Model calculations for a red giant give the buoyancy frequency and the Lamb frequency…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Pulsating stars: the kappa mechanism, the Leavitt law and asteroseismology

Problem

Model calculations for a red giant give the buoyancy frequency

N

and the

\ell = 1

Lamb frequency

S_1

at five fractional radii, with

N/2\pi

and

S_1/2\pi

\mu\mathrm{Hz}

: at

r/R=0.05

N/2\pi=600

and

S_1/2\pi=1500

; at

0.20

150

and

600

; at

0.40

80

and

300

; at

0.70

20

and

90

; at

0.95

5

and

40

. An oscillation of frequency

\nu = 100\,\mu\mathrm{Hz}

(angular frequency

\omega = 2\pi\nu

) is observed. The local radial wavenumber obeys

k_r^2 = \frac{(\omega^2 - N^2)(\omega^2 - S_\ell^2)}{\omega^2c_s^2}.

((a)) At each of the five radii, state whether

k_r^2 > 0

k_r^2 < 0

, and if

k_r^2>0

whether the wave there is locally a g-type or a p-type oscillation. ((b)) Using these results, describe the propagation diagram for this mode: identify the g-mode cavity, the p-mode cavity, and any evanescent region between them, and explain what a mode of this frequency must do to connect the two cavities.

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