### 5.2 Magnetic braking

Update
The magnetic braking process by which stars like the Sun shed angular momentum is the reason why
stellar activity decreases with time and why the solar mass loss/age relation in Figure 15 can be inferred
from the mass loss/activity relation in Figure 14 (see Section 5.1). Winds play an important role in this
process, because it is the wind that the stellar field drags against in slowing down the star’s rotation. The
efficiency of this braking is clearly related to the density of the wind, and therefore to the mass loss rate.
Thus, the wind evolution law in Equation (4) has consequences for how the effectiveness of the
magnetic braking changes with time. Models for magnetic braking suggest relations of the form
where is the angular rotation rate and is the Alfvén radius (Weber and
Davis Jr, 1967; StepieÅ„, 1988; Gaidos et al., 2000). The exponent is a number between 0 and 2,
where corresponds to a purely radial magnetic field. Mestel (1984) claims that more reasonable
magnetic geometries suggest . The Alfvén radius is
where is the stellar wind speed and is the disk-averaged radial magnetic field.
For a star like the Sun, the star’s mass and radius are relatively invariant. If does not vary with
time, which was also an assumption used in the derivation of mass loss rates from the astrospheric
absorption (see Section 4.3), then the time dependence of all quantities in Equations (5) and (6) are known
except for that of . If is expressed as a power law, , Equations (4), (5), and (6)
combined suggest

Assuming that is in the physically allowable range of yields the upper limit ,
while the more likely range of suggested by Mestel (1984) implies . In
any case, the empirical mass loss evolution law in Equation (4) is consistent with theoretical
descriptions of magnetic braking only if disk-averaged stellar magnetic fields decline at least as fast as
.