  The objective of this work is to determine what fraction of red-giant (RG)
stars shows photometric rotational modulation, and understand its origin. One
of the underlying questions is the role of close binarity in this population,
standing upon the fact that RGs in short-period binary systems (<150 days or
so) have been observed to display strong rotational modulation. We select a
sample of about 4500 relatively bright RGs observed by Kepler, and show that
370 of them (8%) display rotational modulation. Almost all have oscillation
amplitudes below the median of the sample, while 30 of them are not oscillating
at all. Of the 85 of these RGs with rotational modulation chosen for follow-up
radial-velocity observation and analysis, 34 show clear evidence of
spectroscopic binarity. Surprisingly, 26 of the 30 non-oscillators are in this
group of binaries. To the contrary, about 85% of the active RGs with detectable
oscillations are not part of close binaries. With the help of stellar masses
and evolutionary states computed from the oscillation properties, it appears
that low-mass red-giant branch stars tend to be magnetically inactive, while
intermediate-mass ones tend to be highly active. The opposite trends are true
for helium-core burning (red clump) stars, whereby the lower-mass clump stars
are comparatively more active and the higher-mass ones less so. In other words,
we find that low-mass red-giant branch stars gain angular momentum as they
evolve to clump stars, while higher-mass ones lose angular momentum. The trend
observed with low-mass stars leads to possible scenarios of planet engulfment
or other merging events during the shell-burning phase. Regarding
intermediate-mass stars, the rotation periods are long with respect to
theoretical expectations reported in the literature, which reinforces the
existence of an unidentified sink of angular momentum after the main sequence.
