What is a star cluster?

Quick explanation

A star cluster is a clump of stars that are formed roughly at the same time.

There are basically two different kinds:
Globular clusters are compact, spherical clumps of old and hence yellow-/reddish stars.
Open clusters are more diffuse clumps of young and hence more bluish stars.

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Globular clusters

A globular cluster is a spherical clump of stars, formed at about the same time. Most globular clusters are very old, formed in the early age of the galaxy. Because they are so old and there is no more gas left to form new stars, all the massive stars — which burn their fuel quickly and with a bluish color — are dead; only the light and yellow/reddish stars are left, giving the globular cluster its color.

When a spiral galaxy was young, it hadn't yet flattened to form its disk; for this reason globular clusters in a spiral galaxy like the Milky Way do not lie in the galaxy's plane, but instead in a more spherical halo around the galaxy.

Over time, globular clusters have become gravitationally very tightly bound, giving them their spherical shape. Whereas the distance between stars in the Sun's neighborhood is typically around 4 light years, the stars in the centers of globular clusters are 100 to 1000 times closer.

There are about 150 known globular clusters in our galaxy, the Milky Way, with perhaps 10-20 pieces yet to be discovered.

See my own observations of globular clusters here.

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M80: This globular cluster is almost 33,000 light-years away, but with its several hundred thousand stars it is nevertheless visible in a small amateur telescope. Despite the stars being formed at the same time, billions of years ago, there are a few young and blue stars, known as blue stragglers; the origin of these is a bit of a mystery.

Open clusters

Open star clusters are much smaller than globular clusters; typically they consist of a few thousand stars. Since they are not so tightly bound by gravity, they dissolve after a few tens to hundreds of millions of years.

That is, an open cluster still has its massive stars, which shine blue and bright. Sometimes, the stars are still in the gas sky they were born in, and this cloud is lit up by the stars. Therefore, open clusters are sometimes seen enshrouded in blue, diffuse nebulae.

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The Pleiades: This open cluster, also known as the Seven Sisters, is easily seen with the naked eye as a 7-14 stars (depending on how far out in the countryside you are), but in even a small telescope you can clearly see hundreds of stars. The Pleiades are actually quite old, and the blue reflection nebula is probably not the cluster's natal cloud, but just a random cloud it's passing through at the moment.
Credit: NASA/ESA/AURA/Caltech