Amplitude modulation and energy conservation of pulsation modes in delta Scuti stars

Abstract

The pulsations in δ Sct stars are excited by a heat engine driving mechanism caused by in-creased opacity in their surface layers, and have pulsation periods of order a few hours. Space based observations in the last decade have revealed a diverse range of pulsational be-haviour in these stars, which is investigated using an ensemble of 983 δ Sct stars observed continuously for 4 yr by the Kepler Space Tele-scope. A statistical search for amplitude modu-lation of pulsation modes is carried out and it is shown that 61.3 per cent of the 983 δ Sct stars exhibit significant amplitude modulation in at least a single pulsation mode, and that this is uncorrelated with effective temperature and surface gravity. Hence, the majority of δ Sct stars exhibit amplitude modulation, with time-scales of years and longer demonstrated to be significant in these stars both observationally and theoretically.
An archetypal example of amplitude modulation in a δ Sct star is KIC 7106205, which contains only a single pulsation mode that varies signifi-cantly in amplitude whilst all other pulsation modes stay constant in amplitude and phase throughout the 4-yr Kepler data set. Therefore, the visible pulsational energy budget in this star, and many others, is not conserved over 4 yr.
Models of beating of close-frequency pulsation modes are used to identify δ Sct stars with fre-quencies that lie closer than 0.001 d−1, which are barely resolved using 4 yr of Kepler observa-tions, and maintain their independent identi-ties over 4 yr. Mode coupling models are used to quantify the strength of coupling and distin-guish between non-linearity in the form of combination frequencies and non-linearity in the form of resonant mode coupling for families of pulsation modes in several stars.
The changes in stellar structure caused by stel-lar evolution are investigated for two high am-plitude δ Sct (HADS) stars in the Kepler data set, revealing a positive quadratic change in phase for the fundamental and first overtone radial modes in KIC 5950759. The observed phase modulation of the radial modes in this star is two orders of magnitude larger than predicted by stellar evolutionary models, yet is consistent with the prediction of increasing pe-riods of radial modes for stars on the main se-quence.
The statistical analysis of 983 δ Sct stars, in-cluding the results from the search for ampli-tude modulation, is a valuable resource for on-going and future space missions such as K2, TESS and PLATO, because the high quality 4-yr Kepler data set will not be surpassed for some time. The observational studies of individual stars in this thesis provide strong evidence that non-linear processes are clearly at work in the majority of δ Sct stars, and provide valuable constraints for future asteroseismic modelling.