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When the Sun runs out of hydrogen to fuse it will grow bigger in size and my question is does it rotate more slowly, like a spinning ice skater extending their arms to reduce angular velocity? What consequences will accompany with a slower dynamo (big ball of plasmas), such as more frequent solar flares or perhaps more dark spots?

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Indeed conservation of angular momentum dictates that in a single star like the the Sun, rotation should be much slower when it becomes a red giant. This is because at the present time the Sun does not rotate at vastly different rates with depth, thus when it expands, the moment of inertia increases drastically and convection in the outer envelope will ensure that slow rotation is enforced throughout most of the star.

The consequence for magnetic activity will be that the Sun will become magnetically inactive (in relative terms - magnetic activity will not be absent, but its signatures will be much reduced when expressed as a fraction of the stellar luminosity) as a red giant, because dynamo-generated magnetic activity is strongly correlated with rotation rate.

In general it is found that giant stars are magnetically inactive and slowly rotating, but there are exceptions. If a star considerably more massive ($\sim 3-5M_{\odot}$) than the Sun evolves to become a giant it may have preserved a considerable amount of angular momentum, since such stars are not magnetically active on the main sequence and are unable to lose their angular momentum through a magnetised wind in the same way that a solar-type star does. Secondly, it is possible that some rapidly rotating giants (e.g. the FK Com stars) could be the result of mergers in binary systems or possibly even giant planet engulfment. In which case the angular momentum is from the binary system and these stars can be very magnetically active. Finally it is also found that giants in close binary systems (the RS CVn stars) can be fast-rotating and magnetically active because tidal locking in the binary system enforces rapid rotation. The FK Com and RS CVn stars manifest many signs of extreme magnetic activity - hot X-ray coronae, chromospheres, coverage of large fractions of the surface by cool starspots. We thus deduce that the difference between these and the vast majority of magnetically-inactive giants is their rapid rotation.

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