COD: An algorithm for shape reconstruction of transiting celestial bodies through topological optimization

G. Nachmani*, T. Mazeh, N. Sochen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a novel algorithm, COD - Compact Opacity Distribution, for shape reconstruction of a celestial body that has been observed to occult a star, using the photometric time-series observations of the occultation. COD finds a solution to the light-curve inversion problem for an optically thick occulter having an approximately convex shape, together with an estimate of its size, impact parameter and velocity, relative to the occulted star. The algorithm is based on an optimization scheme that uses topological constraints and an objective function for the geometry of the occulter. The constraints of the problem follow linear relations, which enable the use of linear programming optimization as the mathematical framework. Multiple tests of the algorithm were performed, all of which resulted in high correlations between the simulated and obtained shapes of the occulting objects, with errors within 5per cent in their projected velocities and horizontal sizes, and within 0.1 in their impact parameters. These tests include a video of a solar eclipse by Phobos, as seen by NASA's Curiosity rover, which was collapsed into its corresponding light curve and reconstructed afterwards. We applied COD to the mysterious case of VVV-WIT-08 - a single deep occultation (sim 96rm per cent) of a giant star lasting for over 200 d. The analysis, which did not assume any specific shape of the occulter, suggested an object with a projected opacity distribution resembling an ellipse with an eccentricity of ∼0.5, tilted at ∼30 degrees relative to the direction of motion, with a semi-minor axis similar to the stellar radius.

Original languageEnglish
Pages (from-to)5301-5313
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
StatePublished - 1 Apr 2022


FundersFunder number
United States-Israel Binational Science Foundation


    • astrometry and celestial mechanics: occultations
    • methods: data analysis
    • planets and satellites: general
    • techniques: photometric


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