Validity of the Poisson multiplicity model

Determine whether a truncated Poisson distribution provides a suitable representation of the real intrinsic planetary-system multiplicity distribution.

Background

ExoMOD models the intrinsic number of planets per system using alternative multiplicity distributions, including a truncated Poisson distribution with a maximum multiplicity of 10. In this formulation, the parameter λ_pl controls the mean multiplicity of the corresponding untruncated Poisson distribution, while the truncation changes the actual mean number of planets per system.

The Poisson model favors systems whose multiplicities are near λ_pl, but the paper explicitly notes that its suitability for real planetary systems is unknown. This uncertainty motivates comparison with a Zipfian multiplicity model and reflects the broader difficulty of inferring intrinsic planetary architectures from transit observations alone.

References

The Poisson distribution favors systems with $m \sim \lambda_{\rm pl}$, but we do not know a priori whether this is a good model for the real multiplicity distribution.

— ExoMOD I. A Forward Model for the Orbital Architecture of Kepler Multi-Planet Systems  (2608.28548 - Nesvorny et al., 28 Aug 2026) in Section 2.2.2, “Multiplicity”