Towards the undestanding of radial velocity pulsation in roAp stars

TL;DR

This paper presents a theoretical analysis of pulsations in the outer layers of roAp stars, aiming to explain observed standing and running waves through simplified atmospheric models considering magnetic and acoustic wave components.

Contribution

It introduces a simplified isothermal, plane-parallel atmospheric model to analyze magnetoacoustic wave behavior in roAp stars, providing analytical solutions for velocity components.

Findings

Estimated velocity components parallel to the line of sight.

Derived amplitude and phase as functions of atmospheric height.

Provided a framework to interpret spectroscopic pulsation observations.

Abstract

High-resolution spectroscopic time series of rapidly oscillating Ap stars show evidence for a co-existence of standing and running waves in their atmospheric layers. With the purpose of understanding these observations we have carried out a theoretical analysis of the pulsations in the outermost layers of these stars, starting from the simplest possible model that still retains all important physical ingredients. In our analysis we considered an isothermal atmosphere in a plane-parallel approximation. Moreover we assumed that in the region considered the magnetic pressure is much larger than the gas pressure and, consequently, that the magnetoacoustic wave has decoupled into its acoustic and magnetic components. Using the analytical solutions for the velocity components appropriate to this model we estimate the velocity component parallel to the line of sight averaged over the visible stellar disk. Fitting the latter to a function of the form Acos($\sigma$t+phase), with $\sigma$ the dimensionless oscillation frequency and t the dimensionless time, we derive the amplitude A and the phase for our model as function of height in the atmosphere.