p- and g-Mode Cavities (Propagation Diagram)

What you are seeing: where a stellar oscillation actually lives. A pulsating cross-section shows the mode displacement field (degree $\ell$ ): large where the mode propagates, evanescent where it cannot. A low-frequency mode is trapped in the radiative-core g-cavity, a high-frequency mode in the acoustic-envelope p-cavity, and an intermediate one is a mixed mode in both. The linked propagation diagram carries $N$ , $S_\ell$ and $\omega$ with the cavities shaded, and the mode energy split between the two cavities is read out.

Figure 1. p- and g-mode cavities of an n=3 polytrope. Top: a pulsating cross-section, the mode displacement field, large in the cavity where it propagates and evanescent elsewhere (red and blue are opposite phase). Bottom: the propagation diagram, the buoyancy frequency N(r) and the Lamb frequency S_l(r) of the real polytrope; the mode propagates above both (p-cavity, envelope) or below both (g-cavity, core), and is evanescent between. Method: Cowling-approximation dispersion k_r^2 = (omega^2 - S_l^2)(omega^2 - N^2)/(omega^2 c^2). Reference: Aerts, Christensen-Dalsgaard and Kurtz (2010), Ch. 3.

ω (mode)2.40

ℓ1

WHAT TO TRY

Start low (omega near 1): the mode is a g-mode, trapped in the core where omega is below both N and S_l; the cross-section rings in the centre.
Raise omega past about 3: it becomes a p-mode, trapped in the envelope where omega is above both frequencies; the ripples move to the outer shell.
Stop in between (omega near 2.4): a mixed mode appears, with a g-cavity in the core and a p-cavity in the envelope coupled through the evanescent gap. Watch the energy split shift between them.
Raise the degree l: S_l rises, so the p-cavity retreats toward the surface and the turning points move outward.