_{\rm act}$ and $P_{\rm act}$ separately. Then the product of the two integrals represents $n(\Gamma_{\rm obs}, P_{\rm obs})$. Figure \ref{fig:n-Pobs-Gammapobs_from_uniform_n-Pact-Gammapact} illustrates the resulting density contours (colored curves) and compares them to a Monte-Carlo simulation (circles) similar to that performed in Figure \ref{fig:n-Pobs_from_uniform_n-Pact}. The miss distance effect drives $\Gamma_{\rm obs}$- and $P_{\rm obs}$-values to the bottom right corner of the plot, consistent with the fact that more distant encounters are more frequent.  diff --git a/layout.md b/layout.md  index a522f76..ad7de6a 100644  --- a/layout.md  +++ b/layout.md 
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These_details_allow_us_to__.tex  Thus_begin_equation_label_eqn__.tex  In_the_next_section_we__.tex  Consistent_with_the_discussion_above__.tex  figures/n-Pobs-Gammapobs_from_uniform_n-Pact-Gammapact/n-Pobs-Gammapobs_from_uniform_n-Pact-Gammapact.png  The_results_presented_here_assume__.tex  section_Comparison_to_Observational_Data__.tex