[Paper Review] Planet formation around binary stars: Tatooine made easy

Benjamin C. Bromley, Scott J. Kenyon|arXiv (Cornell University)|Mar 12, 2015

Astro and Planetary Science4 citations

TL;DR

This paper proposes that circumbinary planets can form in situ around binary stars by settling onto stable, low-eccentricity 'most circular' orbits that avoid destructive collisions. These orbits, derived from analytical perturbation theory, allow gas and planetesimals to damp dynamically without secular excitation, enabling planetesimal growth even in binary systems—offering a solution to the long-standing problem of how 'Tatooine'-like planets form in hostile binary environments.

ABSTRACT

We examine characteristics of circumbinary orbits in the context of current planet formation scenarios. Analytical perturbation theory predicts the existence of nested circumbinary orbits that are generalizations of circular paths around a single star. These orbits have forced eccentric motion aligned with the binary as well as higher frequency oscillations, yet they do not cross, even in the presence of massive disks and perturbations from large planets. For this reason, dissipative gas and planetesimals can settle onto these "most circular" orbits, facilitating the growth of protoplanets. Outside a region close to the binary where orbits are generally unstable, circumbinary planets form in much the same way as their cousins around a single star. Here, we review the theory and confirm its predictions with a suite of representative simulations. We then consider the circumbinary planets discovered with NASA's Kepler satellite. These Neptune- and Jupiter-size planets, or their planetesimal precursors, may have migrated inward to reach their observed orbits, since their current positions are outside of unstable zones caused by overlapping resonances. In situ formation without migration seems less likely, only because the surface density of the protoplanetary disks must be implausibly high. Otherwise, the circumbinary environment is friendly to planet formation, and we expect that many Earth-like "Tatooines" will join the growing census of circumbinary planets.

Motivation & Objective

• To resolve the longstanding challenge of how planets form in the dynamically hostile environment of circumbinary systems.
• To investigate whether stable, low-eccentricity orbits exist around binary stars that allow for gentle planetesimal collisions and growth.
• To test whether in situ planet formation is viable without requiring large-scale migration, contrary to prevailing assumptions.
• To compare theoretical predictions with observed Kepler circumbinary planets and assess the viability of in situ formation models.

Proposed method

• Applying analytical perturbation theory (Lee & Peale, 2006; Leung & Lee, 2013) to derive a family of nested, stable circumbinary orbits with minimal radial excursions.
• Modeling the dynamics of gas and planetesimals on these 'most circular' orbits, which have no free eccentricity and thus avoid phase-locked collisions.
• Using numerical simulations to confirm that these orbits remain non-intersecting and stable under perturbations from massive disks and planets.
• Assessing the role of disk-driven migration and gravitational scattering in delivering planets to observed orbits, particularly for Kepler-16b and similar planets.
• Evaluating the required initial surface densities of protoplanetary disks to support in situ formation, comparing them to the Minimum Mass Solar Nebula (MMSN).
• Comparing theoretical orbital characteristics (eccentricity, inclination) of circumbinary planets with those of planets around single stars to test model consistency.

Experimental results

Research questions

• RQ1 Can stable, low-eccentricity orbits exist around binary stars that prevent destructive collisions between planetesimals?
• RQ2 Do the 'most circular' orbits derived from perturbation theory allow for efficient in situ planetesimal growth in circumbinary disks?
• RQ3 Is in situ planet formation around binaries viable without requiring large-scale migration, given realistic disk surface densities?
• RQ4 How do the orbital characteristics of observed Kepler circumbinary planets compare with predictions from the most circular orbit model?
• RQ5 What role does gas damping play in enabling planetesimals to settle onto stable, non-intersecting orbits in binary systems?

Key findings

• Nested, stable circumbinary orbits exist that are generalizations of circular orbits around single stars, with minimal radial excursions and no intersections.
• These orbits have no free eccentricity, which prevents the phase-locked collisions that lead to destructive stirring in previous models.
• Gas and planetesimals can dynamically cool and settle onto these most circular orbits, enabling gentle, growth-promoting collisions.
• In situ planet formation is viable in circumbinary systems if planetesimals are initialized on these stable orbits, avoiding the need for high initial surface densities.
• The required initial disk surface densities for in situ formation are implausibly high (10–20× MMSN), making migration or scattering more plausible for observed Kepler planets.
• Migration through a gaseous disk avoids unstable resonances and allows planets to form beyond the snow line and reach their current orbits, consistent with observations.