I just learned that the sun spins. And since it’s all plasma, the parts of the sun near its equator spin 3 times as fast as the parts near its poles.
Question: does the sun spin on a similar plane as the plane of the planets’ revolution around it? Does it spin along the same plane as its own revolution around the center of the galaxy?
The sun’s rotational axis is tilted about 7 degrees from being perpendicular to the Earth’s orbital plane. Also, the sun’s equator rotates once in about 25 days while the area near the poles rotates once every 35 days, so nowhere near 3 times as fast.
Is that an indication that all/most stars are in a rotation?
If so I presume some would spin more violently than others?
Could those stars in dual systems have more complex movements eg oscillation?
Pulsars certainly spin.
My understanding is that all stars spin, because it’s part of the conservation of angular momentum from their formation out of dust clouds. I’m open to correction on that. Paging @Chronos !
Just to clarify it is the core of the sun that spins 4x faster. A week vs a month or so on the outer surface.
Yes. It is pretty much impossible for them not to be spinning. In theory a gas cloud could collapse perfectly symmetricaly from all directions at once, but it very profoundly unlikely.
(And, as an aside, that freak spinless star would not have planets. Or enen a circumstellar disc.)
Thanks. Not sure where I got the 3 times from.
Depends on what is meant by “3 times as fast.” Angular velocity (in terms of number of rotations per period of time) apparently not. But keep in mind that a lap around the equator will be much wider (in terms of diameter) than a lap near the pole. So maybe that comes out to three times faster in terms of lateral velocity at any given moment?
If a body, let us say a spheroid, is spinning, then a point on the axis is, to a certain approximation, not moving at all, is it? Much less 3 times as slow as some point on the equator.
Because stars have to conserve angular momentum even if they collapse and become much smaller in diameter, neutron stars often spin quite rapidly even though they are the size of cities. They’re called pulsars if they beam energy rhythmically in doing so (because of their magnetic fields). The fastest one spins 42,960 RPM, faster than a Dremel tool:
Pulsar PSR J1748-2446ad, discovered in 2004, is, as of 2021, the fastest-spinning pulsar currently known, spinning 716 times per second.
That’s from the Wikipedia article on millisecond pulsars.
That seems a fairly useless point however. By that reasoning, every rotating solid sphere, like the Earth or a spinning basketball, also has points on the equator that are moving 3 times faster, 4 times faster, and for that matter 1000 times faster than points near the pole. It says nothing about the more interesting fact that the sun’s angular velocity varies with latitude, unlike a solid sphere.
Is that because of the lack of an accretion disk? But that star would be capable of capturing a rogue planet though, right?
Yep.
It could, but then the star wouldn’t be spinless anymore as gravitational tidal-dragging takes effect (no matter how small the planet). Speaking of which, since gravity operates over infinite distances, technically any star that is not alone in its own observable universe will be subject to a miniscule amount of tidal dragging from other things with mass.
A star that didn’t already have planets also couldn’t capture any, unless you had some truly freak circumstance with multiple rogue planets passing by at once.
For anyone who might get tricked by this description. Pulsars emit a steady stream, but not completely aligned with the axis of rotation, so if we’re in part of the “beam cone” we get the radiation in pulses.
Are there good explanations for this discrepancy?
Thanks, good correction. They don’t beam it rhythmically, except to a specific limited size target (like us).
What makes you think the Earth’s orbital plane is the one that should be the reference. 
Well, not Earth’s orbital plane in particular, but you’d think that the average orbital plane of the solar system and the sun’s tilt would be aligned, absent any major event that disturbed them since initial formation.