Ultra-short-period Planets are Stable Against Tidal Inspiral

It has been unambiguously shown in both individual systems and at the population level that hot Jupiters experience tidal inspiral before the end of their host stars' main sequence lifetimes. Ultra-short-period (USP) planets have orbital periods $P < 1$ day, rocky compositions, and are expected to experience tidal decay on similar timescales to hot Jupiters if the efficiency of tidal dissipation inside their host stars parameterized as $Q_\ast'$ is independent of $P$ and/or secondary mass $M_{\mathrm{p}}$. Any difference between the two classes of systems would reveal that a constant $Q_\ast'$ model is insufficient. If USP planets experience tidal inspiral, then USP planet systems will be relatively young compared to similar stars without USP planets. Because it is a proxy for relative age, we calculate the Galactic velocity dispersions of USP planet candidate host and non-host stars using data from Gaia Data Release 2 supplemented with ground-based radial velocities. We find that main sequence USP planet candidate host stars have kinematics consistent with similar stars in the Kepler field without observed USP planets. This indicates that USP planet hosts have similar ages as field stars and that USP planets do not experience tidal inspiral during the main sequence lifetimes of their host stars. The survival of USP planets requires that $Q_\ast'\gtrsim10^7$ at $P\approx0.7$ day and $M_{\mathrm{p}}\approx2.6~M_{\oplus}$. This result demands that $Q_\ast'$ depend on the orbital period and/or mass of the secondary in the range $0.5\mathrm{~days}\lesssim P\lesssim5$ days and $1~M_{\oplus}\lesssim M_{\mathrm{p}}\lesssim1000~M_{\oplus}$.