The Dynamical Evolution of the Short‐Period Extrasolar Planet around υ Andromedae in the Pre–Main‐Sequence Stage

Abstract

We study the dynamical evolution of short-period planets in the multiple planetary system during the epoch of protostellar disk depletion. Through a detailed case analysis for the triple-planet system around υ Andromedae, we identify the necessary condition for the survival of its short-period planet b. In this study, we calculate the planets' orbit evolution including effects of the post-Newtonian potential of the host star, the potential of an evolving disk, and the potential due to the flattening of the star produced by the stellar rotation and the tide from the planet. At its present-day semimajor axis of 0.059 AU, the negligible eccentricity of planet b is most likely damped by the dissipation of the tidal perturbation induced by the star on the planet. But this process also leads to the heating of the planets' interior and probably the inflation of their sizes. If planet b once had an eccentricity greater than 0.1 at its present location, the tidal dissipation process would induce it to overflow its Roche lobe, lose its mass, and undergo an orbital expansion. Using this constraint, we reconstruct the eccentricity evolution of planet b. We find that even if planet b arrives at its present location on a nearly circular orbit, its eccentricity could have been excited by the sweeping secular resonances of two outer planets, c and d, during the disk depletion. In addition to the contribution from the disk potential, the resonant condition is also modified by the precession of planet b due to the post-Newtonian correction and rotational distortion of υ And's gravitational potential. Today, the former effect offsets the secular resonance, whereas the latter effect is weak. But during the depletion of the disk, precession due to the relativistic correction is outpaced by that due to the disk potential. The passage of the sweeping secular resonance near the surface of υ And cannot be avoided unless it had a sufficiently fast spin to provide a flattened shape with a finite quadrupole moment, which dominates the precession of the planet's orbit. Finally, we show that the survival of planet b requires its eccentricity to be low at all times, which would be possible only if the spin period of υ And was shorter than 2 days during the depletion of the disk.