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This question may sound silly but I'm really not pretty sure whether the stars are rotating or stationary.If they are not rotating what makes them to be stable?

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Who knows why this question has the orbit tag :) –  Py-ser Feb 28 at 9:24
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Stars rotate due to the angular momentum of the gas they formed from. This angular momentum must be conserved, and remains as the rotation of the star and it's satellites. If a star collapsed from a completely static gas cloud it would not rotate, but would still be stable. The stability is provided by the hydrostatic equilibrium between radiation and thermal pressure with gravitation collapsing the star - not the stars rotation.

I don't know any statistics but I expect all stars rotate to some degree; It is usually the turbulence of gas clouds that leads to overdensities that then collapse in to stars.

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Stars are rotating, but that's not the cause for their stability.

The stability is caused by the hydrostatic equilibrium between gas/plasma pressure and gravity. The pressure is mainly caused by the heat of several millions degrees.

More details here.

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More clearly, I would say that the pressure is granted by thermonuclear fusion reactions, releasing enough radiation to support the gravity force. It is radiation pressure that "pushes outward" the stellar mass. –  Py-ser Feb 28 at 1:31
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Radiation pressure is one of several terms adding up to total pressure. Heat is provided by adiabatic compression, and as you state, mainly by thermonuclear fusion. –  Gerald Feb 28 at 9:09
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Like Chris said above, stars rotate to conserve their angular momentum. They have an initial angular momentum from their formation. In a stellar system both energy and momentum, must be conserved for the system to be stable. Throughout the evolution, the system may radiate some angular momentum away in the form of gravity waves (ie. double degenerate binaries). During this process the separation of two stars will be reduced and the rotation rate of the star will spike to conserve angular momentum.

More on this here: http://www.selmademink.com/science/on-the-origin-of-stellar-rotation-rates-and-the-role-binary-interaction/

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