The winds of young Solar-type stars in the Pleiades, AB Doradus, Columba and $\beta$ Pictoris

Solar-type stars, which shed angular momentum via magnetised stellar winds, enter the main sequence with a wide range of rotational periods $P_\text{rot}$. This initially wide range of rotational periods contracts and has mostly vanished by a stellar age $t\sim0.6$ Gyr, after which Solar-type stars spin according to the Skumanich relation $P_\text{rot}\propto\sqrt t$. Magnetohydrodynamic stellar wind models can improve our understanding of this convergence of rotation periods. We present wind models of fifteen young Solar-type stars aged from 24 Myr to 0.13 Gyr. With our previous wind models of stars aged 0.26 Gyr and 0.6 Gyr we obtain thirty consistent three-dimensional wind models of stars mapped with Zeeman-Doppler imaging - the largest such set to date. The models provide good cover of the pre-Skumanich phase of stellar spin-down in terms of rotation, magnetic field, and age. We find that the mass loss rate $\dot M\propto\Phi^{0.9\pm0.1}$ with a residual spread of 150% and that the wind angular momentum loss rate $\dot J\propto{}P_\text{rot}^{-1} \Phi^{1.3\pm0.2}$ with a residual spread of 500% where $\Phi$ is the unsigned surface magnetic flux. When comparing different magnetic field scalings for each single star we find a gradual reduction in the power-law exponent with increasing magnetic field strength.