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

The formation and evolution of ultra-short-period (USP) planets is poorly understood. However, it is widely thought that these planets migrated inwards through interactions with outer neighbours. We aim to confirm and characterise the USP Earth-sized planet K2-157 b ($P_{\rm orb}$ = 8.8 h). To do so, we measured 49 radial velocities (RVs) with the ESPRESSO spectrograph and derived the properties of the system through an RV and transit model. We detect two additional super-Neptune-mass planets within the warm Neptunian savanna, K2-157 c ($P_{\rm orb, c}$ = $25.942^{+0.045}_{-0.044}$ d, $M_{\rm p, c} \, \textrm{sin} \, i$ = $30.8 \pm 1.9$ $\rm M_{\oplus}$), and K2-157 d ($P_{\rm orb, d}$ = $66.50^{+0.71}_{-0.59}$ d, $M_{\rm p,d} \, \textrm{sin}\,i$ = $23.3 \pm 2.5$ $\rm M_{\oplus}$). The mass of K2-157 b, $M_{\rm p,b}$ = $1.14^{+0.41}_{-0.42}$ $\rm M_{\oplus}$ ($<$ 2.4 $\rm M_{\oplus}$ at 3$σ$), together with its radius, $R_{\rm p}$ = 0.935 $\pm$ 0.090 $\rm R_{\oplus}$, make the planet compatible with a rocky composition. K2 data discard non-grazing transit configurations for K2-157 c ($i_{\rm c}$ $<$ 88.4$^{\circ}$ at 3$σ$), and ESPRESSO data constrain the eccentricities of K2-157 c and K2-157 d to $e_{\rm c}$ $<$ 0.2 and $e_{\rm d}$ $<$ 0.5 at 3$σ$. 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 determined by tidal disruption. The orbital architecture of K2-157 is unusual, 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.