Residual eccentricity of an Earth-like planet orbiting a red giant Sun
arXiv:2304.07808 · doi:10.1051/0004-6361/202345860
Abstract
The late phases of the orbital evolution of an Earth-like planet around a Sun-like star are revisited considering the effect of the density fluctuations associated with convective motions inside the star. Such fluctuations produce a random perturbation of the stellar outer gravitational field that excites a small residual eccentricity in the orbit of the planet counteracting the effects of tides that tend to circularize the orbit. We compute the power spectrum of the outer gravitational field fluctuations of the star in the quadrupole approximation and study their effects on the orbit of the planet using a perturbative approach. The residual eccentricity is found to be a stochastic variable showing a Gaussian distribution. Adopting a model of the stellar evolution of our Sun computed with MESA, we find that the Earth will be engulfed close to the tip of the red giant branch evolution phase. We find a maximum mean value of the residual eccentricity of about 0.026 immediately before the engulfment. Considering an Earth-mass planet with an initial orbital semimajor axis sufficiently large to escape engulfment, we find that the mean value of the residual eccentricity is greater than 0.01 for an initial separation up to about 1.4 au. The engulfment of the Earth by the red giant Sun is found to be a stochastic process, in contrast to the deterministic character assumed in previous studies. If an Earth-like planet escapes engulfment, its orbit around its remnant white dwarf star will be moderately eccentric. Such a residual eccentricity on the order of a few hundredths can play a relevant role in sustaining the pollution of the white dwarf atmosphere by asteroids and comets as observed in several objects.
arXiv comment18 pages, 6 figures, 3 appendixes, accepted by Astronomy & Astrophysics; added reference to Kissin & Thompson (2015) and corrected typos in Eqs. (10)-(13) and (65)-(67)
References in corpus (51)
- The chemical composition of the Sun
- Modules for Experiments in Stellar Astrophysics (MESA)
- Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
- Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions
- Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions
- Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation
- The Updated BaSTI Stellar Evolution Models and Isochrones: I. Solar Scaled Calculations
- Asteroseismology of old open clusters with Kepler: direct estimate of the integrated RGB mass loss in NGC6791 and NGC6819
- The Orbital Evolution of Gas Giant Planets around Giant Stars
- A New Version of Reimers' law of Mass Loss Based on a Physical Approach
- Foretellings of Ragnarök: World-engulfing Asymptotic Giants and the Inheritance of White Dwarfs
- Hot Jupiters and Cool Stars
- Distant future of the Sun and Earth revisited
- The Great Escape: How Exoplanets and Smaller Bodies Desert Dying Stars
- Age dissection of the Milky Way discs: red giants in the Kepler field
- Eccentric Planets and Stellar Evolution as a Cause of Polluted White Dwarfs
- On the Orbits of Low-mass Companions to White Dwarfs and the Fates of the Known Exoplanets
- Planet Engulfment by ~1.5-3 Solar-Mass Red Giants
- Uncertainties on near-core mixing in red-clump stars: effects on the period spacing and on the luminosity of the AGB bump
- An Exoplanet's Response to Anisotropic Stellar Mass-Loss During Birth and Death
- Orbital evolution of mass-transferring eccentric binary systems. II. Secular Evolution
- Chaotic Disintegration of the Inner Solar System
- The Role of Planet Accretion in Creating the Next Generation of Red Giant Rapid Rotators
- Star-planet interactions: II. Is planet engulfment the origin of fast rotating red giants?
- Evolution of Planetary Orbits with Stellar Mass Loss and Tidal Dissipation
- Orbital evolution of mass-transferring eccentric binary systems. I. Phase-dependent evolution
- Formation of millisecond pulsars with helium white dwarfs, ultra-compact X-ray binaries and gravitational wave sources
- Star-planet interactions: I. Stellar rotation and planetary orbits
- Magnetic Field, Dust, and Axisymmetrical Mass Loss on the AGB
- Star-planet interactions. V. Dynamical and equilibrium tides in convective zones
- Rotation, Planets, and the "Second Parameter" of the Horizontal Branch
- WD 1856 b: a close giant planet around a white dwarf that could have survived a common-envelope phase
- The Effect of Tides on the Population of PN from Interacting Binaries
- The Red-Giant Branch Bump Revisited: Constraints on Envelope Overshooting in a Wide Range of Masses and Metallicities
- Planetary Systems Around White Dwarfs
- Detecting Transits of Planetary Companions to Giant Stars
- Rotation of Giant Stars
- Planetary Engulfment in the Hertzsprung--Russell Diagram
- Linking long-term planetary -body simulations with periodic orbits: application to white dwarf pollution
- Orbital Decay in Binaries Containing Post-Main Sequence Stars
- How Jupiters save or destroy inner Neptunes around evolved stars
- Long-term dynamics of the solar system inner planets
- Successive common envelope events from multiple planets
- Driving white dwarf metal pollution through unstable eccentric periodic orbits
- Highly stable evolution of Earth's future orbit despite chaotic behavior of the Solar System
- Accounting for planet-shaped planetary nebulae
- Disruption of a planet spiralling into its host star
- A red giant branch common envelope evolution scenario for the exoplanet WD 1856 b
- Resolved imaging of exoplanets with the solar gravitational lens
- The entry geometry and velocity of planetary debris into the Roche sphere of a white dwarf
- Characterising the AGB bump and its potential to constrain mixing processes in stellar interiors