Giants eating giants: Mass loss and giant planets modifying the
  luminosity of the Tip of the Giant Branch
  During the red giant phase, stars loose mass at the highest rate since birth.
The mass-loss rate is not fixed, but varies from star-to-star by up to 5\%,
resulting in variations of the star's luminosity at the tip of the red giant
branch (TRGB). Also, most stars, during this phase, engulf part of their
planetary system, including their gas giant planets and possibly brown dwarfs.
Gas giant planet masses range between 0.1 to 2\% of the host star mass. The
engulfing of their gas giants planets can modify their luminosity at the TRGB,
i.e. the point at which the He-core degeneracy is removed. We show that the
increase in mass of the star by the engulfing of the gas giant planets only
modifies the luminosity of a star at the TRGB by less than 0.1\%, while
metallicity can modify the luminosity of a star at the TRGB by up to 0.5\%.
However, the increase in turbulence of the convective envelope of the star, has
a more dramatic effect, on the star's luminosity, which we estimate could be as
large as 5\%. The effect is always in the direction to increase the turbulence
and thus the mixing length which turns into a systematic decrease of the
luminosity of the star at the TRGB. We find that the star-to-star variation of
the mass-loss rate will dominate the variations in the luminosity of the TRGB
with a contribution at the 5\% level. If the star-to-star variation is driven
by environmental effects, the same effects can potentially create an
environmentally-driven mean effect on the luminosity of the tip of the red
giant branch of a galaxy. Engulfment of a brown dwarf will have a more dramatic
effect. Finally, we touch upon how to infer the frequency, and identify the
engulfment, of exoplanets in low-metallicity RGB stars through high resolution
spectroscopy as well as how to quantify mass loss rate distributions from the
morphology of the horizontal branch.
