The Inner Kernel of the Classical Kuiper Belt

TL;DR

This work addresses the search for additional dynamical substructures in the classical Kuiper belt beyond the known kernel by transforming orbits into barycentric free elements and applying DBSCAN clustering. The authors develop a Hamiltonian-based formalism to extract free inclination $I_{\rm free}$ and free eccentricity $e_{\rm free}$, removing forced components due to planetary perturbations and using solar-system eigenfrequencies $f_i$ and $g_i$. They condition clustering on recovering the known kernel to robustly identify a secondary feature, the inner kernel near $a_{\rm bary} \sim 43$ AU, with tighter $e_{\rm free}$ and $I_{\rm free}$ distributions and a potential link to the 7:4 Neptune resonance. The findings constrain the dynamical heating and may inform formation scenarios, with LSST-era data expected to help determine whether the kernel and inner kernel are distinct structures or parts of a single broader component. Overall, the paper demonstrates a principled way to uncover subtle structures in the Kuiper belt using barycentric free elements and density-based clustering.

Abstract

The `kernel' of the classical Kuiper belt was discovered by Petit et al. (2011) as a visual overdensity of objects with low ecliptic inclinations and eccentricities at semimajor axes near 44 AU. This raises the question - are there other structures present in the classical Kuiper belt? If there are, clustering algorithms applied to orbits transformed into free elements may yield the best chance of discovery. Here, we derive barycentric free orbital elements for objects in the classical Kuiper belt, and use the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to identify a new structure, which we dub the inner kernel, located at $a \sim 43 \mathrm{\; AU}$ just inward of the kernel ($a \sim 44 \mathrm{\; AU}$), which we also recover. It is yet unclear whether the inner kernel is an extension of the kernel or a distinct structure. Forthcoming observations, including those by the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) may provide further evidence for the existence of this structure, and perhaps resolve the question of whether there are two distinct structures.

Figures (4)

• Figure 1: DBSCAN results for $N_{min} = 50$ and $\epsilon = 0.15$. Kernel-like cluster in red, new cluster in blue, non-clustered classicals in gray.
• Figure 2: DBSCAN results for $N_{min} = 50$ and $\epsilon = 0.16$, illustrating (relative to Figure \ref{['fig:scatter']}) that a slightly higher value of $\epsilon$ can lead to a combined kernel plus inner kernel cluster (shown here in purple). As in Figure \ref{['fig:scatter']}, the non-clustered classicals are shown in gray.
• Figure 3: Normalzed histograms of the $a_\text{bary}$, $e_{\text{free}}$, and $I_{\text{free}}$ distributions shown in Figure \ref{['fig:scatter']}. Dotted lines show best-fit Gaussian distribution for $a_\text{bary}$ and Rayleigh distributions for $e_{\text{free}}$ and $I_{\text{free}}$. These kernel-like and newly identified clusters have distributions of $a_\text{bary}$ described by Gaussians with means of $44.00 \mathrm{\; AU}$ and $42.98 \mathrm{\; AU}$ and standard deviations of $0.25 \mathrm{\; AU}$ and $0.24 \mathrm{\; AU}$, respectively. Rayleigh distributions with modes of $0.026$ and $0.046$ describe their respective distributions of $e_{\text{free}}$, and dispersions of $1.4^{\circ}$ and $1.3^{\circ}$ describe their respective distributions of $I_{\text{free}}$. The fit of the $e_{\rm free}$ distributions to the Rayleigh form is not good; fitting these distributions instead with Gaussians would yield means of $0.063$ and $0.036$, and standard deviations of $0.017$ and $0.011$, respectively.
• Figure 4: Normalized histograms of the $a_\text{bary}$, $e_{\text{free}}$, and $I_{\text{free}}$ distributions shown in Figure \ref{['fig:scatter2']}. Dotted lines show best-fit bi-modal Gaussian distribution for $a_\text{bary}$ and Rayleigh distributions for $e_{\text{free}}$ and $I_{\text{free}}$. The distribution of $a_\text{bary}$ is described by two Gaussian distributions with means of $44.01\hbox{;AU}$ and $43.00\hbox{;AU}$, standard deviations of $0.26\hbox{;AU}$ and $0.29\hbox{;AU}$, and relative weights of 0.62 and 0.38, respectively. Rayleigh distributions with modes of $0.040$ and $1.5^{\circ}$ describe the distributions of $e_{\text{free}}$ and $I_{\text{free}}$, respectively. Fitting $e_{\rm free}$ instead with two Gaussians would yield means of $0.037$ and $0.072$, standard deviations of $0.013$ for each, and relative weights of $0.59$ and $0.41$, respectively. Non-clustered classicals in gray.