Title: Oscillations in centrifugally flattened polytrope
1Oscillations in centrifugally flattened polytrope
F. Lignières and M. Rieutord
Observatoire Midi-Pyrénées
- Non-pertubative model
- Polytropic and uniformly rotating model of stars
- The effect of the centrifugal force on this
equilibrium model is fully adressed - At the moment, we neglect the effect of Coriolis
and centrifugal forces on the oscillating motions
2The formalism
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- Projection on
- Because of symmetries, only modes with the same
azimuthal number m and the same parity of degree
are coupled
where is the surface and
3The ODE system
The coupling terms
4The numerical method
- Two different methods
- QZ algorithm
- Incomplete Arnoldi-Chebyshev
- Numerical parameters lmax, nr
Test
The formalism and the numerics have been tested
in the case of a uniform density ellipsoid
(separable)
5Axisymmetric modes (m0), l 0 to 7, n1 to 8 or
10
w
(GM/R3p)1/2
e
6Spherical Harmonic Spectrum of the modes
l2, n5
l6, n4
e 0
e0.1
e 0.15
w
e
7Departure from the order 1 perturbation in e
l0
l1
D w/ w
l2
e
(D w/w) x 200 Hz gtgt 0.1 m Hz
8Large and small separation
e 0
e 0.1
e 0.15
D w
n
n
9Amplitude of the mode at the surface
l4, n4
e 0
e 0
l0, n1
e 0.05
e 0.05
e 0.1
e 0.1
e 0.15
e 0.15
Pole
Pole
Equator
Equator
10l0,n1 at e0.15
r r1/2v
11l2,n5 at e0.15
r r1/2v
12l4,n4 at e0.15
r r1/2v
13CONCLUSION
In the frequency and flatness range considered
- Modes keep memory of their zero rotation degree
number up to large flatness - Differences with order one pertubation in
flatness are significant - The large separation persists the small
separation dont - The mode amplitude is amplified at the equator