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So we know that stars slow down as they age. But total angular momentum must be conserved. Where does that angular momentum go?

The dissipation of Earth's tides somehow transfers Earth's angular momentum to the moon (as shown in my answer at http://www.quora.com/Has-the-Earths-rotational-period-always-been-24-hours-If-not-what-was-it-before-and-what-caused-the-change). But where does a star's dissipation go?

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For single stars (doubles also exhibit the spin-to-orbital angular momentum transfer), Rotation braking states:

Stars slowly lose mass by the emission of a stellar wind from the photosphere. The star's magnetic field exerts a torque on the ejected matter, resulting in a steady transfer of angular momentum away from the star.

A first order approximation is that the rotation velocity decreases by the inverse squareroot of time elapsed.

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Some angular momentum is lost to the ejected material, but the bulk of it is conserved. Stars expand as they age, so the radius is increased - and because of the same law, they must slow down. The reverse happens when the star collapses - its mass suddenly occupies a much smaller volume, so the outer edge starts rotating really fast. That's why pulsars rotate so fast.

To be fair, if planets or other bodies are present in star's orbit, given enough time they will eventually tidally lock to each other. But this effect is much smaller

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    $\begingroup$ Overly simplistic. The Sun has lost the vast majority of its initial angular momentum. $\endgroup$ – Rob Jeffries Mar 21 '17 at 17:40

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