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The magnetic field of the Sun flips during each solar cycle, with the flip occurring when sunspot cycle is near its maximum. Levels of solar radiation and ejection of solar material, the number and size of sunspots, solar flares, and coronal loops all exhibit a synchronized fluctuation, from active to quiet to active again, with a period of 11 years.

Has this phenomenon ever been measured, directly or indirectly, on stars outside the solar system?

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The Sun's magnetic activity cycle of $\sim 22$ years involves a large-scale reversal of the polarity of the magnetic field every $\sim 11$ years.

There are very many observations of other solar-type stars that show, indirectly, they they too have magnetic activity cycles in the form of modulated emission of tracers of the magnetic field - starspots, chromospheric and coronal activity (e.g. Olah et al. 2016 and references therein).

To directly measure the reversing cycles in magnetic polarity requires spatially resolved maps of the vector magnetic field. Such spatially resolved maps are possible for fast-rotating, and hence highly magnetically active stars through Zeeman Doppler Imaging. In general, highly magnetically active stars appear not to show magnetic activity variations as strongly as the Sun. Nevertheless, recent instrumental developments have led to (difficult) observations of some solar-type stars with intermediate rotation rates. There is now plenty of evidence for magnetic polarity reversals in many of these (e.g. in Chi$^1$ Ori, Rosen et al. 2016; in LQ Hya, Lehtinen 2019; in V1358 Ori, Willamo et al. 2021).

Whilst the observations are not densely sampled enough to say for sure that this is cyclical behaviour following the same pattern as the Sun, the reversals have been found to correlate quite well with maxima or minima in the indirect indicators of magnetic activity.

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    $\begingroup$ in principle the sign of an unresolved magnetic field pointing towards us can still be gleaned from circular polarization. I have no idea of the feasibility/practicality of that though, at least for regular (i.e. non-neutron) stars where flips happen. $\endgroup$
    – uhoh
    Apr 23 at 19:51
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    $\begingroup$ @uhoh I think the problem is that you can't tell which hemisphere the field is going into or out of. I guess if you looked at a low inclination object... But even then, I think this signal is dominated by the small-scale fields associated with starspots where you have field going into and out of the star, rather than the large-scale magnetic structure. $\endgroup$
    – ProfRob
    Apr 26 at 11:21

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