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Asymptotic period spacing in red giants

What you are seeing: a vertical cross-section of a red giant with the buoyancy-trapped ℓ=1\ell = 1 g-mode oscillating inside its core cavity. The cavity is where N(r)>0N(r) > 0 (radiative buoyancy region); a convective core or envelope shuts it off. The right panels show the Brunt-Vaisala profile N(r)N(r) that sets the cavity, and the resulting comb of g-mode periods spaced by Π1\Pi_1. Switching between RGB and red-clump profiles changes the buoyancy integral, which changes Π1\Pi_1 from ∼80\sim 80 s to ∼250\sim 250 s

Figure 1. Left: cross-section of the star (radius normalized) with the radial displacement ξn(r) Pℓ(cos⁡θ) cos⁡(ωt)\xi_n(r)\,P_\ell(\cos\theta)\,\cos(\omega t) rendered in a red-blue diverging colormap. Right top: N(r)N(r) profile with the g-mode cavity shaded. Right bottom: period comb Pn=(n+12) ΠℓP_n = (n + \tfrac{1}{2})\,\Pi_\ell, selected mode highlighted
profileRGB
ℓ1
mode order n14
animation speed1

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.