Red giant stars have diameters of around tens to hundreds of times larger than that of the Sun and they occur when stars like the Sun eventually exhaust the supply of hydrogen in their cores and switched to fusing hydrogen in a shell external to the core. The increased temperatures and reaction rates causes the star to expand into a red giant and as the star expands, it spins down due to the conservation of angular momentum. Therefore, red giant stars are expected to rotate much more slowly about their spin axis as compared to stars like the Sun.
An unusual class of red giant stars known as red giant rapid rotators are basically red giant stars that are known to spin much faster than what is predicted for them. Ordinary red giant stars have equatorial velocities of around 2 kilometres per second while red giant rapid rotators have equatorial velocities of around 10 kilometres per second or more. In a paper by Joleen Carlberg, et al. (2010) entitled “The Fate of Exoplanets and the Red Giant Rapid Rotator Connection”, it is suggested that as a red giant star expands; it can consume and accrete planets that happen to be orbiting in close vicinity. Planets accreted in this way can dump sufficient angular momentum into the red giant star and cause the star to spin up to become a red giant rapid rotator.
This mechanism of accreting planets only works for planets whose orbital periods are shorter than the rotational period of their host stars. In other words, the time it takes for the planet to orbit once around its star has to be shorter than the times it takes for the star to complete one rotation about its spin axis. In such a configuration, the tidal bulge raised on the star by the orbiting planet will always be trailing the planet and this allows angular momentum to be transferred from the orbiting planet to the rotation of the star. This causes the planet to lose orbital angular momentum, fall closer towards its host star and eventually getting accreted by the star.
The amount of angular momentum that is dumped into a red giant star by an accreted planet can be many times greater than the angular momentum of the star itself. In our solar system, the Sun holds less than 2 percent of the total angular momentum while the planet Jupiter holds 60 percent of the total angular momentum. However, the orbit of Jupiter is too distant for it to get consumed by the Sun when the Sun expands into a red giant star billions of years from now.
Most of the 500 or so extrasolar planets known to date are Jupiter-like planets which orbit very close to their parent stars, many of which have orbital periods in the range of a few days. These planets are termed hot-Jupiters and they form a large proportion of the currently known planets due to observational biases as these planets are the easiest to detect. Such a hot-Jupiter can dump a huge amount of angular momentum into its host star via accretion when the star expands into a red giant, turning the red giant into a rapid rotator. For example, a Jupiter-mass planet in a Mercury-like orbit around a star that is identical to our Sun will have about 10 times more angular momentum than the star itself.
The lithium abundance of a red giant rapid rotator can also provide further evidence to correlate it with accreted planets. Red giant stars are known to be depleted in lithium due to convective mixing and the accretion of a Jupiter-mass planet can significantly raise the lithium abundance of the red giant star. However, a better understanding of stellar evolution is still required to ensure that any observed lithium abundance or any other observed abundance anomalies are indeed anomalous for a given red giant rapid rotator such that it can be attributed to an accreted planet.