We present the analysis of four first overtone RR Lyrae stars observed with the Kepler space telescope, based on data obtained over nearly 2.5 yr. All four stars are found to be multiperiodic. The strongest secondary mode with frequency f 2 has an amplitude of a few mmag, 20−45 times lower than the main radial mode with frequency f 1 . The two oscillations have a period ratio of P 2 /P 1 = 0.612 − 0.632 that cannot be reproduced by any two radial modes. Thus, the secondary mode is nonradial. Modes yielding similar period ratios have also recently been discovered in other variables of the RRc and RRd types. These objects form a homogenous group and constitute a new class of multimode RR Lyrae pulsators, analogous to a similar class of multimode classical Cepheids in the Magellanic Clouds. Because a secondary mode with P 2 /P 1 ∼ 0.61 is found in almost every RRc and RRd star observed from space, this form of multiperiodicity must be common. In all four Kepler RRc stars studied, we find subharmonics of f 2 at ∼ 1/2f 2 and at ∼ 3/2f 2 . This is a signature of period doubling of the secondary oscillation, and is the first detection of period doubling in RRc stars. The amplitudes and phases of f 2 and its subharmonics are variable on a timescale of 10 − 200 d. The dominant radial mode also shows variations on the same timescale, but with much smaller amplitude. In three Kepler RRc stars we detect additional periodicities, with amplitudes below 1 mmag, that must correspond to nonradial g-modes. Such modes never before have been observed in RR Lyrae variables.

We present our analysis of Kepler observations of 29 RR Lyrae stars, based on 138 d of observation. We report precise pulsation periods for all stars. Nine of these stars had incorrect or unknown periods in the literature. 14 of the stars exhibit both amplitude and phase Blazhko modulations, with Blazhko periods ranging from 27.7 to more than 200 d. For V445 Lyr, a longer secondary variation is also observed in addition to its 53.2‐d Blazhko period. The unprecedented precision of the Kepler photometry has led to the discovery of the the smallest modulations detected so far. Moreover, additional frequencies beyond the well‐known harmonics and Blazhko multiplets have been found. These frequencies are located around the half‐integer multiples of the main pulsation frequency for at least three stars. In four stars, these frequencies are close to the first and/or second overtone modes. The amplitudes of these periodicities seem to vary over the Blazhko cycle. V350 Lyr, a non‐Blazhko star in our sample, is the first example of a double‐mode RR Lyrae star that pulsates in its fundamental and second overtone modes.

We present the first results of our analyses of selected RR Lyrae stars for which data have been obtained by the Kepler Mission. As expected, we find a significant fraction of the RRab stars to show the Blazhko effect, a still unexplained phenomenon that manifests itself as periodic amplitude and phase modulations of the light curve, on timescales of typically tens to hundreds of days. The long time span of the Kepler Mission of 3.5 yr and the unprecedentedly high precision of its data provide a unique opportunity for the study of RR Lyrae stars. Using data of a modulated star observed in the first roll as a showcase, we discuss the data, our analyses, findings, and their implications for our understanding of RR Lyrae stars and the Blazhko effect. With at least 40% of the RR Lyrae stars in our sample showing modulation, we confirm the high incidence rate that was only found in recent high-precision studies. Moreover, we report the occurrence of additional frequencies, beyond the main pulsation mode and its modulation components. Their half-integer ratio to the main frequency is reminiscent of a period doubling effect caused by resonances, observed for the first time in RR Lyrae stars.

Context. Detached eclipsing binaries (dEBs) are ideal targets for accurately measuring the masses and radii of their component stars. If at least one of the stars has evolved off the main sequence (MS), the masses and radii give a strict constraint on the age of the stars. Several dEBs containing a bright K giant and a fainter MS star have been discovered by the Kepler satellite. The mass and radius of a red giant (RG) star can also be derived from its asteroseismic signal. The parameters determined in this way depend on stellar models and may contain systematic errors. It is important to validate the asteroseismically determined mass and radius with independent methods. This can be done when stars are members of stellar clusters or members of dEBs. Aims. This paper presents an analysis of the dEB system KIC 8410637, which consists of an RG and an MS star. The aim is to derive accurate masses and radii for both components and provide the foundation for a strong test of the asteroseismic method and the accuracy of the deduced mass, radius, and age. Methods. We analysed high-resolution, high-signal-to-noise spectra from three different spectrographs. We also calculated a fit to the Kepler light curve and used ground-based photometry to determine the flux ratios between the component stars in the BVRI passbands. Results. We measured the masses and radii of the stars in the dEB, and the classical parameters T eff , log g, and [Fe/H] from the spectra and ground-based photometry. The RG component of KIC 8410637 is most likely in the core helium-burning red clump phase of evolution and has an age and composition that are very similar to the stars in the open cluster NGC 6819. The mass of the RG in KIC 8410637 should therefore be similar to the mass of RGs in NGC 6819, thus lending support to the latest version of the asteroseismic scaling relations. This is the first direct measurement of both mass and radius for an RG to be compared with values for RGs from asteroseismic scaling relations thereby providing an accurate comparison. We find excellent agreement between log g values derived from the binary analysis and asteroseismic scaling relations. Conclusions. We have determined the masses and radii of the two stars in the binary accurately. A detailed asteroseismic analysis will be presented in a forthcoming paper, allowing an informative comparison between the parameters determined for the dEB and from asteroseismology.

Abstract. Results of a search for variable stars in the central region of the globular cluster M 13 are presented. Prior to this study, 36 variable and suspected variable stars were known in this cluster (Osborn 2000;Clement et al. 2001). Of these stars, five were not observed by us. We find v3, v4, v10, v12, and v13 to be constant in light. Surprisingly, only two out of the ten variable star candidates of Kadla et al. (1980) appear to be variable. Both are RRc variables. Additionally, three RR Lyrae stars and one SX Phoenicis variable are discovered. Three close frequencies are detected for an RRc star v36. It appears that this variable is another multi-periodic RR Lyrae star pulsating in non-radial modes. Light curves of the three known BL Herculis stars and all known RR Lyrae stars are presented. The total number of known RR Lyrae stars in M 13 is now nine. Only one is an RRab star. The mean period of RRc variables amounts to 0.36 ± 0.05 d, suggesting that M 13 should be included in the group of Oosterhoff type II globular clusters. Mean V magnitudes and ranges of variation are derived for seven RR Lyrae and three BL Herculis variables. Almost all observed bright giants show some degree of variability. In particular, we confirm the variability of two red giants announced to be variable by Osborn (2000) and in addition find five new cases.