Two neighbours of the ultra-short-period Earth-sized planet K2-157 b in the warm Neptunian savanna

Abstract

[Context] The formation and evolution of ultra-short-period (USP) rocky planets is poorly understood. However, it is widely thought that these planets could not have formed at their present-day close-in orbits, but instead migrated inwards through interactions with outer neighbours. [Aims] We aim to confirm and characterise the USP Earth-sized validated planet K2-157 b (Porb = 8.8 h) and constrain the presence of additional companions in the system through radial velocity (RV) measurements. [Methods] We measured 49 RVs with the ESPRESSO spectrograph and tested different planetary and non-planetary configurations to infer the model that best represents our data set. We derived the orbital and physical properties of the system through a global RV and transit model. [Results] We detected two additional super-Neptune-mass planets located within the warm Neptunian savanna, K2-157 c (Porb,c = 25.942−0.044+0.045d, Mp,c sin i = 30.8 ± 1.9 M⊕) and K2-157 d (Porb,d = 66.50−0.59+0.71d, Mp,d sin i = 23.3 ± 2.5 M⊕). The joint analysis constrains the mass of K2-157 b at the 2.7σ level, Mp,b = 1.14−0.42+0.41 M⊕ (< 2.4 M⊕ at 3σ), which, together with the inferred radius, Rp,b = 0.935 ± 0.090 R⊕, make the planet compatible with a rocky composition with a likely (68% confidence) higher iron-to-silicate mass fraction than Earth. K2 data discard non-grazing transit configurations for K2-157 c (ic < 88.4° at 3σ), and ESPRESSO data constrain the eccentricities of K2-157 c and K2-157 d to ec < 0.2 and ed < 0.5 at 3σ. Our dynamical analysis indicates that the system is stable for eccentricities up to ec, ed ~ 0.3 and mutual inclinations up to ~60°. At a population level, we find that the trend that the closest USP planets tend to orbit late-type stars does not hold when scaling the orbital separation to the Roche limit, which suggests that the orbital distribution of the closest planets across spectral types is primarily determined by tidal disruption. [Conclusions] The orbital architecture of K2-157 is unusual in the known exoplanet plethora, with only one similar case reported to date: 55 Cnc. The USP planets of these systems, being accompanied by massive, long-period, relatively spaced, and possibly misaligned neighbours, could have migrated inwards through eccentricity-based mechanisms triggered by secular interactions.