Abstract
It is commonly accepted that exoplanets with orbital periods shorter than one day, also known as ultra-short-period (USP) planets, formed further out within their natal protoplanetary disks before migrating to their current-day orbits via dynamical interactions. One of the most accepted theories suggests a violent scenario involving high-eccentricity migration followed by tidal circularization. Here we present the discovery of a four-planet system orbiting the bright (V = 10.5) K6 dwarf star TOI-500. The innermost planet is a transiting, Earth-sized USP planet with an orbital period of ~13 hours, a mass of 1.42 ± 0.18 M⊕, a radius of \(1.16{6}_{-0.058}^{+0.061} \,R_{\oplus}\) and a mean density of \(4.8{9}_{-0.88}^{+1.03}\,{{{\rm{g}}}}\,{{{{\rm{cm}}}}}^{-3}\). Via Doppler spectroscopy, we discovered that the system hosts 3 outer planets on nearly circular orbits with periods of 6.6, 26.2 and 61.3 days and minimum masses of 5.03 ± 0.41 M⊕, 33.12 ± 0.88 M⊕ and \(15.0{5}_{-1.11}^{+1.12}\,M_{\oplus}\), respectively. The presence of both a USP planet and a low-mass object on a 6.6-day orbit indicates that the architecture of this system can be explained via a scenario in which the planets started on low-eccentricity orbits then moved inwards through a quasi-static secular migration. Our numerical simulations show that this migration channel can bring TOI-500 b to its current location in 2 Gyr, starting from an initial orbit of 0.02 au. TOI-500 is the first four-planet system known to host a USP Earth analogue whose current architecture can be explained via a non-violent migration scenario.
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Data availability
TESS photometry is available at the Mikulski Archive for Space Telescopes (MAST) at https://exo.mast.stsci.edu under target name TOI-500.01. The raw HARPS spectra can be retrieved from the ESO Science Archive Facility (http://archive.eso.org/cms.html) under ESO programme IDs 1102.C-0923 (PI: D.G.), 0103.C-0442 (PI: M.R.D.), 0102.C-0338 and 0103.C-0548 (PI: T.T.), and 60.A-9700 and 60.A-9709 (ESO technical time). The ground-based photometry obtained with the LCO telescope, as well as the SOAR and Gemini imaging data, are available on the Exoplanet Follow-up Observing Program (ExoFOP) website (https://exofop.ipac.caltech.edu/tess/) under target name TOI-500.01. The raw Gemini data are available at https://archive.gemini.edu/searchform under Program ID GS-2020A-Q-125. The archival WASP data that support the findings of this study are available from the co-author C. Hellier upon reasonable request (c.hellier@keele.ac.uk). The archival SOAR data that support the findings of this study are available from the co-author C. Ziegler (carlziegler@gmail.com) upon reasonable request. The extracted radial velocities and stellar activity indicators are listed in Supplementary Data 2.
Code availability
The numerical code used to test the low-eccentricity migration pathway is available via Zenodo at https://doi.org/10.5281/zenodo.5877066.
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Acknowledgements
This work was supported by the KESPRINT (www.kesprint.science) collaboration, an international consortium devoted to the characterization and research of exoplanets discovered with space-based missions. This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA Explorer Program. We acknowledge the use of TESS Alert data, which is currently in a beta test phase, from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. Resources supporting this work were provided by the NASA High-End Computing Program through the NASA Advanced Supercomputing Division at Ames Research Center for the production of the SPOC data products. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This work makes use of observations made with the ESO 3.6 m telescope at the European Southern Observatory (ESO), La Silla, under ESO programmes 1102.C-0923, 0102.C-0338, 0103.C-0442, 0103.C-0548, 60.A-9700 and 60.A-9709. We are very grateful to the ESO staff members for their precious support during the observations. We warmly thank X. Dumusque and F. Bouchy for coordinating the shared observations with HARPS and J. Alvarado Montes, X. Delfosse, G. Gaisné, M. Hobson and D. Barrado Navascués, who helped collecting the HARPS spectra. This work has made use of data from the European Space Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the Data Processing and Analysis Consortium has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This work makes use of observations from the LCOGT network. LCOGT telescope time was granted by NOIRLab through the Mid-Scale Innovations Program, which is funded by the National Science Foundation. Some of the observations in the paper made use of the high-resolution imaging instrument Zorro. Zorro was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by S. B. Howell, N. Scott, E. P. Horch and E. Quigley. Data was reduced using a software pipeline originally written by E. Horch and M. Everett. Zorro was mounted on the Gemini South telescope and the Near Infrared Imager (NIRI) was mounted on the Gemini North telescope, of the international Gemini Observatory, a programme of the National Science Foundation’s OIR Lab, which is managed by the Association of Universities for Research in Astronomy under a cooperative agreement with the National Science Foundation on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil) and Korea Astronomy and Space Science Institute (Republic of Korea). Data collected under programme GN-2019A-LP-101. This work was based in part on observations obtained at the SOAR telescope, which is a joint project of the Ministério da Ciência, Tecnologia e Inovações do Brasil, the US National Science Foundation’s NOIRLab, the University of North Carolina at Chapel Hill and Michigan State University. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. L.M.S. and D.G. gratefully acknowledge financial support from the CRT foundation under Grant No. 2018.2323 “Gaseous or rocky? Unveiling the nature of small worlds.” E.Gu. acknowledges the generous support by the Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft. I.G., C.M.P., M.Fr. and A.J.M. gratefully acknowledge the support of the Swedish National Space Agency (DNR 174/18, 65/19, 120/19C). J.K. gratefully acknowledges the support of the Swedish National Space Agency (DNR 2020-00104). S.C., M.E., K.W.F.L., S.G. and A.P.H. acknowledge support by DFG grants RA714/14-1 within the DFG Schwerpunkt SPP 1992, “Exploring the Diversity of Extrasolar Planets”. M.R.D. acknowledges the support by Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)-PFCHA/Doctorado Nacional-21140646, Chile. T.D. acknowledges support from MIT’s Kavli Institute as Kavli postdoctoral fellow. T.T. acknowledges support by the DFG Research Unit FOR 2544 “Blue Planets around Red Stars" project No. KU 3625/2-1. T.T. further acknowledges support by the BNSF programme “VIHREN-2021" project No. КП-06-ДВ/5.
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Contributions
L.M.S. performed the periodogram analysis and the joint analysis with pyaneti, wrote most of the text and coordinated the contributions from the other co-authors. D.G. performed the radial velocity analysis using the floating chunk offset method, wrote a significant part of the text and is the principal investigator of the HARPS large programme, which enabled the discovery of three additional planets and the determinations of the planetary (minimum) masses. O.B. performed the multi-dimensional Gaussian process analysis and wrote the relative section. J.K. ran the stability analyses with rebound and SPOCK and wrote the relative section. A.J.M. and F.D. described the most probable formation/migration processes of the system. A.J.M. also ran the numerical simulation to test the low-eccentricity migration pathway and wrote the relative section. M. Fridlund performed the spectral and chemical abundance analysis. K.W.F.L. and S.G. searched the TESS light curve for transit signals. K.A.C. performed the LCOGT observations and analysed the data. J.H.L. analysed the GEMINI and SOAR imaging data. J.A., M.R.D., F.R. and T.T. contributed to the HARPS RV follow-up. W.D.C. computed the probability that TOI-500 belongs to different stellar populations. C.H. analysed the WASP-South light curves. S.E.B. contributed to the analysis of the radial velocity data. S.R. explored the possibility to study the secondary atmosphere of TOI-550 b and wrote the relative section. S.A., S.C., H.J.D., M.E., I.G., E. Goffo, E. Guenther, A.P.H., R.L., F.M., H.L.M.O., E.P., C.M.P., A.M.S.S. and V.V.E. are members of the KESPRINT consortium and contributed to the HARPS large programme. C.Z. and A.W.M. performed the SOAR imaging observations. E.L.N.J. contributed to the LCOGT observations. S.B.H. performed the observations with GEMINI/ZORRO. J.M.J., D.W.L., G.R., S.S., R.V. and J.N.W. are the architects of the TESS mission. K.I.C., T.D., M. Fasnaugh, A.W.M., P.R., A.R. and J.D.T. significantly contributed to the success of the TESS mission, which discovered the USP planet candidate. All authors reviewed the manuscript.
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Extended data
Extended Data Fig. 1 Field of view with the locations of the 78 Gaia DR2 stars checked for NEBs.
The circle marks a 2.5’radius around TOI-500. The background image is from the digitized sky survey 2 (DSS2). The circles on each star represent the current Gaia DR2 position. The different timing between the DSS2 and DR2 databases is the reason for which some of the stars are shifted from the original position, as a consequence of their proper motion.
Extended Data Fig. 2 Gemini/Zorro 5-sigma contrast curve.
and 1.2″ × 1.2″ reconstructed images (inset).
Extended Data Fig. 3 SOAR contrast curve.
and 6″ × 6″ two-dimensional auto-correlation function of SOAR image (inset).
Extended Data Fig. 4 Time series of the HARPS RV measurements.
and activity indicators (FWHM, BIS, S-index, and dLW).
Extended Data Fig. 5 Generalized Lomb-Scargle periodograms of the HARPS SERVAL RV measurements and residuals.
The right and left columns cover two frequency ranges encompassing the Doppler signals of TOI-500 c, d, e, and the stellar rotation frequency f* (left panels), and the orbital frequency of the USP planet TOI-500 b (right panels). From top to bottom: RV data (upper panel); RV residuals following the subtraction of the Doppler signal of TOI-500 d (second panel), TOI-500 d and c (third panel), TOI-500 d, c, and e (fourth panel), TOI-500 d, c, and e plus the stellar signal at 43.4 d (fifth panel); window function (lower panel). The red dashed horizontal lines mark the 0.1 % false alarm probability as derived using the bootstrap method. The vertical dashed lines mark the significant frequencies identified in the HARPS data and discussed in the main text.
Extended Data Fig. 6 Generalized Lomb-Scargle periodograms of the activity indicators following the subtraction of the seasonal median values (see Methods).
The right and left columns cover two frequency ranges encompassing the Doppler signals induced by the 4 orbiting planets and stellar rotation. From top to bottom: FWHM (upper panel), BIS (second panel), S-index (third panel), dLW (fourth panel), window function (lower panel). The red dashed horizontal lines mark the 0.1% false alarm probability as derived using the bootstrap method. The vertical dashed lines mark the significant frequencies identified in the HARPS data and discussed in the main text.
Extended Data Fig. 7 Lomb-Scargle periodograms of the WASP-South light curves of TOI-500.
Left panels, from bottom to top: periodogram of the data acquired in 2008/2009, 2009/2010, 2010/2011, and 2011/2012. The upper left panel displays the periodogram of the combined 4 years of data, showing a possible 0.022d-1 periodic signal, corresponding to a period of about 45 d (upper panel). This peak is marked in all the panels with a red thick line. The dotted horizontal lines show the 1% false alarm probability. The right panels show the WASP-South binned photometry folded at the 45-d rotation period for the years 2008 and 2011, when the 45 d signal is stronger. The displayed phases go from 0 to 1.5, in order to visualize better the periodicity of the photometric variability. The repeated data between phase 0 and 0.25, and phase 1.25 and 1.5 are shown with gray points.
Extended Data Fig. 8 Median-subtracted HARPS SERVAL RVs (upper panel), S-index (middle panel), and FWHM (lower panel).
Upper panel: HARPS SERVAL RVs (blue data points), GP model (green line), and best fitting (GP+planets) model (thick black line). Middle panel: S-index (green data points) and GP model (thick black line). Lower panel: FWHM (red data points) and GP model (thick black line). Nominal error bars are shown in solid colour, and the error bars corrected by jitter are semitransparent. Dark and light shaded areas show the 1- and 2- σ confidence interval of the corresponding GP model, respectively. We note that there is a gap between 1650 and 1820 BJD - 2457000$d.
Extended Data Fig. 9 Scatter plot of exoplanets with atmospheric S/N ratio.
as a function of the dayside predicted equilibrium temperature in Kelvin. TOI-500b is in a favorable position among the top 10 targets of interest for atmospheric characterization.
Supplementary information
Supplementary Data 1
The list of favourable targets for atmospheric analysis. TOI-500 b is ranked 8th.
Supplementary Data 2
HARPS RV measurements and activity indicators of TOI-500.
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Serrano, L.M., Gandolfi, D., Mustill, A.J. et al. A low-eccentricity migration pathway for a 13-h-period Earth analogue in a four-planet system. Nat Astron 6, 736–750 (2022). https://doi.org/10.1038/s41550-022-01641-y
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DOI: https://doi.org/10.1038/s41550-022-01641-y
