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We systematically searched for gravity- and Rossby-mode period spacing patterns in Kepler eclipsing binaries with γ Doradus pulsators. These stars provide an excellent opportunity to test the theory of tidal synchronisation and angular momentum transport in F- and A-type stars. We discovered 35 systems that show clear patterns, including the spectroscopic binary KIC 10080943. Combined with 45 non-eclipsing binaries with γ Dor components that have been found using pulsation timing, we measured their near-core rotation rates and asymptotic period spacings. We find that many stars are tidally locked if the orbital periods are shorter than 10 days, in which the near-core rotation periods given by the traditional approximation of rotation (TAR) are consistent with the orbital period. Compared to the single stars, γ Dor stars in binaries tend to have slower near-core rotation rates, likely a consequence of tidal spin-down. We also find three stars that have extremely slow near-core rotation rates. To explain these, we hypothesise that unstable tidally excited oscillations can transfer angular momentum from the star to the orbit, and slow the star below synchronism, a process we refer to as ‘inverse tides’.

Abstract. We use photometry from the Kepler Mission to study oscillations in γ Doradus stars. Some stars show remarkably clear sequences of g modes and we use period echelle diagrams to measure period spacings and identify rotationally split multiplets with = 1 and = 2. We find small deviations from regular period spacings that arise from the gradient in the chemical composition just outside the convective core. We also find stars for which the period spacing shows a strong linear trend as a function of period, consistent with relatively rapid rotation. Overall, the results indicate it will be possible to apply asteroseismology to a range of γ Dor stars.Gravity modes are extremely valuable for probing stellar interiors. Asteroseismology using g modes has so far produced very good results on three classes of highly evolved stars, namely white dwarfs [1], sdB stars [2] and red giants [3][4][5]. Excellent results have also been obtained for a few SPB stars (slowly pulsating B stars), which lie on the upper main sequence [6,7]. However, the g modes lower on the main sequence, which occur in γ Doradus stars, have proved much more difficult to exploit. They typically have periods close to one day, which makes ground-based study exceedingly difficult. Furthermore, as we show here, they have very dense frequency spectra. Even the first month or so of Kepler data, which revealed many stars with g modes (and many hybrids having both g and p modes), was not enough to properly resolve their frequency spectra [8]. With four years of nearly-continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to γ Dor stars.Applying asteroseismology requires identifying which modes are excited. In γ Dor stars, we are guided by the expectation that g modes should be approximately equally spaced in period, at least for slow rotators. So far, only one γ Dor star has been reported with a clearly measured period spacing. This is KIC 11145123, which was found to have a series of rotationally split = 1 triplets with a regular period spacing of ΔP = 2100 s [9]. Here, we look at this star and other γ Dor pulsators in the Kepler field and show that some of them have remarkably clear sequences of g modes.Solar-like stars have p-mode oscillations that are approximately equally spaced in frequency. The so-calledéchelle diagram is made by dividing the frequency spectrum into equal segments and stacking them one above the other so that modes with a given degree align vertically in ridges [10]. Any departures from regularity are clearly visible as curvature in theéchelle diagram. For g-modes, the regularity is in period rather than frequency, which suggests the use of a periodéchelle diagram [3]. Note that the period spacing of g modes decreases with angular degree according to ΔP ∝ 1/ √ ( + 1), which means a differentéchelle diagram is needed for each value of . Article available at