The multi-planet system TOI-5624: four transiting sub-Neptunes with an outer companion revealed by transit-timing variations

Context . Following the 2022 alert of a TESS object of interest transiting TOI-5624 (a G7 V star ∼ 100 pc away), a CHEOPS campaign in 2023 detected four planetary signals at P b ≈ 3.4, P c ≈ 7.9, P d ≈ 13.7, and P e ≈ 21.5 days. These signals were later confirmed by additional TESS and CHEOPS photometry in 2024-2025. Aims . By using TESS and CHEOPS photometry, along with HARPS-N and SOPHIE high-resolution spectra, we determined the planet properties and performed a dynamical analysis of the system. Methods . After analysing the photometric data, we extracted and modelled the radial velocity (RV) time series using two independent methodologies, both within a Markov chain Monte Carlo framework. We further integrated the N -body equations of motion, while simultaneously fitting the transit times and the detrended RVs, to dynamically characterise the system. Results . We present the discovery of four transiting sub-Neptunes with radii of R b = 2.314 ± 0.035 R ⊕ , R c = 2.474 ± 0.042 R ⊕ , R d = 3.584 −0.050 +0.051 R ⊕ , and R e = 3.247 −0.043 +0.042 R ⊕ , along with masses of M b = 9.4 ± 1.4 M ⊕ , M c = 4.8 ± 1.9 M ⊕ , Md = 4.9 ± 2.2 M ⊕ , and M e = 8.9 −3.0 +2.9 M ⊕ . Our photometric analysis revealed that the outermost transiting planet TOI-5624e shows significant transit-timing variations (TTVs). Indeed, we found a robust Keplerian signal in the RV time series close to the 2:1 period commensurability with TOI-5624 e, which explains the TTV pattern exhibited by TOI-5624 e according to our dynamical analysis. We labelled this non-transiting planet as TOI-5624 f and determined its minimum mass to be M f sin i f = 13.0 ± 3.7 M ⊕ . Conclusions . Among the known systems hosting more than four planets, the remarkable precision with which the radii have been measured (3σ) of the mass for at least three planets has previously been reached only for TRAPPIST-1. Additional photometric observations will enable a better sample of the TTV modulation and a more robust dynamical determination of the masses.