Operating manual on how to find an Earth Trojan asteroid

Introduction
When talking about Trojan asteroids -- bodies orbiting around the L4 or L5 Lagrangian points of a Sun-planet system -- it is inevitable to refer to Jupiter. This giant planet has, by far, the largest reservoir of Trojan asteroids with thousands of objects discovered since 1906. We currently know, however, that other planets are also able to host asteroids in such a peculiar orbital configuration, although in much smaller number. Trojan asteroids can be important to study the formation and evolution of our Solar System since, some of them – called primordials -- might be remnants of the formation processes of the hosting planet. The first Earth Trojan asteroid (ETA) was discovered in 2010 librating around L4. Thenceforth, several dedicated observational campaigns have been scrutinizing L4 and L5 areas, trying to find a second ETA. In this work we describe how we confirmed (614689) 2020 XL5 as the second ETA and we discuss why it is so arduous to detect these objects with groundbased observations.

Fig.1: The Sun-Earth Lagrangian points. 2020 XL5 is librating around L4. (NOIRLab/NSF/AURA/J. da Silva)

Observations

Asteroid 2020 XL5 was discovered by the Pan-STARRS1 survey on 2020 December 12. An initial orbit determination was obtained from follow-up observations gathered during the next few weeks. Some solutions suggested that 2020 XL5’s orbit could be librating around L4, but the short arc covered with observations was still to short for a long term analysis [8]. However, observations were challenging due to the object’s faintness (V~22 mag) and its proximity with the Sun (ε<40°).

Our team started a follow-up campaign and was able to obtain a few new measurements (Fig.2) of the object during February and March 2021 using ESA’s Optical Ground Station (OGS) 1.0 m telescope, the 4.1 m Southern Astrophysical Research (SOAR) telescope and the 4.3 m Lowell Discovery Telescope (LDT). Despite the successful results of the observation campaign and the consequent improvement of the orbit of 2020 XL5, the arc was still too short for a conclusive result. However, the orbit now allowed us for a detective work among the tons of data from the surveys. Precoveries were found in the files of the Catalina Sky Survey (1.5 m Mt. Lemmon telescope), DECam instrument (4.1 m Victor M. Blanco telescope) and the archive of the 1.8 m Pan-STARRS survey (Fig. 3).

Fig.2: LDT detection of 2020 XL5.

Fig.3: Pan-STARRS ancillary data of 2020 XL5.

Results

Fig.4: a The relative mean longitude (λ_r) evolution of the 2020 XL₅ nominal orbit and clones orbit over 29 000 years, where each clone orbit is represented by a different color, while the green line represents the nominal orbit. b Evolution of λ_r for the nominal orbit of 2020 XL₅. c Stack plot representing the behavior of the nominal orbit and the 800 clone orbits. In the plot the time t₀ = 0 is the mean epoch of the orbits.

With all the data in hand, we generated hundreds of clone orbits along a time span of 29 000 years, applying the Cholesky method for multivariate normal distributions [9]. The study of the relative mean longitude of 2020 XL5 (Fig.4) revealed that the object is indeed a transient ETA, which was captured some 500 years ago and will keep librating around L4 for at least 4000 more years. In addition, we performed a preliminar physical characterization of the asteroid by means of photometry. We estimated its absolute magnitude to be Hr =18.58 (+0.16−0.15), and color indices suggestive of a C-complex taxonomy. Assuming an albedo of 0.06 ± 0.03 we obtained a bulk diameter of 1.18 ± 0.08 km.

References

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[2] Connors, M., Wiegert, P. & Veillet, C. Earth’s Trojan asteroid. Nature 475, 481–483 (2011).

[3] Wiegert, P. A., Innanen, K. A. & Mikkola, S. An asteroidal companion to the Earth. Nature 387, 685–686 (1997).

[4] Whiteley, R. J. & Tholen, D. J. A CCD search for Lagrangian asteroids of the Earth-Sun system. Icarus 136, 154–167 (1998).

[5] Markwardt, L. et al. Search for L5 Earth Trojans with DECam. Mon. Not. R. Astron. Soc. 492, 6105–6119 (2020).

[6] Lifset, N., Golovich, N., Green, E., Armstrong, R. & Yeager, T. A search for L4 Earth Trojan asteroids using a novel track-before-detect multiepoch pipeline. Astron. J. 161, 282 (2021).

[7] Santana-Ros et al. Orbital stability analysis and photometric characterization of the second Earth Trojan asteroid 2020 XL5. Nature Communications 13, 447 (2022)

[8] de la Fuente Marcos, C. & de la Fuente Marcos, R. Transient terrestrial Trojans: comparative short-term dynamical evolution of 2010 TK₇ and 2020 XL₅. Res. Notes Am. Astronomical Soc. 5, 29 (2021).

[9] T., T. N. Essentials of Monte Carlo Simulation (Springer-Verlag, New York, 2013).

Acknowledgements

TSR acknowledges funding from the NEO-MAPP project (H2020-EU-2-1-6/870377). This work was (partially) funded by the Spanish MICIN/AEI/10.13039/ the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ‘María de Maeztu’) through grant CEX2019-000918-M.