Radii, masses, and transit-timing variations of the three-planet system orbiting the naked-eye star TOI-396^★

¹ Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
² Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, 10125 Torino, Italy
³ Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala 75120, Sweden
⁴ INAF, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁵ Weltraumforschung und Planetologie, Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
⁶ INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese To, Italy
⁷ Department of Physics, University of Warwick, Coventry CV4 7AL, UK
⁸ Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
⁹ Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário, Natal, RN 59072-970, Brazil
¹⁰ Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The Netherlands
¹¹ Chalmers University of Technology, Department of Space, Earth and Environment, Onsala Space Observatory, SE-439 92 Onsala, Sweden
¹² INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5 Florence, Italy
¹³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁴ School of Physics and Astronomy, Physical Science Building, North Haugh, St Andrews, UK
¹⁵ Rhenish Institute for Environmental Research, Dep. of Planetary Research, University of Cologne, Aachener Str. 209, 50931 Cologne, Germany
¹⁶ Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany
¹⁷ Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany
¹⁸ University Observatory Munich, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany
¹⁹ European Southern Observatory, Alonso de Cordova 3107, Vitacura, Casilla, 19001 Santiago, Chile
²⁰ European Southern Observatory, Alonso de Cordova 3107, Vitacura, Santiago de Chile, Chile
²¹ Centro de Astrobiología (CAB), CSIC-INTA, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada (Madrid), Spain
²² McDonald Observatory, The University of Texas, Austin, TX, USA
²³ Center for Planetary Systems Habitability, The University of Texas, Austin, TX, USA
²⁴ Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA
²⁵ Astronomy Department and Van Vleck Observatory, Wesleyan University, Middletown, CT 06459, USA
²⁶ Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
²⁷ Department of Astronomy of the University of Geneva, chemin Pegasi 51, 1290 Versoix, Switzerland
²⁸ Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
²⁹ National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
³⁰ Astronomical Science Program, Graduate University for Advanced Studies, SOKENDAI, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan
³¹ Instituto de Astrofísica de Canarias (IAC), calle Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
³² Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
³³ Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland
³⁴ Department of Physics and Astronomy, McMaster University, 1280 Main St W, Hamilton, ON L8S 4L8, Canada
³⁵ Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 2, 8093 Zurich, Switzerland

^★★ Corresponding author; andrea.bonfanti@oeaw.ac.at

Received: 28 June 2024
Accepted: 20 November 2024

Abstract

Context. TOI-396 is an F6 V bright naked-eye star (V ≈ 6.4) orbited by three small (R_p ≈ 2 R_⊕) transiting planets discovered thanks to space-based photometry from two TESS sectors. The orbital periods of the two innermost planets, namely TOI-396 b and c, are close to the 5:3 commensurability (P_b ~ 3.6 d and P_c ~ 6.0 d), suggesting that the planets might be trapped in a mean motion resonance (MMR).

Aims. To measure the masses of the three planets, refine their radii, and investigate whether planets b and c are in MMR, we carried out HARPS radial velocity (RV) observations of TOI-396 and retrieved archival high-precision transit photometry from four TESS sectors.

Methods. We extracted the RVs via a skew-normal fit onto the HARPS 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.

Results. Our analysis confirms that the three planets have similar sizes (R_b = 2.004_−0.047^+0.045 R_⊕ ; R_c = 1.979_−0.051^+0.054 R_⊕; R_d = 2.001_−0.064^+0.063 R_⊕) and is thus in agreement with previous findings. However, our measurements are ~ 1.4 times more precise thanks to the use of two additional TESS sectors. For the first time, we have determined the RV masses for TOI-396 b and d, finding them to be M_b = 3.55_−0.96^+0.94 M_⊕ and M_d = 7.1 ± 1.6 M_⊕, which implies bulk densities of ρ_b = 2.44_−0.68^+0.69 g cm⁻³ and ρ_d = 4.9_−1.1^+1.2 g cm⁻³, respectively. Our results suggest a quite unusual system architecture, with the outermost planet being the densest. Based on a frequency analysis of the HARPS activity indicators and TESS light curves, we find the rotation period of the star to be P_rot,⋆ = 6.7 ± 1.3 d, in agreement with the value predicted from log R′_HK-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’s orbital period to the star’s 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 M_c,dyn = 2.24_−0.67^+0.13 M_⊕, 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.

Conclusions. 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.