LEGOLAS spectrum for the equilibrium of Sect. 2.2 with Spitzer–Härm field-aligned thermal conduction, N = 400 grid points). Left: eigenvalue spectrum; the thermal continuum of Fig. 1 is replaced by discrete thermal modes (crosses) and the global thermal mode persists (purple marker). Blue dots are acoustic modes. Right: normalised density eigenfunctions, showing n nodes for the n-th mode.