Bridging magnetothermal winds and photoevaporation to model discs dispersal

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 proportional toΣ q is self-limiting: for q 1/2 depletion alone cannot demagnetise the disc, so dispersal requires independent flux loss, parameterised by the magnetic Reynolds number R m. Integrating the coupled system yields two regimes. Efficient flux loss (R m 1) lets the magnetisation front recede by over an order of magnitude and opens a photoevaporative gap. Flux retention (R m 1) drives the front outward, sustains accretion, and defers dispersal by about2.7 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 base about 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.