Bridging magnetothermal winds and photoevaporation to model discs dispersal

Abstract: Protoplanetary disc dispersal is driven by two processes usually modelled separately: photoevaporative and magnetohydrodynamic (MHD) disc winds. Global simulations indicate that in the inner disc these are not distinct outflows but a single magnetothermal wind. We assemble a closed-form, two-phase model that respects it. A single-field-line wind, whose base is fixed by the irradiated temperature and penetration column, supplies the launch and feeds a secular evolution, with photoevaporation convolved on as a sink. The flux closure $B_z\proptoΣ<sup>q$ is self-limiting: for $q\le1/2$ depletion alone cannot demagnetise the disc, so dispersal requires independent flux loss, parameterised by the magnetic Reynolds number $\mathcal{R}<em>m$. Integrating the coupled system yields two regimes. Efficient flux loss ($\mathcal{R}_m\lesssim1$) lets the magnetisation front recede by over an order of magnitude and opens a photoevaporative gap. Flux retention ($\mathcal{R}_m\gg1$) drives the front outward, sustains accretion, and defers dispersal by $\approx2.7$~Myr. Deriving the base from stellar irradiation instead of prescribing it, we find that the cold-launch approximation is valid during the early stages of disc evolution: anchoring the base at plasma equipartition ($β</em>{\rm base} \sim 1$) confines irradiation's influence on the magnetic lever arm to the magnetothermal annulus, decoupling the peak accretion rate from the incident flux. Both regimes clear the disc inside-out, through either a photoevaporatively amplified cavity wall or an expanding magnetothermal front.