Planetary Engulfment in the Hertzsprung--Russell Diagram

Planets accompany most sun-like stars. The orbits of many are sufficiently close that they will be engulfed when their host stars ascend the giant branch. This Letter compares the power generated by orbital decay of an engulfed planet to the intrinsic stellar luminosity. Orbital decay power is generated by drag on the engulfed companion by the surrounding envelope. As stars ascend the giant branch their envelope density drops and so does the power injected through orbital decay, scaling approximately as $L_{\rm decay} \propto R_*^{-9/2}$. Their luminosity, however, increases along the giant branch. These opposed scalings indicate a crossing, where $L_{\rm decay}= L_*$. We consider the engulfment of planets along isochrones in the Hertzsprung-Russell (H-R) diagram. We find that the conditions for such a crossing occur around $L_*\approx 10^2$~$L_\odot$ (or $a\approx 0.1$~au) for Jovian planetary companions. The consumption of closer-in giant planets, such as hot Jupiters, leads to $L_{\rm decay}\gg L_*$, while more distant planets such as warm Jupiters, $a\approx 0.5$~au, lead to minor perturbations of their host stars with $L_{\rm decay} \ll L_*$. Our results map out the parameter space along the giant branch in the H-R Diagram where interaction with planetary companions leads to significant energetic disturbance of host stars.