Mode Trapping in Evolved Stars

What you are seeing: a buoyancy-frequency glitch (sharp localised variation of $N$ ) imprints a periodic modulation on the g-mode period spacing $\Delta P(P)$ . The modulation amplitude $A$ measures glitch strength; the modulation period $P_{\rm trap}$ measures the glitch position.

Figure 1. Mode trapping in an evolved star. Top: the buoyancy frequency N(r) with a composition glitch, and the displacement eigenfunction of the current g-mode (gold when trapped, green when propagating). Bottom: the observable period-spacing diagram deltaP(P), whose dips mark the trapped modes. Both come from solving the g-mode wave equation psi'' + (l(l+1) N^2/(omega^2 r^2)) psi = 0 on one N(r) profile. Reference: Aerts, Christensen-Dalsgaard and Kurtz (2010), Ch. 3.4; Cunha et al. (2015).

glitch strength A0.45

glitch position0.22

degree ℓ1

WHAT TO TRY

Set the glitch strength to zero: the eigenfunctions all look alike and the period spacing is flat at Pi_1, the asymptotic g-mode result.
Turn the glitch up: the spacing develops dips, and the modes sitting in those dips are the trapped ones, ringing loudly on one side of the glitch.
Move the glitch outward: the modulation period of the dips changes, because it is set by the buoyancy depth of the glitch. This is how the dip pattern locates the glitch.
Watch the sweep: successive modes trap and release as their period passes through the dips.