The curiously warped mean plane of the Kuiper belt (1704.02444v3)

Abstract: We measured the mean plane of the Kuiper belt as a function of semi-major axis. For the classical Kuiper belt as a whole (the non-resonant objects in the semi-major axis range 42--48~au), we find a mean plane of inclination $i_m=1.8^{\circ}$$^{+0.7^{\circ}}_{-0.4^{\circ}}$ and longitude of ascending node $\Omega_m=77^{\circ}$$^{+18^{\circ}}_{-14^{\circ}}$ (in the J2000 ecliptic-equinox coordinate system), in accord with theoretical expectations of the secular effects of the known planets. With finer semi-major axis bins, we detect a statistically significant warp in the mean plane near semi-major axes 40--42~au. Linear secular theory predicts a warp near this location due to the $\nu_{18}$ nodal secular resonance, however the measured mean plane for the 40.3-42~au semi-major axis bin (just outside the $\nu_{18}$) is inclined $\sim13^{\circ}$ to the predicted plane, a nearly 3-$\sigma$ discrepancy. For the more distant Kuiper belt objects of semi-major axes in the range 50--80~au, the expected mean plane is close to the invariable plane of the solar system, but the measured mean plane deviates greatly from this: it has inclination $i_m=9.1^{\circ}$$^{+6.6^{\circ}}_{-3.8^{\circ}}$ and longitude of ascending node $\Omega_m=227^{\circ}$$^{+18^{\circ}}_{-44^{\circ}}$. We estimate this deviation from the expected mean plane to be statistically significant at the $\sim97-99\%$ confidence level. We discuss several possible explanations for this deviation, including the possibility that a relatively close-in ($a\lesssim100$~au), unseen small planetary-mass object in the outer solar system is responsible for the warping.

• The paper identifies that the classical Kuiper Belt’s mean plane (i=1.8° and Ω=77°) slightly deviates from linear secular theory predictions.
• The analysis detects a statistically significant warp near 40–42 AU, aligning with ν18 resonance expectations yet showing a nearly 3-σ discrepancy.
• The study finds distant KBOs (50–80 AU) have a markedly different plane (i=9.1° and Ω=227°), suggesting potential gravitational influence from an unseen planetary-mass object.

The Warped Mean Plane of the Kuiper Belt

This paper, authored by Kathryn Volk and Renu Malhotra, investigates the mean plane of the Kuiper Belt objects (KBOs) as a function of their semi-major axes. The paper challenges previous assumptions about the alignment of the Kuiper Belt's mean plane with the invariable plane of the solar system, suggesting a more complex dynamical structure influenced by both known and potentially unknown planetary bodies.

Key Findings

1. Classical Kuiper Belt Mean Plane: The paper measures the mean plane for the classical Kuiper Belt, defined as non-resonant KBOs within the semi-major axis range of 42–48 AU. The analysis reveals a mean plane with an inclination $i_m=1.8^{\circ}$ and a longitude of ascending node $\Omega_m=77^{\circ}$. These results align well with the predictions from linear secular perturbation theory considering the known planets, albeit with minor deviations.
2. Detection of a Warp: By examining finer bins of semi-major axes, the authors report a statistically significant warp in the mean plane near the semi-major axis range of 40–42 AU. This finding aligns with theoretical expectations of a warp driven by the $\nu_{18}$ nodal secular resonance. However, there is a slight discrepancy, nearly 3-$\sigma$, between the measured mean plane outside the $\nu_{18}$ and the predicted forced plane, hinting at mechanisms not completely accounted for by current secular theory.
3. More Distant Kuiper Belt Objects: KBOs with semi-major axes in the range of 50–80 AU exhibit a mean plane with an inclination $i_m=9.1^{\circ}$ and a longitude of ascending node $\Omega_m=227^{\circ}$, significantly deviating from the expected mean plane close to the solar system's invariable plane. This deviation is statistically significant, with confidence levels between 97% and 99%.

Implications and Speculations

The pronounced deviation observed in the 50–80 AU range invites several potential explanations:

• Unknown Perturbations: A compelling possibility discussed is the gravitational influence of an unseen planetary-mass object located within 100 AU, suggesting that such an object's presence could warp the Kuiper Belt's mean plane. The authors propose that even a Mars-mass body could suffice to create the observed deviations if located at suitable distances and inclinations.
• Implications for Solar System Models: The findings underscore the need for refined models of the solar system's outer dynamics, potentially including contributions from undetected masses. These models have implications for our understanding of the solar system's formation and evolution, particularly regarding the distribution and dynamical behaviors of trans-Neptunian objects.
• Observational Extensions: The work suggests new targets for observational campaigns aimed at hunting for distant planetary bodies. Detection of such perturbers could significantly enhance our understanding of the dynamical history and current structure of the outer solar system.

In conclusion, the paper offers a meticulous analysis of the Kuiper Belt's mean plane, revealing substantial complexity in its orbital alignment. The paper not only challenges existing paradigms but also sets a foundation for future explorations into the outer reaches of our solar apparatus.