arXiv subjects

Jan Zalewski

Publications and source records attributed to Jan Zalewski.

8 recordsLinked to original sources

arXiv2026

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.

astro-ph.SR↗

arXiv2026

Mode power and stability in radial post-AGB pulsations

We examine the relation between mode power and excitation rate for radial pulsations along a sequence of high-luminosity post-AGB envelope models. The net thermodynamic exchange power, including boundary contributions, is compared with the excitation rate and the inertia, compression and horizontal area deformation norms entering the balance relation. We find that positive net exchange power can accompany damping, while negative net exchange power can accompany excitation. Along an individual mode sequence, the power may reverse sign repeatedly without a change of stability. These reversals are associated with changes in the sign of the effective norm. Including the compression contribution in the pressure-force power does not remove this behaviour and can extend the intervals of sign disagreement. Thus, although spatial exchange integrals identify positive and negative contributions to the modal power, the sign of the global power alone does not generally determine mode stability.

astro-ph.SR↗

arXiv2026

Power balance and anomalous exchange in post-AGB pulsations

We develop a complex balance relation for stellar pulsations whose real and imaginary parts give paired relations for the excitation rate and oscillation frequency. The formulation includes thermodynamic exchange, boundary power, and the inertial, compression, horizontal-area, and gravitational-stratification terms, without assuming weak nonadiabaticity. Applied to portions of an envelope, it provides cumulative diagnostics evaluated using the eigenfrequency and eigenfunctions of the complete pulsation problem. We show that a negligible global boundary contribution can coexist with substantial internal boundary power, which may largely compensate the thermodynamic exchange within the envelope. Applications to radial pulsations of post-AGB envelopes illustrate this behaviour for ordinary, strange, and anomalous-exchange modes. The latter have a negative effective norm and opposite signs of net exchange power and excitation rate. For a selected excited anomalous mode, the principal exchange occurs between the He II ionization region and the Z-bump, with less participation from the outer ionization layers than in the comparison modes. Classification by the largest response norm reveals distinct domains across the examined pulsation spectrum. The selected anomalous branch retains horizontal-area dominance across its transition from damping to excitation.

astro-ph.SR↗

arXiv2026

Thermodynamic exchange and mode stability in strongly nonadiabatic radial pulsations

We apply the quadratic balance relation for linear nonadiabatic pulsations to radial modes of a sequence of post-AGB envelope models covering $3.52\leq\log(T_{\rm eff})\leq4.6$. The relation separates the thermodynamic exchange power $\mathcal{P}_{\rm ex}$, response power $\mathcal{P}_{\rm rsp}$, and surface contribution $ΔB$, and introduces an effective norm through $\mathcal{P}_{\rm ex}+ΔB=2γχ_{\rm eff}\mathcal{E}_{\rm kin}$, where $γ$ is the mode growth rate. For nearly adiabatic modes $χ_{\rm eff}$ is close to unity, whereas in strongly nonadiabatic pulsations the compression and horizontal area deformation contributions can make it change magnitude or even reverse its sign. In the cooler models, a broad family of overtone modes has $χ_{\rm eff}<0$ and is damped despite positive thermodynamic exchange power. For these modes the response power supplies the opposing damping. Conversely, two low frequency modes in the hotter models are excited over a range of effective temperatures, even though their thermodynamic exchange power is negative. Their instability is produced by the positive response power. Strange modes generally have $χ_{\rm eff}>0$, apart from a narrow boundary-sensitive transition during which a cold strange mode transforms into an ordinary p-mode. The excited low frequency solution with $χ_{\rm eff}<0$ persists with a finer numerical mesh and such modes are found under the alternative outer boundary formulations examined, although their frequencies are boundary condition dependent. Thus, for strongly nonadiabatic pulsations, the sign of the thermodynamic exchange power alone does not determine mode stability.

astro-ph.SR↗

arXiv2026

A generalized quadratic balance relation for nonradial nonadiabatic pulsations

We derive a generalized quadratic balance relation for linear nonadiabatic, nonradial stellar pulsations, starting from a sesquilinear amplitude analogue of the pressure-volume-rate work. The derivation requires neither weak nonadiabaticity nor averaging over a pulsation cycle. The relation is expressed in terms of work, generalized norm and boundary contributions and is subsequently recast into kinetic-energy-power form $\mathcal{P}+ΔB=2\Re(σ)E_{\rm kin}$. The volume power is decomposed into a thermodynamic exchange term and response terms associated with compression, horizontal-area deformation and gravitational stratification effects. The equivalent forms of the relation provide diagnostics for checking the computed eigenfrequencies and estimating mode excitation rates. The properties of the balance relation for various types of modes in an envelope of a model AGB star are examined. We analyze the terms entering the power $\mathcal{P}$ for radial and nonradial p-modes, strange modes as well as examples of low frequency outer-envelope gravity modes and thermal modes. The results show that the magnitude of mode driving is not determined solely by the thermodynamic work term.

astro-ph.SR↗

arXiv2026

A quadratic balance relation for radial nonadiabatic pulsations

Using a sesquilinear pressure - rate of volume change kernel and linear pulsation equations, we formulate a balance relation combining work integral, surface terms, norm integral and the real part of pulsation frequency (for $\exp({ωt})$ time dependence) in terms of linear radial pulsation variables. The resulting relation is exact within the adopted radial nonadiabatic formulation. We apply the quadratic balance relation to radial pulsations in AGB envelopes and use it to check the accuracy of computation and to obtain information about mode excitation and damping. We also compare the balance relation with the classical formulation based on dissipation and kinetic energy integrals and discuss the meaning of the components made explicit by the present decomposition that appear in our balance equation and their relevance for ordinary and strange modes in AGB envelopes.

astro-ph.SR↗

arXiv2026

On the numerical reliability of nonadiabatic pulsation solutions in AGB envelopes

We re-examine integration methods of linear nonadiabatic radial pulsations in the envelopes of AGB and post-AGB stars using the subspace shooting formulation. In the article the accuracy of the direct integration, the Riccati based method and a continuous renormalization nonlinear integration method are examined. The last method is not widely used in stellar pulsation studies and is therefore of interest in the present comparison. A tracking transformation of the two independent solution vectors is introduced. It helps to improve the accuracy and stability of the solution and can be readily implemented for any of these integration methods. Minimum singular value maps are used to examine the structure of the pulsation spectrum over the complex-frequency plane and also to assess the fidelity with which the integration methods transport the solution subspace. These maps provide a practical alternative to the customarily used maps based on the determinant. We use these maps together with the eigenfrequency spectra to establish mesh conditions required for the reliable transport of the solution subspace, especially in the nonlinear methods. To measure the quality of the subspace transport a spillover measure is introduced. Using this measure it is also possible to verify the placement of the inner boundary, which in the case of radial modes, cannot be guided by propagation criteria based on the Lamb frequency. Visual inspection of the eigenfrequency spectra, the singular value maps, or the eigenmode amplitudes and behavior in the deep envelope does not necessarily imply preservation of the transported-solution subspace. The spillover measure provides a much clearer indicator. This approach provides explicit quantitative diagnostics for assessing the reliability of strongly nonadiabatic pulsation calculations in AGB/post-AGB stellar envelopes.

astro-ph.SR↗

arXiv2026

Boundary conditions for radial pulsations in AGB envelopes

We present a formulation of outer and inner boundary conditions for radial non-adiabatic pulsations in AGB/post-AGB envelopes in terms of local structure of pulsation equations. This approach provides a framework to construct classes of boundary condition selectors. We show that the pulsation spectrum is primarily determined by the choice of the outer boundary selector. Different choices of the two-dimensional subspace at the outer boundary lead to different types of pulsation spectra ranging from p-mode like spectra to ones including strongly excited and damped strange modes. Our results show that the outer boundary conditions control the degree of coupling between acoustic and entropy components in the solution. Selectors dominated by slow (non-acoustic) branches lead to strongly non-adiabatic behavior and emergence of strongly excited/damped strange modes, while selectors including acoustic branches result in weaker coupling and more classical looking spectra. At the inner boundary we found that it is sufficient to enforce that the solution resides in a two-dimensional subspace allowed by the local pulsation equations. This ensures regular behavior and compatibility with WKB asymptotics in deep parts of the envelope. Once this condition is met the detailed form of the inner boundary selector has only minor influence on the resulting pulsation spectrum. We also compare the obtained spectra with those obtained using standard boundary conditions to show that the variations in excitation rates of strange modes reported previously may be interpreted in terms of the subspaces selected by the outer boundary.

astro-ph.SR↗