The role of inner disk edges in shaping ultra-short-period planet systems around late M dwarfs

Abstract

Close-in rocky planets are the most common type of exoplanets around late M dwarfs, ranging from more temperate worlds to highly irradiated lava planets with molten surfaces, and many theoretical studies have attempted to explain their formation. However, the origin of rocky planets with orbital periods shorter than one day, known as ultra-short-period (USP) planets, remains uncertain. We aim to investigate whether the formation and survival of USP planets is connected to the location of the inner edge of the protoplanetary disk, considering different disk edge prescriptions. We use N-body simulations that include planet-disk interactions, star-planet tidal interactions, and relativistic corrections, applied to a sample of lunar-mass planetary seeds growing via pebble accretion in a low-viscosity disk ($α_t = 10^{-4}$). The inner edge of the disk is modeled in three ways: as a fixed close-in edge, as an outward-evolving edge set by the magnetospheric truncation radius, and as an inward-evolving edge defined by the corotation radius. USP planet formation appears to be tightly controlled by the location of the disk's inner edge. Our simulations show that only the close-in-fixed-edge Scenario and the inward-evolving-edge Scenario are capable of producing USP planets, as planets tend to follow the movement of the disk's inner edge. This suggests that USP planet formation is favored when the inner edge remains close to the corotation radius of a rapidly rotating star.

Figures (10)

• Figure 1: Inner disk edge scenarios cartoons. From left to right: FIX Scenario with close-in fixed inner disk edge; OUT[M] Scenario with outwards moving edge based on magnetic flux conservation; IN[C] Scenario with inwards moving edge based on stellar corotation.
• Figure 2: Inner disk edge evolution. Fixed inner edge (FIX) (green dashed line), Outward-migrating edge (OUT[M]) (red dotted line; see Eq. \ref{['eq:rin_description']}), and inward-migrating edge (IN[C]) (purple solid line; see Eq. \ref{['eq:corotation_rin']}). These $r_{\rm in}(t)$ tracks set where Type-I migration halts.
• Figure 3: Dynamical evolution of planetary embryos in a representative simulation of Scenario FIX. Each line corresponds to one embryo: gray lines show all embryos, while colored lines highlight those that survive until the end of the integration at $\sim$ 50 Myr. Panels display the semi-major axis (top left), eccentricity (top right), inclination (bottom left), and planetary mass (bottom right). The horizontal dashed blue line in the semi-major-axis panel marks the fixed inner disk edge at 0.01 au, which is applied only during the gas-disk phase (up to 10 Myr).
• Figure 4: Average close-encounter events per system for each inner-edge scenario (FIX, OUT[M], IN[C]). One Hill radius was applied as the threshold. For a given scenario, we sum the number of close-encounter records across all embryos and runs, and divide by the number of valid runs.
• Figure 5: Fraction of initial embryos per system that experienced an embryo-embryo collision. Percentages are shown for all 10 systems in each scenario. Bar colors correspond to the three inner-edge prescriptions (green = FIX, orange = OUT[M], purple = IN[C]).