Eigenfrequency sensitivity in nonadiabatic stellar pulsations

We derive an adjoint formulation of eigenfrequency sensitivity for linear nonadiabatic stellar pulsations, including the frequency dependence of the boundary conditions. Local sensitivity kernels and their cumulative integrals describe the responses of the excitation rate and oscillation frequency to prescribed scaling of the pulsation matrix and its acoustic, thermal and coupling blocks. Applications to selected radial modes of post-AGB envelopes reveal distinct spatial and subsystem sensitivity profiles. In the cool model, the ordinary mode has weak sensitivity near both boundaries for the slow branch outer boundary conditions, whereas the strange mode exhibits pronounced sensitivity in the outer layers. Selected modes of the hotter model also show appreciable outer-layer sensitivity. The block decomposition reveals differing contributions and cancellations in the excitation-rate and oscillation-frequency responses.