DNS of the kappa-mechanism

TL;DR

This paper models the kappa-mechanism in Cepheid variables using nonlinear DNS and linear stability analysis, identifying key parameters for instability and nonlinear saturation effects.

Contribution

It introduces a purely-radiative hydrodynamic model with a configurable conductivity hollow to study the kappa-mechanism and compares nonlinear simulations with linear stability results.

Findings

Instability strips depend on the hollow's location and shape.

Key parameters are the hollow's amplitude and width.

Nonlinear saturation involves mode couplings and a 2:1 resonance.

Abstract

We present a purely-radiative hydrodynamic model of the kappa-mechanism that sustains radial oscillations in Cepheid variables. We determine the physical conditions favourable for the kappa-mechanism to occur by the means of a configurable hollow in the radiative conductivity profile. By starting from these most favourable conditions, we complete nonlinear direct numerical simulations (DNS) and compare them with the results given by a linear-stability analysis of radial modes. We find that well-defined instability strips are generated by changing the location and shape of the conductivity hollow. For a given position in the layer, the hollow amplitude and width stand out as the key parameters governing the appearance of unstable modes driven by the kappa-mechanism. The DNS confirm both the growth rates and structures of the linearly-unstable modes. The nonlinear saturation that arises is produced by intricate couplings between the excited fundamental mode and higher damped overtones. These couplings are measured by projecting the DNS fields onto an acoustic subspace built from regular and adjoint eigenvectors and a 2:1 resonance is found to be responsible for the saturation of the kappa-mechanism instability.