Possible Dynamical Pathways to the Misalignment of the VHS 1256-1257 System

TL;DR

The paper investigates VHS 1256-1257, a hierarchical triple with an inner brown dwarf binary and a retrograde, nearly polar tertiary, to understand the origin of its extreme misalignment. Using secular three-body dynamics expanded to hexadecapole order (with GR and spin effects), the authors show that EKL-like mechanisms can generate the inner binary's high eccentricity $e_1$ and the tertiary obliquity $\psi_3$, but cannot by themselves produce the observed mutual inclination $i_{ m tot}$. They test three origin pathways: a hidden fourth companion, a stellar flyby, and fragmentation-driven formation; a distant, unseen companion can flip the outer orbit and, together with EKL and spin precession, yield the observed configuration, while flybys are highly unlikely and fragmentation remains a plausible alternative. The study highlights the strengths and limitations of triple dynamics in shaping extreme planetary architectures and outlines observational tests to constrain hidden perturbers.

Abstract

Circumbinary planets (CBPs) provide a unique window into planet formation and dynamical evolution in complex gravitational environments. Their orbits are shaped not only by the protoplanetary disk but also by the perturbations from two stellar hosts, making them sensitive probes of both early- and late-stage dynamical processes. In this work, we investigate the unusual architecture of the VHS J125601.92-125723.9 system, where a retrograde, nearly polar tertiary orbits an extremely low-mass substellar binary in a hierarchical triple configuration. We find that triple body dynamics can naturally reproduce the observed high eccentricity of the inner binary and the tertiary's near-polar obliquity. However, this configuration alone cannot account for the observed mutual inclination, which is both near-polar and retrograde. This tension suggests two possible formation pathways: either the planet formed in an aligned, protoplanetary disk-like configuration and was later tilted by an additional, undetected fourth companion (below current Gaia limits), or the system formed close to its current state. Stellar flybys, in contrast, are unlikely due to their long timescales. Our results highlight both the explanatory power and the limitations of triple dynamics, and the potential role of hidden companions in shaping extreme planetary architectures.

Figures (9)

• Figure 1: A cartoon (not to scale) of the VHS 1256-1257 system depicting the hierarchical configuration and angles of interest. The frame of reference is the invariable plane. $\vec{L}_1$ ($\vec{L}_2$) is the orbital angular momentum of the inner (outer) orbit; The mutual inclination, $i_{\rm tot}$, is the angle between these two orbital angular momentum vectors. $\vec{S}_b$ is the tertiary spin axis, and $\psi_3$, the tertiary obliquity, is the angle between the planet's spin axis and the outer orbital angular momentum vector. The semimajor axes (SMA) are $a_1$ for the inner binary and $a_2$ for the outer binary.
• Figure 2: Left: An example time evolution that landed in the target region. We note that the eccentricity was excited from an initial value of $e_{1i}=0.33$, demonstrating that the final inner orbit eccentricity is not strongly dependent on the initial value. The inclination remains fairly stable, other than small spikes that coincide with the eccentricity excursions. The initial tertiary obliquity for this system was $\psi_{3i}=52.6^{\circ}$. Right: An example time evolution for one of the samples that landed in the target region. We note that the eccentricity was excited from an initial value of $e_{1i}=0.35$. The inclination was stable except for the peaks corresponding to the eccentricity excursions. In this system, the initial tertiary obliquity was $\psi_{3i}=131.4^{\circ}$.
• Figure 3: The evolution outcome of the 2000 sample systems with $q=\frac{m_{\rm A}}{m_{\rm B}}\in[0.9,1.0]$ and $m_{3}\in[15$ M$_{\rm J},17$ M$_{\rm J}]$ corresponding to a deuterium inert-model for VHS 1256 b. Here, we show in total $16\times 10^5$ realizations $120-160$ Myrs. The red dashed lines indicate $90^{\circ}$. The pink shaded boxes highlight the "target region", where we define the target region based on the observational constraints, $e_{1}\in[0.8,0.9]$, $i_{\rm tot}\in[100^{\circ},130^{\circ}]$, and $\psi_{3}\in[65^{\circ},115^{\circ}]$. For each system, $400$ timestamps are considered, ranging from $120$ to $160$ Myr. If at a given timestamp, the system obeys all three observational constraints, the point turns blue. If it does not, it turns beige. Once all timestamps are considered for each system, the blue points are accumulated and displayed by the blue density clouds, while the beige points are accumulated and displayed by the beige density clouds.
• Figure 4: Behavior of $\psi_{1}$ and $\psi_{2}$, the obliquities of VHS 1256 A and VHS 1256 B, respectively, for the systems that evolved to match the observed configuration. The left panel depicts the obliquity distribution for one member of the inner binary, while the right panel depicts the obliquity distribution for the other. In both panels, the purple line corresponds to systems for which $\psi_{1i}$ and $\psi_{2i}$ were independently chosen from uniform distributions between $0$ and $\pi$ and $e_{1i}$ was chosen from a uniform distribution between $0$ and $1$ (i.e., the systems plotted in Figure \ref{['fig:timestamps16']}.) The orange line corresponds to systems for which $\psi_{1i}$ was chosen from a uniform distribution between $0$ and $\pi$, $\psi_{2i}$ was chosen to be the same as $\psi_{1i}$, and $e_{1i}$ was chosen between $0$ and $1$. The green line corresponds to systems for which $\psi_{1i}$ and $\psi_{2i}$ were both initialized at $0$, and $e_{1i}$ was again chosen between $0$ and $1$. The red line depicts systems where $\psi_{1i}$ and $\psi_{2i}$ were chosen independently between $0$ and $\pi$, and $e_1$ was initialized at $e_{1i}=0.883$. In both panels, all $400$ time points between $120-160$ Myr are considered and accumulated into the pictured density contours. There is no correlation between $\psi_1$ and $\psi_2$.
• Figure 5: Left: Stability of a potential fourth companion in the $a_c$–$e_c$ plane. The purple dashed line shows the Mardling+01 criterion for $m_c=35$ M$_{\rm J}$ and $i_{2,c}=65^{\circ}$. The black solid line shows the $\epsilon$ stability criterion from Lithwick+11. If the 1pN precession timescale $t_{\rm 1256\ b}^{\rm 1pN}$ is shorter than the quadrupole timescale $t_{\rm quad}$, eccentricity excitation is suppressed. The blue lines correspond to companion masses from $0$–$100$ M$_{\rm J}$, computed by equating $t_{\rm quad}$ with $t_{\rm 1256\ b}^{\rm 1pN}$. Below each line, GR precession suppresses inclination/eccentricity excitation; above each line, EKL can flip the orbit. Right: Stability of a potential fourth companion in the $a_c$–$m_c$ plane. The dashed green line is where the octupole timescale equals the system age ($140$ Myr) for $e_c=0.01$. Above this line, $t_{\rm oct}>140$ Myr and flips are not expected. Blue lines show eccentricities $0.01$–$0.9$, set by $t_{\rm quad}=t^{\rm 1pN}_{\rm 1256\ b}$; above these lines, EKL can excite VHS 1256 b's eccentricity and produce flips, while below GR precession suppresses them. The purple dashed line shows the Mardling+01 criterion for $e_c=0.5$. The black line shows the Lithwick+11$\epsilon$ criterion. Stable configurations require the companion's minimum pericenter to exceed the maximum apocenter of VHS 1256 b. The pink dashed line marks this equality for $e_c=0.5$; below the black line, the system is unstable. We note these parameters fall below the Gaia exclusion region.