TY - JOUR

T1 - COD

T2 - An algorithm for shape reconstruction of transiting celestial bodies through topological optimization

AU - Nachmani, G.

AU - Mazeh, T.

AU - Sochen, N.

N1 - Publisher Copyright:
© 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - 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.

AB - 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.

KW - astrometry and celestial mechanics: occultations

KW - methods: data analysis

KW - planets and satellites: general

KW - techniques: photometric

UR - http://www.scopus.com/inward/record.url?scp=85126818723&partnerID=8YFLogxK

U2 - 10.1093/mnras/stac135

DO - 10.1093/mnras/stac135

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AN - SCOPUS:85126818723

SN - 0035-8711

VL - 511

SP - 5301

EP - 5313

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 4

ER -