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We extend a magnetic braking (MB) model, which has been used earlier toaddress the evolution of cataclysmic variables, to address the spin period$P_\mathrm{spin}$ evolution of fully convective M dwarf (FCMD) stars. The MBmechanism is an $\alpha-\Omega$ dynamo, which leads to stellar winds that carryaway angular momentum. We model our MB torque such that the FCMDs experience aMB torque, approximately scaling as $P_\mathrm{spin}^{-1}$ at shorter periods,before transitioning into a Skumanich-type MB torque, scaling as$P_\mathrm{spin}^{-3}$. We also implement a parametrized reduction in the windmass loss owing to the entrapment of winds in dead zones. We choose a set ofinitial conditions and vary the two free parameters in our model to find a goodmatch of our spin trajectories with open clusters containing FCMDs such asNGC2547, Pleiades, NGC2516 and Praesepe. We find that our model can explain thelong spin periods of field stars and that a spread in spin distributionpersists till over 3 Gyr. An advantage of our model is in relating physicallymotivated estimations of the magnetic field strength and stellar wind toproperties of the stellar dynamo, which other models often remain agnosticabout. We track the spin dependence of the wind mass losses, Alfv\'en radii andsurface magnetic fields and find good agreement with observations. We discussthe implications of our results on the effect of the host FCMD on any orbitingexoplanets and our plans to extend this model to explain solar-like stars inthe future.

monthly notices of the royal astronomical society

Towards a holistic magnetic braking model from the evolution of  cataclysmic variables to stellar spin-down -- I: the spin-down of fully  convective M-dwarfs