In the posting "The rotation of stars and their complex magnetism" I described how stellar rotation generates magnetic fields and how the rotation rates of stars like the Sun slow down over time.  At about 4.6 billion years old the Sun is well into its middle-age and currently rotates once about every 25 days.  When it was a hundred times younger, or only a few tens of millions of years old, it would have been rotating about ten times faster - once in a day or so (also see posting from 2013 April 27).  The spin-down over time occurs because stars like the Sun lose mass to a wind.  The wind is essentially completely ionized, and it clings to the stellar magnetic field for a distance of a few stellar radii before it manages to break free.  The drag of the magnetic field in the wind applies what is referred to as a magnetic brake - a drag, or torque, that very gradually slows the rotation down.  The efficacy of the brake depends mostly on the rate mass is lost to the wind and the strength of the magnetic field.

SAO researcher Ofer Cohen and I have used magnetohydrodynamic simulations of the wind of a Sun-like star to investigate how strong the magnetic brake might have been through time - from the young, rapidly-rotating Sun to its present middle-age and beyond.  We assumed different values for the surface magnetic field and the plasma density at the base of the wind, and computed the resulting wind model and its torque on the star.  The figure illustrates the local wind mass loss rate and the surface at which the wind breaks free of the magnetic field (the "Alfven surface") for four different models.  We found that mass loss rates are largely controlled by the magnetic field strength and that most of the torque is applied through low-latitude regions around the equator where the model finds the wind density to be higher.  In order to match observed spin-down rates of stars, the magnetic field strength should vary approximately with the square of the rotation rate.  This work was published in the 2014 March 1 edition of the Astrophysical Journal.