While researching rotation curves, I've noticed a variety of velocity behaviors in different galaxies. In some, the velocity decreases, in others, it remains relatively constant, and in some cases, it increases, particularly in the outer regions. Is there a mathematical equation or method to objectively determine these patterns rather than relying on visual inspection?
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$\begingroup$ You could make up a formula and fit its parameters. Then you'd have to subjectively interpret the parameters. What would you learn? $\endgroup$– John DotyCommented Oct 29, 2023 at 11:17
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The nature of galactic rotation curves largely depends on the density and velocity distribution of the invisible dark matter medium.
There are theoretical approaches that you can use to infer the density and velocity distribution of the (particle-like) dark matter (e.g., see section 1.1-1.2 here), but they have shortcomings.
N-body simulations help to fix some of these issues, e.g., the NFW profile (see section 1.3 here), but again, the net dynamic would depend on the formation and evolution history, something that might vary from galaxy to galaxy.
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$\begingroup$ I'm uncertain if my question has been properly understood. To provide more context, I have two rotation curve graphs. One of them exhibits a faster decline in the outer region compared to the other. While I can visually observe this difference, I'm inquiring if there exists an equation or method to empirically demonstrate this variation. $\endgroup$– mahsumCommented Oct 29, 2023 at 10:34
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$\begingroup$ What we unanimously see is flattening of the rotation curves but as I said above the net dark matter dynamic of the galaxy would depend on the formation and evolution history, something that might vary from galaxy to galaxy. Hence the rotation curves would also appear different. $\endgroup$– S.GCommented Oct 29, 2023 at 11:20