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I understand that ellipticity is a very important concept in weak gravitational lensing because it describes the shape properties of the transformed galaxy. Shear, on the other hand, also describes the shape properties of the transformed galaxy. Since shear can also describe the shape properties of the transformed galaxy, I don't see why ellipticity is so important. It is not used to calculate shear. It is not used to figure out the matter power spectrum. I don't see why we want to measure ellipticity. I am confused.

Can anyone explain this for me? Thanks so much!

Gene
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    Welcome to Stack Exchange! For ellipticity or shear, does either one alone describe *some of the, or all of the* shape properties? What does "the shape properties" even mean? How many are they? What are they called? When premising a question it's best to cite, link to and quote the source the basis of the premise. – uhoh Feb 10 '24 at 07:35
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    Shear does not describe the "shape property" of a galaxy; it describes how the intrinsic shape is modified (or "transfomred"). You need to combine that with (some assumption about) the intrinsic ellipticity of the galaxy in order to end up with the observed ellipticity of the galaxy. – Peter Erwin Feb 10 '24 at 16:42
  • Thank you. I now understand. @PeterErwin – Gene Feb 12 '24 at 15:01

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