How to Correctly Stitch Together {\it Kepler} Data of a Blazhko Star
L. Çelik, F. Ekmekçi, J. Nemec, K. Kolenberg, J. M. Benkő, R. Szabó, D. W. Kurtz, K. Kinemuchi, H. V. Şenavcı
备注：
This study was presented at the 20th Stellar Pulsation Conference Series on Impact of new instrumentation \& new insights in stellar pulsations, Granada, 5-9 September 2011. This manuscript will be published in AP\&SS
One of the most challenging difficulties that precedes the frequency analysis of {\it Kepler} data for a Blazhko star is stitching together the data from different seasons (quarters). We discuss the preliminary steps in the stitching, detrending and rescaling process using the data for long-term Blazhko stars. We present the process on {\it Kepler} data of a Blazhko star with a variable Blazhko cycle and some first results of our analysis.
We study the 1.28 million short cadence {\it Kepler} data points (Q5-Q14) for RR Lyrae covering 24 cycles of the Blazhko variation, and more than one half of the 4-year modulation of the Blazhko variation. This very rich data set clearly shows variability of the 0.5667 day pulsation period (from 0.5655 to 0.5685 day) with each Blazhko cycle, as well as a variation of the Blazhko period itself (from 39.2 days at amplitude maximum to 38.4 days at amplitude minimum) during the 4 year modulation, as well as a rapid increase in Blazhko period as the new cycle commences.
The first detection of the period doubling phenomenon is reported in the Kepler RR Lyrae stars RR Lyr, V808 Cyg and V355 Lyr. Interestingly, all these pulsating stars show Blazhko modulation. The period doubling manifests itself as alternating maxima and minima of the pulsational cycles in the light curve, as well as through the appearance of half-integer frequencies located halfway between the main pulsation period and its harmonics in the frequency spectrum. The effect was found to be stronger during certain phases of the modulation cycle. We were able to reproduce the period doubling bifurc…
We analyzed the long and short cadence light curves of the Kepler non-Blazhko RRab stars. We prepared the Fourier spectra, the Fourier amplitude and phase variation functions, time-frequency representation, the O-C diagrams and their Fourier contents. Our main findings are: (i) All stars which are brighter a certain magnitude limit show significant cycle-to-cycle light curve variations. (ii) We found permanently excited additional modes for at least one third of the sample and some other stars show temporarily excited additional modes. (iii) The presence of the Blazhko effect was carefully che…
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…
We present our analysis of the long cadence Kepler data for the well-studied Blazhko star RR Lyr, gathered during the first two quarters of the satellite's observations and covering a total of 127d. Besides being of great importance for our understanding of RR Lyrae stars in general, these RR Lyr data can be regarded as a case study for observations of bright stars with Kepler. Kepler can perform high-precision photometry on targets like RR Lyr, as the saturated flux is conserved to a very high degree. The Kepler data on RR Lyr are revolutionary in several respects. Even with long-cadence samp…
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 detecte…
This paper summarizes the main results of our recent study of the non-Blazhko RR Lyrae stars observed with the Kepler space telescope. These stars offer the opportunity for studying the stability of the pulsations of RR Lyrae stars and for providing a reference against which the Blazhko RR Lyrae stars can be compared. Of particular interest is the stability of the low-dispersion (sigma < 1mmag) light curves constructed from ~18,000 long-cadence (30-min) and (for FN Lyr and AW Dra) the ~150,000 short-cadence (1-min) photometric data points. Fourier-based [Fe/H] values and other physical charact…
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. Fourteen of the stars exhibit both amplitude and phase Blazhko modulations, with Blazhko periods ranging from 27.7 to more than 200 days. 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, …
Spectroscopic iron-to-hydrogen ratios, radial velocities, atmospheric parameters, and new photometric analyses are presented for 41 RR Lyrae stars (and one probable high-amplitude delta Scuti star) located in the field-of-view of the Kepler space telescope. Thirty-seven of the RR Lyrae stars are fundamental-mode pulsators (i.e., RRab stars) of which 16 exhibit the Blazhko effect. Four of the stars are multiperiodic RRc pulsators oscillating primarily in the first-overtone mode. Spectroscopic [Fe/H] values for the 34 stars for which we were able to derive estimates range from -2.54 +/- 0.13 (NR…
The origin of the conspicuous amplitude and phase modulation of the RR Lyrae pulsation - known as the Blazhko effect - is still a mystery after more than 100 years of its discovery. With the help of the Kepler space telescope we have revealed a new and unexpected phenomenon: period doubling in RR Lyr - the eponym and prototype of its class - as well as in other Kepler Blazhko RR Lyrae stars. We have found that period doubling is directly connected to the Blazhko modulation. Furthermore, with hydrodynamic model calculations we have succeeded in reproducing the period doubling and proved that th…
Rapid and strong changes in the Blazhko modulation of RR Lyrae stars, as they have recently been detected in high precision satellite data, have become a crucial topic in finding an explanation of the long-standing mystery of the Blazhko effect. We present here an analysis of the most extreme case detected so far, the RRab star V445 Lyr (KIC 6186029) which was observed with the Kepler space mission. V445 Lyr shows very strong cycle-to-cycle changes in its Blazhko modulation, which are caused both by a secondary long-term modulation period as well as irregular variations. In addition to the com…
The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequen…
Homogeneous metallicities and continuous high-precision light curves play key roles in studying the pulsation properties of RR Lyrae stars. By cross-matching with LAMOST DR6, we have determined 7 and 50 Non-Blazhko RRab stars in the Kepler and K2 fields, respectively, who have homogeneous metallicities determined from low-resolution spectra of the LAMOST-Kepler/K2 project. The Fourier Decomposition method is applied to the light curves of these stars provided by the Kepler space based telescope to determine the fundamental pulsation periods and the pulsation parameters. The calculated amplitud…
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 …
RR Lyr is one of the most studied variable stars. Its light curve has been regularly monitored since the discovery of the periodic variability in 1899. Analysis of all observed maxima allows us to identify two primary pulsation states defined as pulsation over a long (P0 longer than 0.56684 d) and a short (P0 shorter than 0.56682 d) primary pulsation period. These states alternate with intervals of 13-16 yr, and are well defined after 1943. The 40.8 d periodical modulations of the amplitude and the period (i.e. Blazhko effect) were noticed in 1916. We provide homogeneous determinations of the …
Nineteen of the ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, KIC 7021124 has been found to …
We found a possible relationship between the modulation period and the amplitude of the Blazhko RR Lyrae stars: long modulation period generally implies high modulation amplitude while the short modulation period results in small amplitude. Although this effect is much more a tendency than a strict rule, it can be detected easily in the space-born time series data produced by Kepler and CoRoT. Good quality ground-based data show this relation, too. This phenomenon could give us constraints for the physics of the Blazhko effect.
In a recent paper (Kovacs 2018) we examined the incidence rate of the modulated RR Lyrae stars by using the data from Campaigns 01 - 04 of the Kepler K2 mission. We found an observed rate of ~90%, implying near 100% underlying rate, after correcting for detection bias due to observational noise. In this work we extend the sample to Campaign 08 and check the reliability of our earlier estimate. We get the same high rate, stressing the importance of full time series modelling (including systematics) in searching for shallow signals in the presence of large amplitude variabilities.
As a response to the Kepler white paper call, we propose to keep Kepler pointing to its current field of view and continue observing thousands of large amplitude variables (Cepheid, RR Lyrae and delta Scuti stars among others) with high cadence in the Kep-Cont Mission. The degraded pointing stability will still allow observation of these stars with reasonable (better than millimag) precision. The Kep-Cont mission will allow studying the nonradial modes in Blazhko-modulated and first overtone RR Lyrae stars and will give a better view on the period jitter of the only Kepler Cepheid in the field…
The unprecedented photometric precision along with the quasi-continuous sampling provided by the Kepler space telescope revealed new and unpredicted phenomena that reformed and invigorated RR Lyrae star research. The discovery of period doubling and the wealth of low-amplitude modes enlightened the complexity of the pulsation behavior and guided us towards nonlinear and nonradial studies. Searching and providing theoretical explanation for these newly found phenomena became a central question, as well as understanding their connection to the oldest enigma of RR Lyrae stars, the Blazhko effect.…
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 time scales of typically tens to hundreds of days. The long time span of the Kepler Mission of 3.5 yrs, 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 t…
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 th…
Harmonics as a Hidden Window into the Turbulent Convective Envelope of non-Blazhko RRab Stars
Institute of Theoretical Physics, Shanxi University（山西大学理论物理研究所）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
With the step-and-stare approach of the K2 mission, Kepler will be able to observe a large number of Cepheid an RR Lyrae stars. In this paper we describe the target selection efforts, and the first impressions based on the K2 two-wheel engineering test data. We also summarize the scientific goals that can be achieved by Kepler, including the understanding of the various additional modes and the Blazhko effect, population studies and the possibilities to observe extragalactic stars in selected campaigns.
RR Lyrae stars for a long time had the reputation of being rather simple pulsators, but the advent of high-precision space photometry has meanwhile changed this picture dramatically. This article summarizes the results obtained for two remarkable Blazhko RR Lyrae stars and discusses how our view of RR Lyrae stars has changed since the availability of ultra-precise satellite photometry as it is obtained by CoRoT and Kepler. Both stars, CoRoT 105288363 and V445 Lyrae, show a multitude of phenomena that were impossible to observe from the ground, either because of the small amplitude of the effec…
The long-term behaviours of the pulsation and Blazhko periods of RR Lyr are investigated by means of Kepler and ground-based observations. The difficulties in detecting additional modes in the Cepheids monitored with CoRoT are discussed.
The study of RR Lyrae stars has recently been invigorated thanks to the long, uninterrupted, ultra-precise time series data provided by the Kepler and CoRoT space telescopes. We give a brief overview of the new observational findings concentrating on the connection between period doubling and the Blazhko modulation, and the omnipresence of additional periodicities in all RR Lyrae subtypes, except for non-modulated RRab stars. Recent theoretical results demonstrate that if more than two modes are present in a nonlinear dynamical system such as a high-amplitude RR Lyrae star, the outcome is ofte…
We search for signs of period doubling in CoRoT RR Lyrae stars. The occurrence of this dynamical effect in modulated RR Lyrae stars might help us to gain more information about the mysterious Blazhko effect. The temporal variability of the additional frequencies in representatives of all subtypes of RR Lyrae stars is also investigated. We pre-process CoRoT light curves by applying trend and jump correction and outlier removal. Standard Fourier technique is used to analyze the frequency content of our targets and follow the time dependent phenomena. The most comprehensive collection of CoRoT RR…
We present the first observations of extragalactic pulsating stars in the K2 ecliptic survey of the Kepler space telescope. Variability of all three RR Lyrae stars in the dwarf spheroidal galaxy Leo IV were successfully detected, at a brightness of Kp~21.5 mag, from data collected during Campaign 1. We identified one modulated star and another likely Blazhko candidate with periods of 29.8+-0.9 d and more than 80 d, respectively. EPIC 210282473 represents the first star beyond the Magellanic Clouds for which the Blazhko period and cycle-to-cycle variations in the modulation were unambiguously m…
The \textit{Kepler} space telescope observed thousands of RR Lyrae stars in the K2 mission. In this paper we present our photometric solutions using extended apertures in order to conserve the flux of the stars to the highest possible extent. With this method we are able to avoid most of the problems that RR Lyrae light curves produced by other pipelines suffer from. For post-processing we apply the K2SC pipeline to our light curves. We provide the EAP (Extended Aperture Photometry) of 432 RR Lyrae stars observed in campaigns 3, 4, 5, and 6. We also provide subclass classifications based on Fo…
The RV Tauri stars constitute a small group of classical pulsating stars with some dozen known members in the Milky Way. The light variation is caused predominantly by pulsations, but these alone do not explain the full complexity of the light curves. High quality photometry of RV Tau-type stars is very rare. DF Cygni is the only member of this class of stars in the original Kepler field, hence allowing the most accurate photometric investigation of an RV Tauri star to date. The main goal is to analyse the periodicities of the RV Tauri-type star DF Cygni by combining four years of high-quality…
