Abstract
Pulsating variables of γ Doradus type (γ Dor) and slowly pulsating B-type (SPB) stars are found on and near the main sequence with typical periods varying between one and several days, making them rather hard to detect from the ground. It is only with space missions such as CoRoT and Kepler that we became truly capable of determining their oscillation frequencies with enough precision to perform in-depth analyses. Here we present an efficient and easy-to-implement seismic tool, in which the frequency (ν) and the square root of the frequency difference ($ \sqrt{\Delta \nu} $) are plotted against each other as the abscissa and the ordinate, respectively. This allows us to immediately (1) perform mode identification; (2) estimate the average rotation rate and the characteristic period of gravity modes; and (3) recognise certain physical effects, including buoyancy glitches and avoided crossings. This diagnostic tool can only be applied to prograde sectoral g modes. To validate the tool presented here, we used stellar models and also applied it to three γ Dor (KIC 12066947, KIC 5608334 and KIC 4846809) and one SPB star (KIC 3459297), all observed with Kepler. Furthermore, we show that the rotation rates determined using this new tool are consistent with the results of previous studies.
Highlights
Gamma Doradus (γ Dor) stars are a class of pulsating variable stars located on and near the main sequence with spectral types from late-A to early-F
Pulsating variables of γ Doradus type (γ Dor) and slowly pulsating B-type (SPB) stars are found on and near the main sequence with typical periods varying between one and several days, making them rather hard to detect from the ground
We show that the internal rotation rate of γ Dor and slowly pulsating B-type (SPB) stars can be estimated in a model-independent way by using a simple linear relation between the oscillation frequency and the square-root of the frequency difference
Summary
Gamma Doradus (γ Dor) stars are a class of pulsating variable stars located on and near the main sequence with spectral types from late-A to early-F. We show that the internal rotation rate of γ Dor and slowly pulsating B-type (SPB) stars can be estimated in a model-independent way by using a simple linear relation between the oscillation frequency and the square-root of the frequency difference. This method can only be applied to prograde sectoral g modes, which is fortunate as observations (e.g. Saio et al 2018a; Li et al 2019) show that γ Dor stars predominantly pulsate in these modes.
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