Engulfment of a hot Jupiter as a possible origin of the rapid spin and internal spin misalignment of the planet-hosting red giant Kepler-56

TL;DR

Kepler-56 presents a rare spin configuration on the red-giant branch, with a rapidly rotating envelope and a core–envelope misalignment. The authors compare angular-momentum supply from the known planets (Kepler-56 b and c) against engulfment of a hot Jupiter, using simplified angular-momentum evolution anchored by MESA-derived stellar properties. They find tides alone cannot deliver the required AM within observationally plausible $Q'$ values, while engulfing a hot Jupiter with $M_{pl,eng} \sim 0.5$–$2\,M_J$ and $P_{orb,eng} \sim 1$–$6$ d can plausibly account for the spin features. The work highlights Kepler-56 as a benchmark for planetary engulfment imprints on RG spin evolution and discusses broader implications for rapid-rotating RGs and future observational tests.

Abstract

A recent asteroseismic analysis suggests that Kepler-56 -- a planet-hosting red giant -- exhibits a unique spin structure: (1) the spin axes of the core and envelope are misaligned; and (2) the envelope rotates approximately an order of magnitude faster than typical red giants. In this paper, we investigate a feasible scenario to reproduce this spin structure by estimating the amount of the angular momentum (AM) supply from the planets through the simplified calculation of the time evolution of AM. As a result, unless the tidal efficiency is extremely high, we show that the tidal interactions between the known close-in planets (Kepler-56 b and c) are insufficient to supply the AM required to accelerate Kepler-56 from the spin rate observed in typical red giants. We also show that the engulfment of a hot Jupiter can be expected to provide sufficient AM supply for the acceleration ant that the mass and orbit of the engulfed hot Jupiter are constrained by a mass of 0.5-2 Jupiter masses and an orbital period of 1-6 days. On the other hand, if Kepler 56 was already rapidly spinning before entering the RG stage and requires no acceleration, the obliquity damping by the known close-in planets can reproduce the spin structure of Kepler-56. Even in such cases, planetary engulfment during the MS stage might be involved in achieving rapid spin before the tidal alignment. These discussions demonstrate the importance of Kepler-56 as a candidate for planetary engulfment that may leave traces of its spin structure.

Figures (7)

• Figure 1: Comparison of the spin rates in envelope (ordinate of top panel) and core (ordinate of bottom panel) between Kepler-56 and other RGs Li2024AA with 1.20–1.45 $\mathrm{M}_\odot$. The abscissae in both panels are the stellar radius. Kepler-56 is marked in the star-shaped symbol, while other RGs are marked in the circle symbols.
• Figure 2: Schematic picture of our scenario to reproduce the spin profile of Kepler-56. Initially, the spin axes of the core and envelope were aligned in a direction offset from the orbit. After AM supply from the planetary orbit to the stellar envelope, the envelope spins more rapidly in a direction offset from the core. This AM supply is considered to occur during the post-MS stage (refer to the main text for details).
• Figure 3: Comparison of Kepler-56 (points with error bars) and MESA evolutionary tracks for the stars with $M_\mathrm{s} = 1.20 -1.45 \, \mathrm{M}_\odot$ and $\mathrm{[Fe/H]} = 0.20$ (coloured lines). The colours of the lines correspond to the stellar mass shown in the colour bar inside the top panel. (Top) Comparison of them in the HR diagram. (Bottom) Gyration radius, $\hat{r}_g \equiv \sqrt{I_\mathrm{s}/(M_\mathrm{s}R_\mathrm{s})}$, as a function of stellar radius. The plotted gyration radius of Kepler-56 ($\hat{r}_g=0.381^{+0.005}_{-0.006}$) is estimated from its radius. The inset shows a close-up of the position of Kepler-56.
• Figure 4: Time evolution of the orbital periods of Kepler-56 b and c ($P_\mathrm{orb, b}$ and $P_\mathrm{orb, c}$, respectively) and the amounts of maximised AM supply to Kepler-56 for the spin acceleration ($L_\mathrm{calc, max}$) through the tidal interaction with Kepler-56 b and c at each $Q'$. The horizontal axis represents time, with the current time set to 0. The line colours correspond to the $Q'$ values (see the colour-bar). Panels (a) and (b) show the histories of $P_\mathrm{orb, b}$ and $P_\mathrm{orb, c}$ for each $Q'$, respectively. Panel (c) shows the histories of $L_\mathrm{calc, max}$ for each $Q'$. The values at $t=0$, which means the total amount of maximised AM supply, are highlighted with the circle symbols. For comparison, $L_\mathrm{acc}$ is shown as the grey shaded region (see Section \ref{['subsec:meth-Lacc']}).
• Figure 5: Relationship between the total amount of maximised AM supply and $Q'$. For comparison, $L_\mathrm{acc}$ is shown as the grey shaded region (see Section \ref{['subsec:meth-Lacc']}). The observational constraints on $Q'$ and the range of $Q'$ that can supply $L_\mathrm{acc}$ are indicated in blue and orange hatched regions, respectively.