where there is a simplification by sin ft (same remark for the sign). From this expression and (17.41), we get the following general relation between the flux of angular momentum and of kinetic energy for given (—,£, m), m
in g s-2. One defines an "angular momentum luminosity" Cwg(—,£,m), i.e., the total change of angular momentum over the spherical surface at a level r per unit of time, as
in g cm2 s-2. In the adiabatic limit, i.e., without the term with e-T/2, the angular momentum luminosity would be conserved . The total angular momentum is the sum on all waves —,£,m) excited at the edge rc of the convective zone, each wave being damped by the factor e-T/2,
—,l,m since the luminosity depends on u2, the damping factor becomes e-T. Figure 17.3 shows the angular momentum luminosity as a function of degree I and frequency for a 1M0 star. The frequencies — are smaller than the N value at the lower edge of the convective zone in agreement with Fig. 16.8. The I values range from 1 to about 6o, which corresponds to the characteristic length scale of convective motions, i.e., the mixing length. The various m modes are assumed to have the same excitation. One sees that Lang decreases for higher frequencies and that low I values carry more angular momentum. Consistently with Fig. 17.2, these low I waves are less absorbed.
The transport of angular momentum by gravity waves introduces an additional term in Eq. (10.122) for the transport of angular momentum, which expresses the change of angular momentum per volume and time units,
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