Thermodynamic exchange and mode stability in strongly nonadiabatic radial pulsations
Abstract
We apply the quadratic balance relation for linear nonadiabatic pulsations to radial modes of a sequence of post-AGB envelope models covering 3.52≤log(Teff)≤4.6. The relation separates the thermodynamic exchange power 𝒫ex, response power 𝒫rsp, and surface contribution ΔB, and introduces an effective norm through 𝒫ex+ΔB=2γχeffℰkin, where γ is the mode growth rate. For nearly adiabatic modes χeff 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 χeff<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 χeff>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 χeff<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.
Related
- Eigenfrequency sensitivity in nonadiabatic stellar pulsations
- Power balance and anomalous exchange in post-AGB pulsations
- Mode power and stability in radial post-AGB pulsations
- Quasi-periodic pulsations in solar and stellar flares
- A0538-66: A transient ultraluminous X-ray source with a relativistic outflow, 69,ms pulsations, and anomalous optical activity
BibTeX
@misc{zalewski2026thermodynamic,
title = {{Thermodynamic exchange and mode stability in strongly nonadiabatic radial pulsations}},
author = {Jan Zalewski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14364},
eprint = {2609.14364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14364},
}
RIS
TY - UNPB
TI - Thermodynamic exchange and mode stability in strongly nonadiabatic radial pulsations
AU - Jan Zalewski
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14364
UR - https://arxiv.org/abs/2609.14364
AB - We apply the quadratic balance relation for linear nonadiabatic pulsations to radial modes of a sequence of post-AGB envelope models covering 3.52≤log(T_eff)≤4.6. The relation separates the thermodynamic exchange power 𝒫_ex, response power 𝒫_rsp, and surface contribution ΔB, and introduces an effective norm through 𝒫_ex+ΔB=2γχ_effℰ_kin, where γ is the mode growth rate. For nearly adiabatic modes χ_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_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_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_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.
ER -