[Paper Review] Galactic tide and orbital evolution of comets

Ladislav Kómar, J. Klačka+1 more|arXiv (Cornell University)|Dec 17, 2009

Astro and Planetary Science16 references3 citations

TL;DR

This paper presents a numerically detailed model of comet orbital evolution in the Oort cloud under the influence of the galactic tide, incorporating the Sun's vertical oscillation through the galactic plane and the full gravitational potential including $Γ$-terms. It finds that physically accurate models yield secular orbital periods 1.7 times shorter than conventional models, resulting in approximately twice as many comet returns to the inner Solar System, supporting the hypothesis that a comet from the Oort cloud could have caused the Cretaceous-Paleogene extinction 65 million years ago.

ABSTRACT

Equation of motion for a comet in the Oort cloud is numerically solved. Orbital evolution of the comet under the action of the gravity of the Sun and the Galaxy is presented for various initial conditions. Oscillations of the Sun with respect to the galactic equatorial plane are taken into account. Real values of physical quantities concerning the gravitational action of the galactic neighbourhood of the Sun are important. The results are compared with currently used more simple models of the galactic tide. It turns out that physically improved models yield results which significantly differ from the results obtained on the basis of the conventional models. E.g., the number of returns of the comets into the inner part of the Solar System are about two times greater than it is in the conventional models. It seems that a comet from the Oort cloud can be a source of the dinosaurs extinction at about 65 Myr ago. A close encounter of a star or an interstellar cloud disturbed a comet of the Oort cloud in the way that its semi-major axis increased/decreased above the value 5 $ imes$ 10$^{4}$ AU and the comet hit the Earth.

Motivation & Objective

• To improve the physical accuracy of galactic tide models affecting comet dynamics in the Oort cloud by including the Sun's vertical oscillation through the galactic plane.
• To investigate the role of $Γ$-terms in the galactic tidal potential, which couple the $z$-component of position to $x$- and $y$-accelerations.
• To compare the orbital evolution of comets under improved models with conventional models that neglect these terms and the Sun's vertical motion.
• To assess the implications of enhanced comet return frequency for the hypothesis that a comet impact caused the Cretaceous-Paleogene mass extinction.

Proposed method

• Numerical integration of the full equation of motion for comets in the Oort cloud, including gravitational forces from the Sun and the galactic tide.
• Incorporation of the Sun's vertical oscillation through the galactic plane with a period of 72.6 Myr, affecting the galactic tidal potential.
• Use of a physically improved tidal potential model that includes $Γ$-terms, which account for the coupling between vertical and radial accelerations.
• Computation of osculating orbital elements (semi-major axis, eccentricity, inclination, etc.) at each time step to track secular evolution.
• Comparison of results from the improved model (Model II) with conventional models that neglect $Γ$-terms and the Sun's vertical motion.
• Analysis of perihelion distance evolution and timing of comet returns to the inner Solar System to assess extinction event correlations.

Experimental results

Research questions

• RQ1 How do the $Γ$-terms in the galactic tidal potential affect the secular evolution of comet orbital elements in the Oort cloud?
• RQ2 What is the impact of the Sun's vertical oscillation through the galactic plane on the frequency of comet returns to the inner Solar System?
• RQ3 How does the orbital evolution under a physically accurate tidal model compare to that under conventional simplified models?
• RQ4 Can the enhanced frequency of comet returns in the improved model explain the timing of the Cretaceous-Paleogene extinction 65 Myr ago?
• RQ5 What semi-major axis and initial orbital phase are required for a comet to be perturbed into an Earth-crossing orbit during a solar passage near the galactic plane?

Key findings

• The inclusion of $Γ$-terms in the tidal potential leads to a 1.7-fold reduction in the secular evolution period of comet orbital elements compared to conventional models.
• The frequency of comet returns to the inner Solar System is approximately twice as high in the improved model compared to conventional models.
• The minimum perihelion distance evolution is most strongly reduced in the best physical model (Model II), indicating stronger perturbations toward the inner Solar System.
• A comet from the Oort cloud could have caused the Cretaceous-Paleogene extinction 65 Myr ago, with the timing consistent with the Sun's passage through the galactic plane.
• For the extinction event to align with the Sun's vertical oscillation, the comet's semi-major axis must be approximately 5.1 × 10⁴ AU when $\varepsilon < 1/2$, corresponding to initial aphelion conditions.
• The model suggests a periodicity of 4.5–5.0 × 10⁸ years for potential mass extinctions driven by galactic tides, which is twice the period previously estimated.