We analyse the eccentric response of a low-mass coplanar circumbinary disc to secular tidal forcing by a Keplerian eccentric orbit central binary. The disc acquires a forced eccentricity whose magnitude depends on the properties of the binary and disc. The largest eccentricities occur when there is a global apsidal resonance in the disc. The driving frequency by the binary is its apsidal frequency, which is equal to zero. A global resonance occurs when the disc properties permit the existence of a zero apsidal frequency free eccentric mode. Resonances occur for different free eccentric modes, which differ in the number of radial nodes. For a disc not at resonance, the eccentricity distribution has somewhat similar form to the eccentricity distributions in discs at resonance that have the closest matching disc aspect ratios. For higher disc aspect ratios, the forced eccentricity distribution in a 2D disc is similar to that of the fundamental free mode. The forced eccentricity distribution in a 3D disc is similar to that of higher order free modes, not the fundamental mode, unless the disc is very cool. For parameters close to resonance, large phase shifts occur between the disc and binary eccentricities that are locked in phase. Forced eccentricity may play an important role in the evolution of circumbinary discs and their central binaries.
Planets migrating in their natal discs can be captured into mean-motion resonance (MMR), in which the planets’ periods are related by integer ratios. Recent observations indicate that planets in MMR can be either apsidally aligned or anti-aligned. How these different configurations arise is unclear. In this paper, we study the MMR capture process of migrating planets, focusing on the property of the apsidal angles of the captured planets. We show that the standard picture of MMR capture, in which the planets undergo convergent migration and experience eccentricity damping due to planet–disc interactions, always leads to apsidal anti-alignment of the captured planets. However, when the planets experience eccentricity driving from the disc, apsidally aligned configuration in MMR can be produced. In this configuration, both planets’ resonance angles circulate, but a ‘mixed’ resonance angle librates and traps the planets near the nominal resonance location. The MMR capture process in the presence of disc eccentricity driving is generally complex and irregular, and can lead to various outcomes, including apsidal alignment and anti-alignment, as well as the disruption of the resonance. We suggest that the two resonant planets in the K2-19 system, with their moderate eccentricities and aligned apsides, have experienced eccentricity driving from their natal disc in the past.
more » « less- PAR ID:
- 10378474
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 517
- Issue:
- 3
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 4472-4488
- Size(s):
- p. 4472-4488
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
ABSTRACT -
more » « less
ABSTRACT We study the evolution of eccentricity and inclination of massive planets in low-density cavities of protoplanetary discs using three-dimensional (3D) simulations. When the planet’s orbit is aligned with the equatorial plane of the disc, the eccentricity increases to high values of 0.7–0.9 due to the resonant interaction with the inner parts of the disc. For planets on inclined orbits, the eccentricity increases due to the Kozai–Lidov mechanism, where the disc acts as an external massive body, which perturbs the planet’s orbit. At small inclination angles, ${\lesssim}30^\circ$, the resonant interaction with the inner disc strongly contributes to the eccentricity growth, while at larger angles, eccentricity growth is mainly due to the Kozai–Lidov mechanism. We conclude that planets inside low-density cavities tend to acquire high eccentricity if favourable conditions give sufficient time for growth. The final value of the planet’s eccentricity after the disc dispersal depends on the planet’s mass and the properties of the cavity and protoplanetary disc.
-
more » « less
ABSTRACT We develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of secular planet–disc interactions and internal disc pressure, self-gravity, and viscosity. Adopting the ansatz that the disc precesses coherently with aligned apsides, the eccentricity evolution equations of the planet–disc system reduce to a set of linearized ordinary differential equations, which allows for fast computation of the evolution of planet–disc eccentricities over long time-scales. Applying our model to ‘giant planet + external disc’ systems, we are able to reproduce and explain the secular behaviours found in previously published hydrodynamical simulations. We re-examine the possibility of eccentricity excitation (due to secular resonance) of multiple planets embedded in a dispersing disc, and find that taking into account the dynamics of eccentric discs can significantly affect the evolution of the planets’ eccentricities.
-
more » « less
Abstract We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to nonadiabatic effects associated with gas cooling and can retain its eccentricity in long-lived coherently precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a large value as the system goes through the resonance. In this work, we solve the eccentric modes of a model disk for a wide range of masses. We then adopt an approximate secular dynamics model to calculate the long-term evolution of the “planet + dispersing disk” system. The planet attains a large eccentricity (between 0.1 and 0.6) in our calculations even though the disk eccentricity is quite small (≲0.05). This eccentricity excitation can be understood in terms of the mode conversion (“avoided crossing” between two eigenstates) phenomenon associated with the evolution of the “planet + disk” eccentricity eigenstates.
-
more » « less
ABSTRACT The active galactic nucleus (AGN) disc has been proposed as a potential channel for the merger of binary black holes. The population of massive stars and black holes in AGN discs captured from the nuclei cluster plays a crucial role in determining the efficiency of binary formation and final merger rate within the AGN discs. In this paper, we investigate the capture process using analytical and numerical approaches. We discover a new constant integral of motion for one object’s capture process. Applying this result to the whole population of the nuclei cluster captured by the AGN disc, we find that the population of captured objects depends on the angular density and eccentricity distribution of the nuclei clusters and is effectively independent of the radial density profile of the nuclei cluster and disc models. An isotropic nuclei cluster with thermal eccentricity distribution predicts a captured profile dN/dr ∝ r−1/4. The captured objects are found to be dynamically crowded within the disc. Direct binary formation right after the capture would be promising, especially for stars. The conventional migration traps that help pile up single objects in AGN discs for black hole mergers might not be required.
