Dynamical model for spindown of solar-type stars

After their formation, stars slow down their rotation rates by the removal of angular momentum from their surfaces, e.g., via stellar winds. Explaining how this rotation of solar-type stars evolves in time is currently an interesting but difficult problem in astrophysics. Despite the complexity of the processes involved, a traditional model, where the removal of angular momentum by magnetic fields is prescribed, has provided a useful framework to understand observational relations between stellar rotation, age, and magnetic field strength. Here, for the first time, a spindown model is proposed where loss of angular momentum by magnetic fields evolves dynamically, instead of being prescibed kinematically. To this end, we evolve the stellar rotation and magnetic field simultaneously over stellar evolution time by extending our previous work on a dynamo model which incorporates nonlinear feedback mechanisms on rotation and magnetic fields. We show that our extended model reproduces key observations and is capable of explaining the presence of the two branches of (fast and slow rotating) stars which have different relations between rotation rate Ω versus time (age), magnetic field strength $| B| $ versus rotation rate, and frequency of magnetic field ${\omega }_{\mathrm{cyc}}$ versus rotation rate. For fast rotating stars we find that: (i) there is an exponential spindown ${\rm{\Omega }}\propto {e}^{-1.35t}$, with t measured in Gyr; (ii) magnetic activity saturates for higher rotation rate; (iii) ${\omega }_{\mathrm{cyc}}\propto {{\rm{\Omega }}}^{0.83}$. For slow rotating stars we find: (i) a power-law spindown ${\rm{\Omega }}\propto {t}^{-0.52}$; (ii) that magnetic activity scales roughly linearly with rotation rate; (iii) ${\omega }_{\mathrm{cyc}}\propto {{\rm{\Omega }}}^{1.16}$. The results obtained from our investigations are in good agreement with observations. The Vaughan–Preston gap is consistently explained in our model by the shortest spindown timescale in this transition from fast to slow rotators. Our results highlight the importance of self-regulation of magnetic fields and rotation by direct and indirect interactions involving nonlinear feedback in stellar evolution.