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View submission: Why are galaxies not round?
There are two possible questions here:
1. Many galaxies are disk-shaped. Why don't they have three-dimensional extent as spheres?
2. The galaxies that have significant three-dimensional extent can still be very ellipsoidal, rather than spherical. Why is that?
1.
The disk shape arises because material loses orbital energy through inelastic processes. For example, energy is lost as emitted radiation. Energy is also "sequestered" into compact objects or orbital subsystems (like binary stars), which behave as a single object within the larger galactic system.
Why does such energy loss ("cooling") produce disks? Because while the material loses energy, it does not also lose angular momentum. Any initial angular momentum that the system had must be preserved. Therefore the system settles into a configuration that -- compared to a sphere -- has a higher ratio of angular momentum to energy: a disk.
This is the same reason planetary systems tend to be planar.
2.
Ellipsoidal galaxies tend to be galaxies that recently had a large influx of energy, such as through accretion of a lot of new material. Per the above, the injection of energy explains why they are not disks. But why are they ellipsoidal and not necessarily spherical? (They certainly can be spherical.)
It's more insightful to think about why things tend to be spherical in the first place. Spheres are energetically favorable from a gravitational standpoint: they minimize the gravitational energy for any given volume. Planets and stars are (nearly) spherical because they are supported by pressure while being held together by gravity, and these competing effects favor a spherical shape.
Galaxies are not pressure supported. Ellipsoidal galaxies specifically are *velocity dispersion*-supported, which means that large random velocities maintain the galaxy's shape. In particular, there are very few actual collisions between objects. Without collisions, there is little to drive the galaxy toward a spherical shape.
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Also, there is an dynamical instability (the "radial orbit instability") that suppresses the abundance of highly spherical cosmic structures. If a galaxy forms by pulling in material from a long distance away that is otherwise relatively undisturbed, then the material ends up on highly eccentric orbits. Unfortunately, a spherical system with only highly eccentric orbits is unstable: the orbits tend to cluster in angles to produce a more ellipsoidal object. This effect doesn't mean galaxies can't be spherical: if a galaxy accretes material with high angular momenta -- which settles into more circular orbits -- then a spherical configuration can be stable. But it makes spherical configurations less likely.
There's nothing here!