Mass constraints for the K2-223 system planets: An ultra-short-period sub-Earth, a short-period super-Earth, and a tentative long-period giant planet

We present mass constraints of two short-period, terrestrial-sized planets transiting K2-223, based on high-precision radial velocity measurements from HARPS-N and ESPRESSO, as well as a tentative indication of an outer, Jupiter-like planet orbiting the G1V dwarf K2-223. With a radius of R b=0.79 plus or minus0.10 R and 3- σ upper mass limit M b<2.8 M, K2-223 b belongs to the small group of known sub-Earth planets and is currently the smallest known ultra-short-period (USP) planet (P b about 0.5 day) transiting a solar-type star. With a radius of R c=1.41 plus or minus0.15 R, a mass of M c=4.2 plus or minus1.3 M and a density of ρ c=8.3 plus or minus3.7 g,cm-3, K2-223 c is a short-period (P c about 4.5 days) super-Earth. Thanks to almost six and a half years of radial velocity monitoring of K2-223 with the HARPS-N spectrograph, we identified a tentative giant planet with an orbital period of P d=4.53+0.32-0.34 years and a minimum mass of 1.29+0.23-0.17 M Jup. Two close-in small planets accompanied by a distant candidate Jupiter-like companion would make K2-223 a system with a rare architecture, valuable for testing scenarios of planetary formation and evolution. The extreme proximity of K2-223 b to the parent star necessitates the consideration of relativistic and tidal perturbations to Newtonian gravity. We discuss the timescales and amplitudes of these effects in the context of the RV model and dynamical simulations of the K2-223 multiple-planet system. We also present a parametrisation of the planets with directly measured masses, radii, and bulk densities in terms of the orbital period normalised by the Roche period, providing an alternative representation in the context of the Neptune desert.