  Rapid rotation in field red giant stars is a relatively rare but well-studied
phenomenon; here we investigate the potential role of planet accretion in
spinning up these stars. Using Zahn's theory of tidal friction and stellar
evolution models, we compute the decay of a planet's orbit into its evolving
host star and the resulting transfer of angular momentum into the stellar
convective envelope. This experiment assesses the frequency of planet ingestion
and rapid rotation on the red giant branch (RGB) for a sample of 99 known
exoplanet host stars. We find that the known exoplanets are indeed capable of
creating rapid rotators; however, the expected fraction due to planet ingestion
is only ~10% of the total seen in surveys of present-day red giants. Of the
planets ingested, we find that those with smaller initial semimajor axes are
more likely to create rapid rotators because these planets are accreted when
the stellar moment of inertia is smallest. We also find that many planets may
be ingested prior to the RGB phase, contrary to the expectation that accretion
would generally occur when the stellar radii expand significantly as giants.
Finally, our models suggest that the rapid rotation signal from ingested
planets is most likely to be seen on the lower RGB, which is also where
alternative mechanisms for spin-up, e.g., angular momentum dredged up from the
stellar core, do not operate. Thus, rapid rotators on the lower RGB are the
best candidates to search for definitive evidence of systems that have
experienced planet accretion.
