A theoretical tool for the study of radial velocities in the atmospheres of roAp stars

Abstract

Over the last decade significant amounts of high-spectral and time-resolution spectroscopic data have been acquired for a number of rapidly oscillating Ap stars. Progress in the understanding of the information held by these data requires the development of theoretical models that can be directly compared with them. In this work we present a theoretical model for the radial velocities of roAp stars that takes full account of the coupling between the pulsations and the magnetic field. We explore the impact on the radial velocities of changing the position of the observer, the mode frequency and angular degree, as well as of changing the region of the disk where the elements are concentrated. We find that for integrations over the full disc, in the outermost layers the radial velocity is generally dominated by the acoustic waves, showing a rapid increase in amplitude. The most significant depth-variations in the radial velocity phase are seen for observers directed towards the equator and for even degree modes with frequencies close to, or above the acoustic cutoff. Comparison between the radial velocities obtained for spots of elements located around the magnetic poles and around the magnetic equator, shows that these present distinct amplitude-phase relations, resembling some of the differences seen in the observations. Finally, we discuss the conditions under which one may expect to find false nodes in the pulsation radial velocity of roAp stars.

TESS cycle 1 observations of roAp stars with 2-min cadence data

“…Beside the photometric observations of TIC 402546736, there have been substantial spectroscopic studies using high time resolution spectra. These studies (e.g., Baldry et al 1998aBaldry et al , 1999Kochukhov & Ryabchikova 2001;Balona & Laney 2003;Ryabchikova et al 2007) have shown that the principal pulsation mode can have an amplitude up to 1 km s −1 , with some spectral lines pulsating in anti-phase with others, suggesting a node, or false node, in the atmosphere of the star (Sousa & Cunha 2011;Quitral-Manosalva et al 2018).…”

On the first δ Sct–roAp hybrid pulsator and the stability of p and g modes in chemically peculiar A/F stars

“…In deeper layers (where c s c A ), the acoustic stellar pulsation waves decouple from the magnetic (slow) wave, which is generated by pulsation in upper layers. The slow wave propagates inwards, having progressively shorter spatial wavelengths, and is considered to dissipate before reaching the stellar centre (Roberts & Soward 1983;Cunha & Gough 2000;Quitral-Manosalva, Cunha & Kochukhov 2018). In other words, in the outer layers of the star, a fraction of the pulsation energy is converted to a magnetic oscillation that propagates inwards and is eventually dissipated in the deep interior, the overall effect of which is to damp stellar pulsation.…”

Discovery of multiple p-mode pulsation frequencies in the roAp star, HD 86181

“…Khomenko & Kochukhov 2009) have shown that properties of pulsations change rapidly with height in the stellar atmosphere and modes are substantially distorted by the magnetic field. Sousa & Cunha (2011) and Quitral-Manosalva, Cunha & Kochukhov (2018a) have also studied this extensively theoretically.…”

“…In roAp stars part of the pulsation mode energy can be refracted back into the star by the influence of the magnetic field, even when the frequency of the mode is above the acoustic cut-off frequency, νac (Sousa & Cunha 2008;Quitral-Manosalva, Cunha & Kochukhov 2018b). Therefore, there is no reason to assume that very high frequency modes will not be observed in these pulsators.…”