arXiv subjects

Jan Zalewski

Publications and source records attributed to Jan Zalewski.

4 recordsLinked to original sources

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 $\mathcal{P}+\Delta B=2\Re(\sigma)E_{\rm kin}$. 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 $\exp({\omega t})$ 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↗