# Why doesn't the centrifugal force cause rotating dark halos to flatten?

• Consider a spherical cloud of dark matter like the spherical halo around our galaxy. Please see the diagram below

• Assuming that the halo is purely made up of dark matter which has only gravitational interaction and nothing else. Therefore, it cannot dissipate energy with time.

• Now imagine the system is given a uniform rotation at $$t=0$$ about the axis shown in the figure.

Wouldn't such a motion cause the dark matter distribution to flatten out and take up the shape of a disc? After all, these dark matter particles will experience a centrifugal force. But this is not observed for the galactic halo. The halo retains its spherical shape even though the galaxy is rotating. What is wrong with my reasoning? Isn't the halo also expected to rotate like the visible matter in the galaxy?

• I would not discuss the flattening of colliding gas in terms of "centrifugal force". nI mean, you can, but I wouldn't advise it because I don't see it as a win for comprehension. – dmckee Apr 6 at 23:20

• Current constraints on the Milky Way dark halo shape from the orbits of globular clusters suggest an axis ratio of $$\sim 1.3$$: Posti & Helmi (2019).
• The dimensionless halo spin parameter is $$\lambda\sim0.035$$, indicating that dark halos are mostly supported by dispersion (random motions) rather than rotation, so flattening into a disc is not expected, but a slight elongation is : Mo, van den Bosch & White (2010), p. 358-359 - this is a textbook reference, there are also many articles on this well-studied topic.