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I'm still new to gravitational lensing, and I've been trying to read a paper that has to do with calculating the week lensing signal of galaxy-galaxy interactions in a sample of galaxies. I understand the equations so far and that the signal is defined by the excess projected surface density $\Delta \Sigma = \Sigma(<r) - \Sigma(r)$, where $r$ is a chosen radius. Then the sample is divided into radial bins of logarithmically increasing $r$, then $\Delta \Sigma$ or $r.\Delta \Sigma$ are plotted versus $r$.

However, I don't really understand the resulting plots where $\Delta \Sigma$ is decreasing, or the variation of $r.\Delta \Sigma$ with $r$.

Any help would be appreciated.

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    $\begingroup$ Hi, welcome! To assist people here, please include a reference to the paper(s) you mention, preferably with a link that lets us download or read the document. Failing that, at least post images of the graphs that are causing you trouble. $\endgroup$ – Carl Witthoft Jun 28 at 14:56

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