Coupled orbital and interior structure evolution of lava planets

Lava planets likely did not form in their current orbits, instead migrating inward via orbital decay, which influenced the evolution of their magma oceans. We introduce a coupled thermal-orbital evolution model to explore how rocky planets migrate from the inner edge of the protoplanetary disk, with periods of 1-10 days, to orbital periods of less than a day. In our model, mantle melting is controlled by tidal heating and stellar flux, while orbits evolve via tidal migration. The mantle's tidal quality factor varies with its temperature and structure, creating a feedback loop between thermal evolution and orbital decay. We use our numerical model to simulate the migration of seven known lava planets: K2-141b, K2-360b, TOI-141b, TOI-431b, TOI-2431b, HD 3167b and GJ 367b. Migration occurs in two stages: an initial high-eccentricity stage reducing the semi-major axis by a factor of $\sim 2$, followed by a low-eccentricity stage reducing it by a factor of $\sim 5$. A successful migration from $\sim 0.1$ AU to a present-day orbit requires starting eccentricities $\ge 0.9$ and sustained eccentricity forcing with $e_{\mathrm{min}} \ge 10^{-2}$. The rate of migration depends on the state of the mantle: slow when mostly molten, fast when mostly solid. This pathway works for most lava planets, but not for TOI-431b or GJ-367b, suggesting that multiple migration pathways are possible for lava planets.