N-body interactions and collisions in circumstellar disks for planar and inclined binary star configurations

TL;DR

This study investigates terrestrial planet formation in S-type circumstellar disks around binary stars with varying inclinations, focusing on the post-gas phase where embryo–planetesimal gravity dominates. Using GPU-accelerated N-body simulations (GANBISS) with two distinct initial disk states (EIC and PIC), the authors analyze dynamical evolution, migration, and stability over $10\,\mathrm{Myr}$ and post-process collisions with the Lei–Ste12 analytic model. Key findings show that a misaligned secondary tends to align disk objects with the binary plane and induces mild inward migration of embryos, while collision outcomes shift toward more destructive and hit-and-run events in inclined configurations, reducing accretion efficiency. The results emphasize that binary alignment and initial disk conditions critically determine the final planetary architectures, with implications for planet formation in binaries with separations $a_b$ of tens to hundreds of au. Long-term stability and realistic fragmentation require further work beyond perfect merging, including SPH treatments and fragmentation modeling.

Abstract

The discovery of exoplanets in binary star systems-now numbering about 850 of the nearly 4,600 known exoplanet systems-raises questions about whether observational bias or stellar companions inhibit planet formation. While most studies on terrestrial planet formation assume planar configurations, wide binaries likely feature random inclinations, potentially disrupting planet-forming disks. This study explores the evolution of embryo-planetesimal disks in S-type motion in misaligned binary systems, focusing on the stage after the gas phase when terrestrial planet formation begins and gravitational interactions dominate. Using our GPU-accelerated N-body code GANBISS, we simulate disks with 2,000 planetesimals and 25 planetary embryos, studying the influence of the planetesimals on the evolution of the embryos and tracking their growth through collisions. After the simulations, we analyse collision outcomes with an analytical model. Moreover, for certain inclined binary configurations, we compare dynamically excited (perturbed by the secondary star) with cold disks in inclined configurations, as the distribution after the gas phase in misaligned binaries remains unclear. Our simulations reveal two key outcomes: (i) embryos migrate slightly inward in misaligned systems, and (ii) The initial large oscillations in embryos' inclinations and nodes around the respective values of the secondary star dampen over time. Collision analysis shows distinct differences: planar systems favour accretive collisions, while inclined configurations exhibit more destructive events. These findings underscore the sensitivity of planet formation dynamics to binary star alignment and initial disk conditions.

Figures (11)

• Figure 1: Snapshots of the evolution of eccentricity $e_d$, inclination $i_d$, and the longitude of the ascending nodes $\Omega_d$ of the disk objects for the configuration a30-e02-i20-EIC. The blue circles represent the planetesimals and the red ones the planetary embryos. The radius of the circles are proportional to their size. The orange dashed line in the middle panel indicates the inclination of the secondary star ($i_b=20\degr$).
• Figure 2: Comparison of the evolution of the inner disk of planetary embryos ($a_{\mathrm{emb}}\leq 2\ \mathrm{au}$, shown in orange) and the outer one ($a_{\mathrm{emb}}>2\ \mathrm{au}$, shown in blue) for the same configurations shown in Fig. \ref{['fig:semMaj']}. Left panels show for each configuration the mass-weighted evolution of the inclination, middle panels the evolution of the mass-weighted inclination of the planetary embryos with respect to the binary stars plane $i_{d-b}\left(=\|i_d - i_b\| \right)$, and right panels the evolution of the mass-weighted ascending node.
• Figure 3: The evolution of the semi-major axis of the planetary embryos (color coded) and the planetesimals (gray) for $10\ \mathrm{Myr}$. In the top panels tight binary star configurations ($a_b=30\ \mathrm{au}$) are shown, while in the bottom panels the evolution in wider binary star configurations ($a_b=100\ \mathrm{au}$) is presented. The evolution is displayed for planar binary star configurations (left panels), inclined binary star configurations ($i_b=20\degr$) with an initially dynamically cold disk (middle panels), and inclined binary star configurations with an initially dynamically excited disk (right panels).
• Figure 4: Overview of the disk objects' migration according to the evolution of the mass weighted semi-major axis (equation (\ref{['eq:mw']})) of the planetary embryos $\langle a_{\mathrm{emb}}\rangle$ plotted against the mass weighted semi-major axis of the planetesimals $\langle a_{\mathrm{plt}}\rangle$ for all binary star configurations. The black circle shows the starting value at the beginning of the simulation, the black cross at the end of the simulation. Different line styles (dotted, dashed, and solid) correspond to different inclinations of the binary system $i_b$. Different colours correspond to different binary and initial disk configurations.
• Figure 5: The same as in Fig. \ref{['fig:multiTStep30a02e20iE']}, but for a initially dynamically cold planetary embryo-planetesimal disk and for the configuration: a100-e02-i20.