The Blazhko effect and additional excited modes in RR Lyrae stars

Recent photometric space missions, such as CoRoT and Kepler revealed that many RR Lyrae stars pulsate -- beyond their main radial pulsation mode -- in low amplitude modes. Space data seem to indicate a clear trend, namely overtone (RRc) stars and modulated fundamental (RRab) RR Lyrae stars ubiquitously show additional modes, while non-Blazhko RRab stars never do. Two Kepler stars (V350 Lyr and KIC 7021124), however, apparently seemed to break this rule: they were classified as non-Blazhko RRab stars showing additional modes. We processed Kepler pixel photometric data of these stars. We detected small amplitude, but significant Blazhko effect for both stars by using the resulted light curves and O$-$C diagrams. This finding strengthens the apparent connection between the Blazhko effect and the excitation of additional modes. In addition, it yields a potential tool for detecting Blazhko stars through the additional frequency patterns even if we have only short but accurate time series observations. V350 Lyr shows the smallest amplitude multiperiodic Blazhko effect ever detected.Comment: 6 pages, 4 figures and 2 tables. Accepted for publication in ApJ Letter

Unexpected series of regular frequency spacing of delta Scuti stars in the non-asymptotic regime -- I. The methodology

A sequence search method was developed to search regular frequency spacing in delta Scuti stars by visual inspection and algorithmic search. We searched for sequences of quasi-equally spaced frequencies, containing at least four members per sequence, in 90 delta Scuti stars observed by CoRoT. We found an unexpectedly large number of independent series of regular frequency spacing in 77 delta Scuti stars (from 1 to 8 sequences) in the non-asymptotic regime. We introduce the sequence search method presenting the sequences and echelle diagram of CoRoT 102675756 and the structure of the algorithmic search. Four sequences (echelle ridges) were found in the 5-21 d^{-1} region, where the pairs of the sequences are shifted (between 0.5-0.59 d^{-1}) by twice the value of the estimated rotational splitting frequency (0.269 d^{-1}). The general conclusions for the whole sample are also presented in this paper. The statistics of the spacings derived by the sequence search method, by FT and that of the shifts are also compared. In many stars, more than one almost equally valid spacing appeared. The model frequencies of FG Vir and their rotationally split components were used to reveal a possible explanation that one spacing is the large separation, while the other is a sum of the large separation and the rotational frequency. In CoRoT 102675756, the two spacings (2.249 and 1.977 d^{-1}) agree better with the sum of a possible 1.710 d^{-1} large separation and two or one times, respectively, the value of the rotational frequency.Comment: 12 pages, 10 figures, accepted for publication in Ap

Unexpected series of regular frequency spacing of delta Scuti stars in the non-asymptotic regime -- II. Sample -- echelle diagrams and rotation

A sequence search method was developed for searching for regular frequency spacing in delta Scuti stars by visual inspection and algorithmic search. The sample contains 90 delta Scuti stars observed by CoRoT. An example is given to represent the visual inspection. The algorithm (SSA) is described in detail. The data treatment of the CoRoT light curves, the criteria for frequency filtering and the spacings derived by two methods (three approaches: VI, SSA and FT) are given for each target. Echelle diagrams are presented for 77 targets, for which at least one sequence of regular spacing was identified. Comparing the spacing and the shifts between pairs of echelle ridges revealed that at least one pair of echelle ridges is shifted to midway between the spacing for 22 stars. The estimated rotational frequencies compared to the shifts revealed rotationally split doublets, triplets and multiplets not only for single frequencies, but for the complete echelle ridges in 31 delta Scuti stars. Using several possible assumptions for the origin of the spacings, we derived the large separation ($\Delta\nu$), which are distributed along the mean density versus large separations relation derived from stellar models Suarez 2014.Comment: 25 pages, 16 figures, 9 tables. Accepted for publication in ApJ

Kepler RR Lyrae stars: beyond period doubling

We examined the complete short cadence sample of Kepler RR Lyrae stars to further investigate the recently discovered dynamical effects such as period doubling and additional modes. Here we present the findings on four stars. V450 Lyr may be a non-classical double-mode RR Lyrae star pulsating in the fundamental mode and the second overtone. In three cases we observe the interaction of three different modes. Since the period ratios are close to resonant values, we observe quasi-repetiting patterns in the pulsation cycles in the stars. These findings support the mode-resonance explanations of the Blazhko effect.Comment: 2 pages, 1 figure. Proceedings of the 301st IAU Symposium, Precision Asteroseismology, August 2013, Wroc{\l}aw. V2: small corrections to the wordin

Nonlinear dynamical analysis of the Blazhko effect with the Kepler space telescope: the case of V783 Cyg

We present a detailed nonlinear dynamical investigation of the Blazhko modulation of the Kepler RR Lyrae star V783 Cyg (KIC 5559631). We used different techniques to produce modulation curves, including the determination of amplitude maxima, the O-C diagram and the analytical function method. We were able to fit the modulation curves with chaotic signals with the global flow reconstruction method. However, when we investigated the effects of instrumental and data processing artefacts, we found that the chaotic nature of the modulation can not be proved because of the technical problems of data stitching, detrending and sparse sampling. Moreover, we found that a considerable part of the detected cycle-to-cycle variation of the modulation may originate from these effects. According to our results, even the four-year-long, unprecedented Kepler space photometry of V783 Cyg is too short for a reliable nonlinear dynamical analysis aiming at the detection of chaos from the Blazhko modulation. We estimate that two other stars could be suitable for similar analysis in the Kepler sample and in the future TESS and PLATO may provide additional candidates.Comment: 9 pages, 12 figures, accepted for publication in MNRA

On the interchange of alternating-amplitude pulsation cycles

We characterized the time intervals between the interchanges of the alternating high- and low-amplitude extrema of three RV Tauri and three RR Lyrae stars.Comment: 2 pages, Proceedings of the 301st IAU Symposium, Precision Asteroseismology, August 201

Long time-scale behavior of the Blazhko effect from rectified Kepler data

In order to benefit from the 4-year unprecedented precision of the Kepler data, we extracted light curves from the pixel photometric data of the Kepler space telescope for 15 Blazhko RR Lyrae stars. For collecting all the flux from a given target as accurately as possible, we defined tailor-made apertures for each star and quarter. In some cases the aperture finding process yielded sub-optimal result, because some flux have been lost even if the aperture contains all available pixels around the star. This fact stresses the importance of those methods that rely on the whole light curve instead of focusing on the extrema (O-C diagrams and other amplitude independent methods). We carried out detailed Fourier analysis of the light curves and the amplitude independent O-C diagram. We found 12 (80%) multiperiodically modulated stars in our sample. This ratio is much higher than previously found. Resonant coupling between radial modes, a recent theory to explain of the Blazhko effect, allows single, multiperiodic or even chaotic modulations. Among the stars with two modulations we found three stars (V355 Lyr, V366 Lyr and V450 Lyr) where one of the periods dominate in amplitude modulation, but the other period has larger frequency modulation amplitude. The ratio between the primary and secondary modulation periods is almost always very close to ratios of small integer numbers. It may indicate the effect of undiscovered resonances. Furthermore, we detected the excitation of the second radial overtone mode $f_2$ for three stars where this feature was formerly unknown. Our data set comprises the longest continuous, most precise observations of Blazhko RR Lyrae stars ever published. These data which is made publicly available will be unprecedented for years to come.Comment: 19 pages, 17 figures, accepted for publication in Astrophys. J. Suppl. Rectified data are here: http://www.konkoly.hu/KIK/data.htm