Discovery and characterisation of two exoplanets orbiting the metal-poor, solar-type star TOI-5788 with TESS, CHEOPS, and HARPS-N

We present the discovery and characterisation of two transiting exoplanets orbiting the metal-poor, solar-type star TOI-5788. From our analysis of six \textit{TESS} sectors and a dedicated \textit{CHEOPS} programme, we identify an inner planet (TOI-5788~b; $P = 6.340758\pm0.000030\,\si{\day}$) with radius $1.528\pm0.075\,\mathrm{R_\oplus}$ and an outer planet (TOI-5788~c; $P = 16.213362\pm0.000026\,\si{\day}$) with radius $2.272\pm0.039\,\mathrm{R_\oplus}$. We obtained 125 radial-velocity spectra from HARPS-N and constrain the masses of TOI-5788~b and~c as $3.72\pm0.94\,\mathrm{M_\oplus}$ and $6.4\pm1.2\,\mathrm{M_\oplus}$, respectively. Although dynamical analyses indicate that a third planet could exist in a stable orbit between 8 and 14 days, we find no evidence of additional planets. Since the TOI-5788 system is one of the few systems with planets straddling the radius gap, and noting that there are even fewer such systems around metal poor stars, it is a promising system to constrain planet formation theories. We therefore model the interior structures of both planets. We find that TOI-5788~b is consistent with being a rocky planet with almost no envelope, or having an atmosphere of a high mean molecular weight. We find that TOI-5788~c is consistent with both gas-dwarf and water-world hypotheses of mini-Neptune formation. We model the atmospheric evolution history of both planets. Whilst both scenarios are consistent with the atmospheric evolution of TOI-5788~c, the gas-dwarf model is marginally preferred. The results of the atmospheric evolution analysis are not strongly dependent on stellar evolution. This makes the system a promising target to test internal structure and atmospheric evolution models.