Ecole doctorale de Physique de la région Parisienne (ED107)

S xx
Sp(S xx )
0.2
0.1
0
-0.1
4.6 Strong Cowling approximation in GR 141
-0.2
0
0.2
10
t Ω
20
0.1
0
0 2 4 6 8 10
3ω / Ω
Figure 4.26 – 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 Figures 4.24 and 4.25. We can see the almost monochromatic associated
spectrum with exactly the same frequency as the mode that appears in the previous
figures.
V θ
2
1.5
1
0.5
θ = π/2
θ = 9π/16
θ = 5π/8
θ = 21π/32
θ = 11π/16
θ = 3π/4
θ = 13π/16
θ = 7π/8
θ = 15π/16
θ = π
0
0 0.2 0.4 0.6 0.8 1
ξ / R
Figure 4.27 – ϑ component of the velocity versus the radius for several values of ϑ. We
can see the kind of concentration of the motion near the surface and the equatorial plane.
This calculation was done with the strong Cowling and anelastic approximations and the
free surface BC. The background star is a γ = 2 relativistic rigidly rotating polytrope
with 1.74 solar masses and a radius equal to 12.37 km. The initial data are the Newtonian
linear l = m = 2 r-mode. This figure corresponds to the velocity after a time equal to 15
oscillations of the linear l = m = 2 r-mode.