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

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. 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. 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. We present the discovery of four transiting sub-Neptunes with radii of R_b=2.314 ,R_⊕, and R_e=3.247_ ^ R_c=2.474 ^ R_d=3.584_ -0.050 +0.051 -0.043 +0.042 ,R_⊕, along with masses of M_b=9.4 M_c=4.8 ,M_⊕. Our photometric analysis revealed that the outermost transiting planet TOI-5624,e 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 =13.0 M_d=4.9 ^ and M_e=8.9_ -3.0 +2.9 i_f Among the known systems hosting more than four planets, the remarkable precision with which the radii have been measured ($<1.7%$) and the firm assessment (>,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.