The Kresáks’ diagram: Hyperbolic meteoroid orbits and their confidence level

¹ INAF – Astrophysical Observatory of Turin, Via Osservatorio 20, 10025 Pino Torinese, TO, Italy
² Department of Physics, University of Turin, Via Pietro Giuria 1, 10125 Torino, Italy
³ Astronomical Institute, Slovak Academy of Sciences, Dubravska cesta 9, 85404 Bratislava, Slovakia
⁴ Department of Astronomy, Physics of the Earth, and Meteorology, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina 1, 84215 Bratislava, Slovakia
⁵ Astronomical Institute of the Czech Academy of Sciences, Fricova 298, 25165 Ondřejov, Czech Republic

^★ Corresponding author: dario.barghini@inaf.it; sdurisova@ta3.sk; maria.hajdukova@savba.sk

Received: 26 February 2025
Accepted: 16 July 2025

Abstract

Context. Improving the precision and accuracy of meteor measurements and reliably determining the uncertainties of meteor parameters are two of the main challenges in meteor astronomy research today. These parameters significantly affect the computation of meteoroid orbits, and using erroneous orbits can distort the analysis of the inferred meteoroid population.

Aims. We aim to provide a tool to estimate the required accuracy of meteor data in order to unambiguously identify each orbit type and evaluate the reliability of database uncertainties, focusing in particular on hyperbolic orbits. This work assists database authors by improving data-reduction processes and database users by simplifying data selection according to accuracy needs.

Methods. By simultaneously visualising meteor parameters and meteoroid orbits, we assessed uncertainties and their propagation, starting from measurement errors that are provided in meteor databases. In particular, our analysis scheme suggests whether or not a hyperbolic meteor candidate could be considered, at a given significance level, to be of interstellar nature. In order to do so, and for each candidate, we evaluated the extension of its confidence region beyond the parabolic limit on a plot displaying geocentric speed against radiant elongation.

Results. The application of the proposed procedures to several meteor and fireball databases revealed the ineffectiveness of a 3σ filtering process in identifying interstellar meteor candidates among the population of hyperbolic meteors. To test whether or not this evidence can be attributed to an underestimation of measurement errors, we developed an estimator, R, quantifying the slope of the relative decrease of the hyperbolic fraction with increasing confidence levels. According to our model, R > 1 suggests an underestimation of measurement errors. By referring to two recently established networks, we determined R = 1.19 ± 0.05 for the Fireball Recovery and InterPlanetary Observation Network (FRIPON) and R = 3.10 ± 0.02 for the Global Meteor Network (GMN). These results suggest a more reliable uncertainty determination for FRIPON, despite the lower precision of its data compared to that of the GMN data.

Conclusions. Our results indicate that when analysing individual meteoroid orbits of a database, it is essential to firstly evaluate the entire database, as this provides an independent assessment of the reported accuracy of the orbits. It is commonly observed that the parameter uncertainties reported in meteor databases reflect the measurement precision within data processing, rather than the actual accuracy limits, thus providing less relevant information for users. The proposed name for the tool introduced for this purpose is the Kresáks’ diagram, named in honour of the authors of the original representation.