Ecole doctorale de Physique de la région Parisienne (ED107)

V θ
Sp(V θ )
10
5
0
-5
-10
4.6 Strong Cowling approximation in GR 135
0 10
t Ω
20
3
2
1
0
0 2 4 6 8 10
3ω / Ω
Figure 4.19 – Time evolution of the ϑ component of velocity in the same calculation as
in Figure 4.18. The curve and the associated power spectrum show that there are several
modes, but only one of them appears in the Sij tensor with quite a huge amplitude.
Moreover, it has a frequency very close to the frequency of the linear r-mode. See also
the Figure 4.20. Note finally that the same frequency also appears in the spectrum of the
radial velocity.
S xx
Sp(S xx )
0.4
0.2
0
-0.2
-0.4
0
0.2
10
t Ω
20
0.1
0
0 2 4 6 8 10
3ω / Ω
Figure 4.20 – Time evolution of one of the two independent components of the Sij[t]
tensor that appears in the RR force. This calculation was done during the same run as
the results in Figure 4.18 and 4.19. We can see there seems to be one main frequency and
a second one of smaller importance. The first one has exactly the same frequency as the
unstable mode that appears in the previous figures and calculations where the RR force
was on.