The Roche limit for close-orbiting planets: Minimum density, composition constraints, and application to the 4.2-hour planet KOI 1843.03

TL;DR

This paper derives a minimum density limit for close-orbiting planets based on their Roche limit, constraining their composition and applying it to the ultra-short period planet KOI 1843.03, indicating it is likely mostly iron.

Contribution

It introduces a Roche limit-based density constraint for ultra-short period planets and applies it to determine the composition of KOI 1843.03.

Findings

KOI 1843.03 must have a density >7 g/cm^3.

The planet's composition is likely mostly iron.

The density constraint is independent of stellar property errors.

Abstract

The requirement that a planet must orbit outside of its Roche limit gives a lower limit on the planet's mean density. The minimum density depends almost entirely on the orbital period and is immune to systematic errors in the stellar properties. We consider the implications of this density constraint for the newly-identified class of small planets with periods shorter than half a day. When the planet's radius is known accurately, this lower limit to the density can be used to restrict the possible combinations of iron and rock within the planet. Applied to KOI 1843.03, with a radius of 0.6 Earth radii and the shortest known orbital period of 4.245 hr, the planet's mean density must be greater than approximately 7 g/cm^3. By modeling the planetary interior subject to this constraint, we find the composition of the planet must be mostly iron, with at most a modest fraction of silicates (less than approximately 30% by mass).