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I was reading an article in which it said that mostly ring galaxies are present in the ‘field’ instead of rich galaxy clusters. Can anyone explain why is it so? I read about it's formation and i cannot understand as to how the formation is not better in centre of clusters.

Here is the article https://bigthink.com/starts-with-a-bang/ring-galaxies/

And here is the line I am talking about Quote “In addition, when you look at where ring galaxies are located, they’re overwhelmingly located in what astronomers call “the field,” as opposed to the central locations of rich galaxy groups and clusters. Although this set of features might seem bizarre and unrelated, they’re all cosmic clues to the origins of these features.”

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Let me preface my answer by pointing out that the article you link to confuses two different two different types of "ring galaxy". The main discussion is clearly about "collisional ring" systems, which are indeed quite rare. But there are also so-called outer rings in barred galaxies (see, e.g., the discussion here), where the ring is understood as resulting from the interaction of a rotating central bar with gas in the outer disk, at the bar's "outer Lindblad resonance". These are much more common than collisional ring galaxies, and one or two of the pictured galaxies (possible NGC 6028 and definitely NGC 1291) are barred outer-ring systems, not collisional rings.

But to stick with collisional ring galaxies: the basic idea is that these need to be gas-rich in order for the collisional interaction to produce the rings. Most galaxies in clusters are gas-poor, having lost their gas long ago when they fell into the cluster (e.g., via ram pressure stripping).

(There's also the fact that although clusters have lots of galaxies, they are themselves rare; most galaxies of all kinds -- really massive elliptical galaxies excepted -- are in the field rather than in clusters.)

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