Disc settling and dynamical heating: histories of Milky Way-mass stellar discs across cosmic time in the FIRE simulations

We study the kinematics of stars both at their formation and today within 14 Milky Way (MW)-mass galaxies from the FIRE-2 cosmological zoom-in simulations. We quantify the relative importance of cosmological disc settling and post-formation dynamical heating. We identify three eras: a Pre-Disc Era (typically ≳ 8 Gyr ago), when stars formed on dispersion-dominated orbits; an Early-Disc Era (≈8-4 Gyr ago), when stars started to form on rotation-dominated orbits but with high velocity dispersion, σ_form; and a Late-Disc Era (≲ 4 Gyr ago), when stars formed with low σ_form. σ_form increased with time during the Pre-Disc Era, peaking ≈8 Gyr ago, then decreased throughout the Early-Disc Era as the disc settled and remained low throughout the Late-Disc Era. By contrast, the dispersion measured today, σ_now, increases monotonically with age because of stronger post-formation heating for Pre-Disc stars. Importantly, most of σ_now was in place at formation, not added post-formation, for stars younger than ≈10 Gyr. We compare the evolution of the three velocity components: at all times, σ_{R, form} > σ_{φ, form} > σ_{Z, form}. Post-formation heating primarily increased σ_R at ages ≲ 4 Gyr but acted nearly isotropically for older stars. The kinematics of young stars in FIRE-2 broadly agree with the range observed across the MW, M31, M33, and PHANGS-MUSE galaxies. The lookback time that the disc began to settle correlates with its dynamical state today: earlier-settling galaxies currently form colder discs. Including stellar cosmic-ray feedback does not significantly change disc rotational support at fixed stellar mass.