Pulsational Frequency and Amplitude Modulation in the $\delta$\,Sct star KIC\,7106205

TL;DR

This study analyzes the pulsational behavior of the extit{Kepler} star KIC 7106205, revealing a unique amplitude modulation in a single pressure mode over 1470 days, while other modes remain stable, indicating non-conservation of pulsation energy.

Contribution

It introduces a method to track amplitude and phase variations of pulsation modes over time and reports the first observation of amplitude modulation in a single pressure mode in a extit{Kepler} extit{delta} Sct star.

Findings

One pressure mode shows significant amplitude and phase modulation.

Other pressure and gravity modes remain stable in amplitude and phase.

The pulsation mode energy appears not to be conserved within the star.

Abstract

Analysis of the \textit{Kepler} $\delta$\,Sct star KIC\,7106205 showed amplitude modulation in a single pressure mode, whilst all other pressure and gravity modes remained stable in amplitude and phase over the 1470\,d length of the dataset. The \textit{Kepler} dataset was divided into a series with time bins of equal length for which consecutive Fourier transforms were calculated. An optimum fixed frequency, calculated from a least-squares fit of all data, allowed amplitude and phase of each pulsation mode for each time bin to be tracked. The single pressure mode at $\nu$\,=\,13.3942\,d$^{-1}$ changed significantly in amplitude, from 5.16\,$\pm$\,0.03 to 0.53\,$\pm$\,0.06\,mmag, but also varied quasi-sinusoidally in phase, with a characteristic period similar to the length of the dataset. All other p and g\,modes were stable in both amplitude and phase, which is clear evidence that the visible pulsation mode energy is not conserved within this star. Possible causes of the observed amplitude and phase modulation and the missing mode energy are discussed.