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

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 accurately known, 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, a 0.6 R _⊕ planet with the shortest known orbital period of 4.245 hr, the planet's mean density must be ≳ 7 g cm^-3. By modeling the planetary interior subject to this constraint, we find that the composition of the planet must be mostly iron, with at most a modest fraction of silicates (≲ 30% by mass).