{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T12:30:25Z","timestamp":1764937825370,"version":"3.32.0"},"reference-count":159,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":6,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["A&amp;A"],"accepted":{"date-parts":[[2024,11,20]]},"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p><jats:italic>Context<\/jats:italic>. TOI-396 is an F6 V bright naked-eye star (<jats:italic>V<\/jats:italic> \u2248 6.4) orbited by three small (<jats:italic>R<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub> \u2248 2 <jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub>) transiting planets discovered thanks to space-based photometry from two <jats:italic>TESS<\/jats:italic> sectors. The orbital periods of the two innermost planets, namely TOI-396 b and c, are close to the 5:3 commensurability (<jats:italic>P<\/jats:italic><jats:sub><jats:italic>b<\/jats:italic><\/jats:sub> ~ 3.6 d and <jats:italic>P<\/jats:italic><jats:sub><jats:italic>c<\/jats:italic><\/jats:sub> ~ 6.0 d), suggesting that the planets might be trapped in a mean motion resonance (MMR).<\/jats:p>\n<jats:p><jats:italic>Aims<\/jats:italic>. To measure the masses of the three planets, refine their radii, and investigate whether planets b and c are in MMR, we carried out <jats:italic>HARPS<\/jats:italic> radial velocity (RV) observations of TOI-396 and retrieved archival high-precision transit photometry from four <jats:italic>TESS<\/jats:italic> sectors.<\/jats:p>\n<jats:p><jats:italic>Methods<\/jats:italic>. We extracted the RVs via a skew-normal fit onto the <jats:italic>HARPS<\/jats:italic> cross-correlation functions and performed a Markov chain Monte Carlo joint analysis of the Doppler measurements and transit photometry, while employing the breakpoint method to remove stellar activity from the RV time series. We also performed a transit timing variation (TTV) dynamical analysis of the system and simulated the temporal evolution of the TTV amplitudes of the three planets following an N-body numerical integration.<\/jats:p>\n<jats:p><jats:italic>Results<\/jats:italic>. Our analysis confirms that the three planets have similar sizes (<jats:italic>R<jats:sub>b<\/jats:sub><\/jats:italic> = 2.004<jats:sub>\u22120.047<\/jats:sub><jats:sup>+0.045<\/jats:sup> <jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub> ; <jats:italic>R<jats:sub>c<\/jats:sub><\/jats:italic> = 1.979<jats:sub>\u22120.051<\/jats:sub><jats:sup>+0.054<\/jats:sup> <jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub>; <jats:italic>R<jats:sub>d<\/jats:sub><\/jats:italic> = 2.001<jats:sub>\u22120.064<\/jats:sub><jats:sup>+0.063<\/jats:sup> <jats:italic>R<\/jats:italic><jats:sub>\u2295<\/jats:sub>) and is thus in agreement with previous findings. However, our measurements are ~ 1.4 times more precise thanks to the use of two additional <jats:italic>TESS<\/jats:italic> sectors. For the first time, we have determined the RV masses for TOI-396 b and d, finding them to be <jats:italic>M<jats:sub>b<\/jats:sub><\/jats:italic> = 3.55<jats:sub>\u22120.96<\/jats:sub><jats:sup>+0.94<\/jats:sup> <jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub> and <jats:italic>M<\/jats:italic><jats:sub><jats:italic>d<\/jats:italic><\/jats:sub> = 7.1 \u00b1 1.6 <jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub>, which implies bulk densities of <jats:italic>\u03c1<jats:sub>b<\/jats:sub><\/jats:italic> = 2.44<jats:sub>\u22120.68<\/jats:sub><jats:sup>+0.69<\/jats:sup> g cm<jats:sup>\u22123<\/jats:sup> and <jats:italic>\u03c1<jats:sub>d<\/jats:sub><\/jats:italic> = 4.9<jats:sub>\u22121.1<\/jats:sub><jats:sup>+1.2<\/jats:sup> g cm<jats:sup>\u22123<\/jats:sup>, respectively. Our results suggest a quite unusual system architecture, with the outermost planet being the densest. Based on a frequency analysis of the <jats:italic>HARPS<\/jats:italic> activity indicators and <jats:italic>TESS<\/jats:italic> light curves, we find the rotation period of the star to be <jats:italic>P<\/jats:italic><jats:sub>rot,\u22c6<\/jats:sub> = 6.7 \u00b1 1.3 d, in agreement with the value predicted from log <jats:italic>R<\/jats:italic>\u2032<jats:sub>HK<\/jats:sub>-based empirical relations. The Doppler reflex motion induced by TOI-396 c remains undetected in our RV time series, likely due to the proximity of the planet\u2019s orbital period to the star\u2019s rotation period. We also discovered that TOI-396 b and c display significant TTVs. While the TTV dynamical analysis returns a formally precise mass for TOI-396 c of <jats:italic>M<\/jats:italic><jats:sub><jats:italic>c<\/jats:italic>,dyn<\/jats:sub> = 2.24<jats:sub>\u22120.67<\/jats:sub><jats:sup>+0.13<\/jats:sup> <jats:italic>M<\/jats:italic><jats:sub>\u2295<\/jats:sub>, the result might not be accurate, owing to the poor sampling of the TTV phase. We also conclude that TOI-396 b and c are close to but out of the 5:3 MMR.<\/jats:p>\n<jats:p><jats:italic>Conclusions<\/jats:italic>. A TTV dynamical analysis of additional transit photometry evenly covering the TTV phase and super-period is likely the most effective approach for precisely and accurately determining the mass of TOI-396 c. Our numerical simulation suggests TTV semi-amplitudes of up to five hours over a temporal baseline of ~ 5.2 years, which should be duly taken into account when scheduling future observations of TOI-396.<\/jats:p>","DOI":"10.1051\/0004-6361\/202451300","type":"journal-article","created":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T20:07:29Z","timestamp":1733342849000},"page":"A90","source":"Crossref","is-referenced-by-count":2,"title":["Radii, masses, and transit-timing variations of the three-planet system orbiting the naked-eye star TOI-396"],"prefix":"10.1051","volume":"693","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1916-5935","authenticated-orcid":false,"given":"A.","family":"Bonfanti","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0410-6215","authenticated-orcid":false,"given":"I.","family":"Amateis","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8627-9628","authenticated-orcid":false,"given":"D.","family":"Gandolfi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0066-9268","authenticated-orcid":false,"given":"L.","family":"Borsato","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1628-4231","authenticated-orcid":false,"given":"J. 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