Capture into Apsidal Resonance and the Decimation of Planets around In-spiraling Binaries

TL;DR

The paper identifies a secular mechanism by which general-relativistic precession of a tightening binary can be resonantly coupled to the planet's precession, pumping the planet's eccentricity and draining its angular momentum as the binary shrinks. By mapping the resonance in phase space and performing orbit-averaged population syntheses that include tides, PN GR effects, and Newtonian forcing, the authors quantify capture probabilities and diverse outcomes for circumbinary planets. They find that a large fraction of CBPs encounter the resonance during binary decay, with most resonant planets destroyed or ejected and survivors typically on distant, eccentric, hard-to-detect orbits; this provides a plausible explanation for the paucity of transiting CBPs around tight binaries. The work highlights the importance of GR-driven secular resonances in shaping circumbinary architectures and suggests incorporating these resonances into future studies of planet formation and evolution in close binaries, including scenarios with magnetic braking and disk dispersal. The results imply a fundamental link between binary tidal evolution and the observed CBP desert, with observable implications for eccentric survivors and their transit probabilities.

Abstract

Transiting circumbinary planets (CBPs) are conspicuously rare, and entirely absent around stellar binaries with periods $\leq 7$ days. Here, we exploit a secular resonance to stimulate the orbit of a CBP into strong, disruptive interactions with the host binary. The process requires no tertiary companion and is triggered when the general-relativistic precession of a tightening binary matches the Newtonian precession it induces in its companion planet. Adiabatic capture in this resonance sees the binary draining angular momentum from the CBP's orbit which grows steadily in eccentricity until destabilization, and eventual ejection or engulfment. We map this resonance in phase space, then investigate the dynamical outcomes of encounter in the course of tidally shrinking binaries. With the help of orbit averaged simulations of a suite of systems, we find that, around tightening binaries: eight out of ten CBPs encounter and are captured in the resonance; three out of four are `destroyed'; and survivors lurk on remote, low-transit-probability orbits. This suggests that the very process which forms tight binaries effectively clears the region where transiting CBPs could reside.

Figures (6)

• Figure 1: Locating the resonance in orbital periods parameter space. Plotted is a contour surface of the function $\text{sgn}(\dot{\varpi}_{\rm p}-\dot{\varpi}_{\rm AB})\times\log_{10}(1+|\dot{\varpi}_{\rm p}-\dot{\varpi}_{\rm AB}|).$ The precession rates of the host binary and the CBP equate at the dashed black curve, identifying the resonance. We adopt the test particle approximation for the planet here, therefore $\dot{\varpi}_{\rm AB}$ is driven by GR, while $\dot{\varpi}_{\rm p}$ is driven by the binary's torque. We use $m_{\rm A} = 2M_{\odot}$, $m_{\rm B} = 1M_{\odot}$, and $e_{\rm AB} = 0.2$. The instability zone on the upper left follows the criterion of holman1999long.
• Figure 2: Phase portraits in $(\zeta_{\rm p},\eta_{\rm p})-$space corresponding to the Hamiltonian of Eq. (\ref{['Hamiltonian_1']}), which governs the planar dynamics of a circumbinary test particle planet around a stellar binary precessing under GR. The phase portraits are restricted to the region around the resonance of interest. Moving from left to right, level curves of the Hamiltonian are plotted in different panels for decreasing values of the drift parameter $\alpha=a_{\rm AB}/a_{\rm p}$, i.e., showing the phase space of the CBP as the binary's orbit shrinks. Beyond a critical value of $\alpha$, the secular precession resonance understudy is encountered, giving rise to the libration island around apse alignment ($\varpi_{\rm p}=\varpi_{\rm AB}; \eta_{\rm p}=0)$, with the latter growing in eccentricity as $\alpha$ decreases further. At the center of the libration island lies the equilibrium point, shown in red, at which $\dot{\varpi}_{\rm p} = \dot{\varpi}_{\rm AB}$, located by solving the equilibrium condition of Eq. (\ref{['equilibria_de_planar']}). Here we adopted $m_{\rm A} = 2M_{\odot}$, $m_{\rm B} = 1M_{\odot}$, and $e_{\rm AB} = 0.35$.
• Figure 3: Profiles of CBP equilibrium eccentricity when apse-aligned with the binary: (Top) at different locations for the binary and the planet with $e_{\rm AB}=0.2$; (Bottom) for different binary location and eccentricity with $a_{\rm p}=1.5$ AU. The realistic dynamical behavior of a CBP is expected to develop around this equilibrium structure if the system is captured in resonance and evolves in time while maintaining adiabaticity. Here we have adopted $m_{\rm A} = 2M_{\odot}$, $m_{\rm B} = 1M_{\odot}$, while the CBP is treated as a test particle.
• Figure 4: Distributions of the initial and end states of the dynamical evolution of 1630 triple systems of binaries and CBPs. The population synthesis is described in the main text and the secular evolution follows the equations of motion in Appendix \ref{['Appendix_EQM']}. Shown, in order, are the population's initial and final binary orbital period $P_{\rm orb;AB}$, binary eccentricity $e_{\rm AB}$, planetary eccentricity $e_{\rm p}$, and the systems prescribed ages compared to the times at which unstable planets are destabilized. The binaries orbital decay and eccentricity decrease are driven by the binary tides, while the planets' eccentricity growth and probable destabilization are driven by capture into the secular apsidal precession resonance.
• Figure 5: Sample simulations representing the outcome regimes of the population synthesis study of Figure \ref{['Fig_Final_tidal_distributions']}. For each regime, the first panel plots the evolution of the orbital periods of the binary, the planet, and the boundary of the circumbinary instability zone georgakarakos2024empirical; the second plots the eccentricity evolution of the binary and the planet; the third plots the evolution of the rate of change of the longitude of the periaspse for both the binary and the planet; while the fourth plots the resonant angle $\varpi_{\rm p}-\varpi_{\rm AB}$. From left to right, $m_{\rm AB}=2.28, 1.58, 2.33,$ and $1.95\,M_{\odot}$. The first regime corresponds to CBPs that do not encounter the sweeping resonance in the course of the binary's tidal decay. Regime B showcases the resonant capture and subsequent ejection of the planet from the system. The third column shows resonance capture that leaves the planet on a stable eccentric orbit, saved by the binary stopping its orbital decay upon circularization. The fourth column shows the richer dynamics of Regime D where the planet is first captured by, and later escapes the resonance. We elaborate further on the dynamical pathways of these regimes in the main text.