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Galaxies commonly interact and collide with other galaxies. Is it possible that clusters of galaxies similarly interact and collide? Have people tried to study this phenomenon previously? I couldn't find anything specific in the literature.

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Yes.

Theoretically, structure is expected to form first on small scales (stars and stellar clusters), and later on increasingly larger scales — galaxies, groups, and eventually galaxy clusters (see e.g. Longair 2006). This is confirmed, at least to some extent, observationally. For instance, galaxies have been detected out to a redshift of $z=11.2$ (400 million years after Big Bang; Oesch et al. 2016), while cluster have only been detected out to $z=2.5$ (2.6 billion years after Big Bang; Wang et al. 2016).

Thus, when clusters formed, the Universe had already expanded so much that interaction between them is rather rare.

It does happen, however. One of the most important examples is the Bullet Cluster, which consists of two colliding galaxy clusters. The reason I mention this is that it really beautifully confirmed the existence of dark matter. The image below (from NASA's Astronomy Picture of the Day) shows the two clusters after the collision. The stars and galaxies are so far apart that collisions between galaxies are rare, and collisions between stars virtually never happen. Thus, they have just passed right through each other, as seen in the image. The gas between the galaxies, however, collides, slows down, and is separated from the galaxies. This heats the gas to millions of degrees, emitting X-rays (seen in red). The blue stuff is a map of the mass distribution, made using gravitational lensing. This mass is clearly separate from the gas, but coincides with the galaxies, and gives a much higher mass than the visible mass, roughly 5.5 times more, which is exactly what is found for the ratio between dark and normal matter using other methods.

bullet

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    $\begingroup$ thank you for the great answer and the bullet cluster example. $\endgroup$ – Akim Sep 3 '17 at 21:07
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    $\begingroup$ found a relevant review: arxiv.org/abs/astro-ph/0701821 $\endgroup$ – Akim Sep 3 '17 at 23:22
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Watch this video, I think it will give you an answer, sometimes it is better at once to see , then 10 times to read: Laniakea: Our home superclaster

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