Modelling Long-Period Variables - I. A new grid of O-rich and C-rich pulsation models

TL;DR

This paper introduces a comprehensive grid of non-adiabatic pulsation models for Long-Period Variables, covering a wide parameter space and including detailed opacities, to better understand their variability and evolution.

Contribution

It provides the first systematic set of models accounting for variability in C-stars, with improved opacities and a new analytic prescription for dominant pulsation modes.

Findings

Overtones are largely determined by global stellar properties.

The frequency of the most excited overtone scales with the acoustic cut-off frequency.

Models align well with observed long-period variability evolution.

Abstract

We present a new grid of non-adiabatic, linear pulsation models of Long-Period Variables (LPVs), including periods and growth rates for radial modes from the fundamental to the fourth overtone. The models span a wide range in mass, luminosity, metallicity, C/O ratio and helium abundance, effectively covering the whole thermally-pulsing asymptotic giant branch (TP-AGB) evolution, and representing a significant update with respect to previous works. The main improvement is the inclusion of detailed atomic and molecular opacities, consistent with the models chemical mixture, that makes the present set of models the first to systematically account for variability in C-stars. We examine periods and growth rates in the models, and find that, while the fundamental mode is affected by the structure of the envelope, overtones are less sensitive to the interior and largely determined by the global properties. In the models, the frequency of the overtone with the largest degree of excitation is found to scale with the acoustic cut-off frequency at the stellar surface, a behaviour similar to that observed for the frequency of maximum oscillation power for solar-like oscillations in less evolved red giants. This allows us to provide a simple analytic prescription to predict the most-likely dominant mode as a function of stellar parameters. Best-fit relations for periods are also provided. By applying results of pulsation models to evolutionary tracks, we present a general picture of the evolution of long-period variability during the TP-AGB, that we find consistent with observations. Models are made public through a dedicated web interface.