Ecole doctorale de Physique de la région Parisienne (ED107)

Sp(V r )
V r
4
2
0
-2
4.5 Differential rotation 131
-4
0
0.75
50
t Ω
100 150
0.5
0.25
0
0 2 4 6 8 10 12
3ω / Ω
Figure 4.14 – Time evolution of the radial component of velocity in a γ = 2 polytrope
with anelastic approximation and Gaussian noise for initial data. A huge RR force acts
(something like what should exist in a star with angular velocity equal to 1000 Hz) and
the background star is assumed to be differentially rotating with the law corresponding
to βn = 0.4. We see that a polar counterpart of the mode now grows.
V θ
Sp(V θ )
100
0
-100
20
15
10
5
0 50 100 150
t Ω
0
0 2 4 6 8 10
3ω / Ω
Figure 4.15 – Time evolution of the ϑ component of velocity in the same calculation
as in Figure 4.14. The associated power spectrum shows that there is one mode driven
to instability that is the same as in Figure 4.14 and has a frequency very close to the
expected frequency of the r-mode. See also the Figure 4.16.