[Paper Review] Pair-correlation analysis of HD 10180 reveals a possible planetary orbit at about 0.92 AU

Kasper Olsen, J. Bohr|arXiv (Cornell University)|Sep 28, 2010

Stellar, planetary, and galactic studies10 references3 citations

TL;DR

This study applies pair-correlation analysis to the exoplanetary system HD 10180, using logarithmic orbital positions and Gaussian-smoothed planet distributions to detect long-range correlations. The method reveals a statistically significant, nearly equidistant peak structure in the pair-correlation function, indicating a regular orbital architecture; notably, the pattern implies a seventh, unconfirmed planet at 0.92 ± 0.05 AU, consistent with the six known planets but not with the previously reported unconfirmed object.

ABSTRACT

The pair-correlations between the positions of the six known planets in the exoplanetary system HD 10180 are studied. There are six non-trivial and almost equally spaced peaks. This demonstrates longer-ranged positional order between the orbits and suggests a seventh orbit at 0.92 AU that is consistent with these correlations.

Motivation & Objective

• To detect underlying orbital regularities in exoplanetary systems without relying on arbitrary planet numbering schemes.
• To investigate whether long-range correlations exist between planetary orbits in HD 10180, a system with six confirmed and one unconfirmed planet.
• To determine if the observed orbital spacing suggests the presence of an additional, yet-undetected planet.

Proposed method

• The pair-correlation function P(Δ) is computed using the integral P(Δ) = ∫ρ(x+Δ)ρ(x)dx, where ρ(x) is a sum of Gaussian functions centered at the logarithmic semi-major axes of the planets.
• Logarithmic orbital positions are defined as x_i = log(a_i / 10^6 km), with σ = 0.075 to model measurement uncertainty.
• All planet weights α_i are set to unity, as the pair-correlation is insensitive to their exact values.
• The analysis detects the number of side-peaks in P(Δ) to infer the number of planets and identify potential missing orbits.
• The method is invariant under renumbering of planets, avoiding biases from arbitrary indexing.
• A mesh scan over candidate orbital positions between planets f and g identifies the optimal location for a potential seventh planet.

Experimental results

Research questions

• RQ1 Does the pair-correlation function of HD 10180’s planets reveal long-range orbital regularities independent of planet numbering?
• RQ2 Is there evidence for a missing planetary orbit consistent with the observed six planets in the system?
• RQ3 Does the unconfirmed object at 0.022 AU belong to the same dynamical group as the six known planets?

Key findings

• The pair-correlation function P(Δ) for HD 10180 exhibits six side-peaks on each side of the central peak, indicating a regular orbital structure with six planets.
• The presence of six side-peaks instead of the expected five for six planets suggests the existence of a seventh orbital position.
• The optimal position for the seventh planet is determined to be at 0.92 ± 0.05 AU, located between planets f and g.
• Including the unconfirmed object at 0.022 AU disrupts the correlation pattern, indicating it is not part of the same orbital group.
• The method successfully identifies a missing orbit without relying on planet numbering or prior assumptions about orbital order.
• The analysis demonstrates that orbital regularities can be detected via correlation structure even when the number of planets is not known in advance.