A substellar flyby that shaped the orbits of the giant planets

TL;DR

The paper investigates whether the solar system's giant planets' modest eccentricities and inclinations can arise from an external perturbation rather than solely from planet–planet interactions. It uses a Monte Carlo suite of $5\times10^4$ flybys in an open-cluster environment, sampling substellar masses from the IMF and integrating with $N$-body methods; a log-spectral distance metric $\mathcal{M}$ compares the post-flyby secular spectra to a solar-system reference ensemble. They find about $0.844\%$ of close flybys produce solar-system-like spectra, with a best-match case at $m_\star\simeq 8.27\,M_J$, $q_\star\simeq 1.69\mathrm{AU}$, $v_\infty\simeq 2.69\mathrm{km\,s^{-1}}$, and $i_\star\simeq 131^\circ$, closely reproducing the giant planets' fundamental secular modes. The inferred probability of such an encounter shaping the solar system is around $1$ in $9{,}005$ per cluster lifetime, implying that substellar flybys are a plausible contributor to planetary architectures and have broad implications for Kuiper belt dynamics and exoplanet system histories, with terrestrial planets often surviving the encounter.

Abstract

The modestly eccentric and non-coplanar orbits of the giant planets pose a challenge to solar system formation theories which generally indicate that the giant planets emerged from the protoplanetary disk in nearly perfectly circular and coplanar orbits. We demonstrate that a single encounter with a 2-50 Jupiter-mass object, passing through the solar system at a perihelion distance less than 20 AU and a hyperbolic excess velocity of 1-3 km/s, can excite the giant planets' eccentricities and mutual inclinations to values comparable to those observed. We describe a metric to evaluate how closely a simulated flyby system matches the eccentricity and inclination secular modes of the solar system. We estimate that there is about a 1-in-9000 chance that such a flyby occurs during the solar system's residence in its primordial cluster and produces a dynamical architecture similar to that of the solar system. The scenario of an ancient close encounter with a substellar object offers a plausible explanation for the origin of the moderate eccentricities and inclinations and the secular architecture of the planets. We discuss some broader implications of disruptive flyby encounters on planetary systems in the Galaxy.

Figures (10)

• Figure 1: A comparison of IMFs. While there is uncertainty in the substellar regime, most IMF models are consistent in modeling the number density of substellar objects within one order of magnitude. This paper uses the Chabrier (2003) IMF. We also highlight the approximate mass range for which flybys successfully produce a dynamical architecture similar to the solar system (see also Fig. \ref{['fig:flyby-params']}).
• Figure 2: Here we show the distributions of the flyby parameters ($m_\star$, $q_\star$, $v_\infty$) in our simulations as well as the subset of those parameters that led to a close match with the solar system. We highlight in blue the flyby systems that are similar to the solar system when compared to itself.
• Figure 3: A snapshot of the flyby simulation that produces the best match to the solar system. The flyby parameters for the encounter are $m_\star = 8.27\,\mathrm{M}_\mathrm{J}$, $q_\star = 1.69\,\mathrm{AU}$, $v_\infty = 2.69\,\mathrm{km\,s}^{-1}$, and $i_\star = 131^{\circ}$.
• Figure 4: The time evolution of the giant planets before, during, and after the flyby shown in Figure \ref{['fig:orbit-plot']}. The encounter time is indicated by the vertical line at $t\approx0.2\,\mathrm{Myr}$. The upper panel shows the inclination of the planets (with respect to the final invariant plane) while the lower panel shows the semi-major axes, the perihelia, aphelia distances. The maximum eccentricity range of each planet is also indicated.
• Figure 5: Power spectra of the complex eccentricities (left column) and complex inclinations (right column). The black line shows the best matching flyby case (as in Figures \ref{['fig:orbit-plot']} and \ref{['fig:flyby-effect']}), while the color-shaded plots show the ensemble of spectra of the solar system taken in 20 Myr--long segments from an ensemble of 5 Gyr--long integrations. The median power at each frequency of the solar system ensemble is shown as a dark coloured line, with lighter shaded regions representing the one--, two-- and three--$\sigma$ deviations. The median power spectrum of the solar system is very similar to the simulated best case flyby.