Magnetic braking

5.2 Magnetic braking

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 $Ω$ is the angular rotation rate and $RA$ is the Alfvén radius (Weber and Davis Jr, 1967 ; Stepień, 1988 ; Gaidos et al., 2000 ). The exponent $m$ is a number between 0 and 2, where $m = 2$ corresponds to a purely radial magnetic field. Mestel (1984

) claims that more reasonable magnetic geometries suggest $m = 0– 1$ . The Alfvén radius is

where $Vw$ is the stellar wind speed and $Br$ is the disk-averaged radial magnetic field.

For a star like the Sun, the star’s mass and radius are relatively invariant. If $Vw$ 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 $Br$ . If $Br$ is expressed as a power law, $α Br ∝ t$ , Equations (4 ), (5 ), and (6 ) combined suggest

Assuming that $m$ is in the physically allowable range of $m = 0 –2$ yields the upper limit $α < − 1.3$ , while the more likely range of $m = 0 –1$ suggested by Mestel (1984 ) implies $α < − 1.7$ . 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 $t−1.3$ .