Blazhko RR Lyrae Research Articles

Two Different Weak Modulations in ab-type RR Lyrae Variable V838 Cyg, and Potential Influence of Metal Abundance on Blazhko Modulation

Noting the weakest modulation and relatively high metal abundance of the ab-type RR Lyrae star V838 Cyg, we collected the photometric data of this star from several sky surveys to carry out an in-depth analysis. The O − C diagram shows that the pulsation period of V838 Cyg increases linearly over a long timescale. In a reanalysis of the high-precision Kepler data, we confirmed the modulation with a period of 59.45 ± 0.07 days found by Benkő et al., and also found an additional weak modulation with a longer period (840 ± 21 days). After a series of analyses, we incline to the view that the mechanisms causing the two modulations are different: the former is more similar to the typical Blazhko effect, while the mechanism leading to the latter may be an extrinsic factor. We also collected and compared the modulation and physical parameters of other Blazhko RR Lyrae stars from several works in the literature, and find that there is a potential negative correlation between the modulation amplitude (or upper limit of amplitude) and the metal abundance. We infer that the relatively high metal abundance will promote convection in the outer stellar atmosphere, and then inhibit those factors (turbulence, shock wave, etc.) that may cause Blazhko modulation. Future observations and research work can be carried out with reference to this viewpoint. We also introduce the moiré effects that appear in the Kepler long-cadence light curves and their possible interference in the previous analyses.

A novel approach for variable star classification based on imbalanced learning

Abstract The advent of time-domain sky surveys has generated a vast amount of light variation data, enabling astronomers to investigate variable stars with large-scale samples. However, this also poses new opportunities and challenges for the time-domain research. In this paper, we focus on the classification of variable stars from the Catalina Surveys Data Release 2 and propose an imbalanced learning classifier based on Self-paced Ensemble (SPE) method. Compared with the work of Hosenie et al. (2020), our approach significantly enhances the classification Recall of Blazhko RR Lyrae stars from 12% to 85%, mixed-mode RR Lyrae variables from 29% to 64%, detached binaries from 68% to 97%, and LPV from 87% to 99%. SPE demonstrates a rather good performance on most of the variable classes except RRab, RRc, and contact and semi-detached binary. Moreover, the results suggest that SPE tends to target the minority classes of objects, while Random Forest is more effective in finding the majority classes. To balance the overall classification accuracy, we construct a Voting Classifier that combines the strengths of SPE and Random Forest. The results show that the Voting Classifier can achieve a balanced performance across all classes with minimal loss of accuracy. In summary, the SPE algorithm and Voting Classifier are superior to traditional machine learning methods and can be well applied to classify the periodic variable stars. This paper contributes to the current research on imbalanced learning in astronomy and can also be extended to the time-domain data of other larger sky survey projects (LSST, etc.).

Evaluating the V-band Photometric Metallicity with Fundamental Mode RR Lyrae in the Kepler Field

The aim of this work is to evaluate the performance of photometric metallicity [Fe/H], determined based on V-band light curves photometrically transformed from the gr-band light curves. We tested this by using a set of homogeneous samples of fundamental mode RR Lyrae located in the Kepler field. It was found that the color term is necessary in such photometric transformation. We demonstrated that when including the color term the determined photometric [Fe/H] are in good agreement with the spectroscopic [Fe/H], either based on the calibrated or the transformed V-band light curves. We also tested the impact of Blazhko RR Lyrae in determining the photometric [Fe/H], and found that Blazhko RR Lyrae can give consistent photometric [Fe/H]. Finally, we derived independent gVr-band [Fe/H]–ϕ 31–P relations (where ϕ 31 and P are the Fourier parameter and pulsation period, respectively) using our light curves. The V-band relation is in good agreement with the most recent determination given in the literature.

A Double-modulation Effect Detected in a Double-mode High-amplitude δ Scuti Star: KIC 10284901

Abstract In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 10284901. The Fourier transform of the high-precision light curve reveals seven independent frequencies for its light variations. Among them, the first two frequencies are main pulsation modes: F0 = 18.994054(1) day−1 and F1 = 24.335804(4) day−1; the ratio F0/F1 = 0.7805 classifies this star as a double-mode high-amplitude δ Scuti (HADS) star; another two frequencies, f m1 = 0.4407 day−1 and f m2 = 0.8125 day−1, are detected directly, and the modulations of f m1 and f m2 to F0 and F1 modes (seen as quintuplet structures centered on these two modes in the frequency spectrum) are also found. This is the first detection of a double-modulation effect in the HADS stars. The features of the frequency pattern and the ratio (f m1/f m2 ≈ 1:2), as well as the cyclic variation of amplitude of the two dominant pulsation modes, which seem to be similar to that in Blazhko RR Lyrae stars, indicate this modulation might be related to the Blazhko effect. A preliminary analysis suggests that KIC 10284901 is in the bottom of the HADS instability strip and situated in the main sequence.

On the connection between almost periodic functions and Blazhko light curves

In this paper it is shown that the mathematical form which most precisely describes the Blazhko RR Lyrae light curves is connected to almost periodic functions and not to the mathematics of modulation. That is, the Blazhko effect is more than a simple external modulation of the pulsation signal. The mathematical framework of almost periodic functions predicts a new observable effect: a shift of the Fourier harmonics of the main pulsation frequency from the exact harmonic position. This phenomenon is called as harmonic detuning effect (HDE).The published deviations of the harmonics of V445 Lyr are explained with this effect. HDE is also found for V2178 Cyg, another Blazhko star observed by the Kepler space telescope. HDE is detectable only if the phase variation part of the Blazhko effect is of large amplitude and non-periodic enough, additionally, the time span of the observed light curve is sufficiently long for obtaining precise frequencies. These three conditions restrict the number of stars showing detectable HDE and explain why this effect has not been discovered up to now.

The first Baade–Wesselink analysis of Blazhko RR Lyrae stars: discrepancies between photometrically and spectroscopically determined radius variations

Abstract The simultaneous photometric and spectroscopic observations of the RR Lyrae variables in the globular cluster, M3, published in Jurcsik et al. (2017, Paper I) made it possible to perform Baade–Wesselink (BW) analysis of a large sample of Blazhko stars for the first time. The BW distances of Blazhko stars turned out to be unreliable, as significantly different distances were obtained for the stars of the Blazhko sample and also for the same star in different modulation phases. Even the results of small modulation–amplitude Blazhko stars may be doubtful. This result warns that the application of the BW method to Blazhko stars is not trustworthy. Keeping the distance fixed for each Blazhko star in each modulation phase, a significant difference between the spectroscopic and the photometric radius (Rsp, Rph) variations is detected. The phase and amplitude variations of Rsp follow the changes of the light curve during the Blazhko cycle but the Rph curve seems to be not (or only marginally) affected by the modulation. The asynchronous behaviour of Rsp and Rph supports the interpretation of the Blazhko effect as a depth-dependent phenomenon, as the spectroscopic radius variation reflects the radial displacement of the line-forming region high in the atmosphere, while the photospheric radius variation is derived from the information of the observed visual-band light emitted mostly by the lower photosphere. The stability of Rph may be interpreted as a strong argument against the non-radial-mode explanation of the Blazhko phenomenon.

The Blazhko RR Lyrae variables and phase modulation in binary systems

With the help of the Fourier transform, I verify that some stars classified as Blazhko variables are actually regularly pulsating RR Lyrae stars in binary systems.

V473 Lyr, a modulated, period-doubled Cepheid, and U TrA, a double-mode Cepheid observed by MOST

Space-based photometric measurements first revealed low-amplitude irregularities in the pulsations of Cepheid stars, but their origins and how commonly they occur remain uncertain. To investigate this phenomenon, we present MOST space telescope photometry of two Cepheids. V473 Lyrae is a second-overtone, strongly modulated Cepheid, while U Trianguli Australis is a Cepheid pulsating simultaneously in the fundamental mode and first overtone. The nearly continuous, high-precision photometry reveals alternations in the amplitudes of cycles in V473 Lyr, the first case of period doubling detected in a classical Cepheid. In U TrA, we tentatively identify one peak as the $f_X$ or 0.61-type mode often seen in conjunction with the first radial overtone in Cepheids, but given the short length of the data, we cannot rule out that it is a combination peak instead. Ground-based photometry and spectroscopy were obtained to follow two modulation cycles in V473 Lyr and to better specify its physical parameters. The simultaneous data yield the phase lag parameter (the phase difference between maxima in luminosity and radial velocity) of a second-overtone Cepheid for the first time. We find no evidence for a period change in U TrA or an energy exchange between the fundamental mode and the first overtone during the last 50 years, contrary to earlier indications. Period doubling in V473 Lyr provides a strong argument that mode interactions do occur in some Cepheids and we may hypothesise that it could be behind the amplitude modulation, as recently proposed for Blazhko RR Lyrae stars.

Connection between the period and the amplitude of the Blazhko effect

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.

Revisiting CoRoT RR Lyrae stars: detection of period doubling and temporal variation of additional frequencies

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 Lyrae stars, including new discoveries is presented and analyzed. We found alternating maxima and in some cases half-integer frequencies in four CoRoT Blazhko RR Lyrae stars, as clear signs of the presence of period doubling. This reinforces that period doubling is an important ingredient to understand the Blazhko effect - a premise we derived previously from the Kepler RR Lyrae sample. As expected, period doubling is detectable only for short time intervals in most modulated RRab stars. Our results show that the temporal variability of the additional frequencies in all RR Lyrae sub-types is ubiquitous. The ephemeral nature and the highly variable amplitude of these variations suggest a complex underlying dynamics of and an intricate interplay between radial and possibly nonradial modes in RR Lyrae stars. The omnipresence of additional modes in all types of RR Lyrae - except in non-modulated RRab stars - implies that asteroseismology of these objects should be feasible in the near future (Abridged).

MOST light-curve analysis of theγDoradus pulsator HR 8799, showing resonances and amplitude variations

Context: The central star of the HR 8799 system is a gamma Doradus-type pulsator. The system harbours four planetary-mass companions detected by direct imaging, and is a good solar system analogue. The masses of the companions are not known accurately, because the estimation depends strongly on the age of the system, which is also not known with sufficient accuracy. Asteroseismic studies of the star might help to better constrain the age of HR 8799. We organized an extensive photometric and multi-site spectroscopic observing campaign for studying the pulsations of the central star. Aims: The aim of the present study is to investigate the pulsation properties of HR 8799 in detail via the ultra-precise 47-d-long nearly continuous photometry obtained with the MOST space telescope, and to find as many independent pulsation modes as possible, which is the prerequisite of an asteroseismic age determination. Methods: We carried out Fourier analysis of the wide-band photometric time series. Results: We find that resonance and sudden amplitude changes characterize the pulsation of HR 8799. The dominant frequency is always at f1 = 1.978 c/d. Many multiples of one ninth of the dominant frequency appear in the Fourier spectrum of the MOST data: n/9 f1, where n={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18}. Our analysis also reveals that many of these peaks show strong amplitude decrease and phase variations even on the 47-d time-scale. The dependencies between the pulsation frequencies of HR 8799 make the planned subsequent asteroseismic analysis rather difficult. We point out some resemblance between the light curve of HR 8799 and the modulated pulsation light curves of Blazhko RR Lyrae stars.

LONG-TIMESCALE 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.

Blazhko effect in Cepheids and RR Lyrae stars

AbstractThe Blazhko effect is the conspicuous amplitude and phase modulation of the pulsation of RR Lyrae stars that was discovered in the early 20th century. The field of study of this mysterious modulation has recently been invigorated thanks to the space photometric missions providing long, uninterrupted, ultra-precise time-series data. In this paper I give a brief overview of the new observational findings related to the Blazhko effect, such as extreme modulations, irregular modulation cycles and additional periodicities. I argue that these findings together with dedicated ground-based efforts provide us now with a fairly complete picture and a good starting point to theoretical investigations. Indeed, new, unpredicted dynamical phenomena have been discovered in Blazhko RR Lyrae stars, such as period doubling, high-order resonances, three-mode pulsation and low-dimensional chaos. These led to the proposal of a new explanation to this century-old enigma, namely a high-order resonance between radial modes. Along these lines I present the latest efforts and advances from the theoretical point of view. Lastly, amplitude variations in Cepheids are discussed.

Are RRab stars fully radial?

AbstractThanks to the space missions CoRoT and Kepler new oscillation frequencies have been discovered in the Fourier spectra of Blazhko RR Lyrae stars. The period doubling (PD) yields half-integer frequencies between the fundamental mode and its harmonics. In many cases the first and/or second radial overtone frequencies also appear temporally. Some stars show extra frequencies that were identified as potential non-radial modes. We show here that all these frequencies can be explained by pure radial pulsation as linear combinations of the frequencies of radial fundamental and overtone modes.

RR Lyrae stars seen from space

AbstractRR 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 effect, or because uninterrupted long‐term monitoring was required for a detection. Not only was it found that strong and irregular cycle‐to‐cycle changes of the Blazhko effect can occur, and that seemingly chaotic phenomena need to be accounted for when modeling the Blazhko effect, but also a rich spectrum of low‐amplitude frequencies was detected in addition to the fundamental radial pulsation in RRab stars. The so‐called period doubling phenomenon, higher radial overtones and possibly also non‐radial modes make RR Lyrae stars more multifaceted than previously thought. This article presents the various aspects of irregularity of the Blazhko effect, questioning its long‐standing definition as a “periodic modulation”, and also discusses the low‐amplitude pulsation signatures that had been hidden in the noise of observations for centuries (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The light-curve modulation of XY And and UZ Vir: two Blazhko RR Lyrae stars with additional frequencies

A thorough analysis of multicolour CCD observations of two modulated RRab-type variables, XY And and UZ Vir is presented. These Blazhko stars show relatively simple light-curve modulation with the usual multiplet structures in their Fourier spectra. One additional, independent frequency with linear-combination terms of the pulsation frequency is also detected in the residual spectrum of each of the two stars. The amplitude and phase relations of the triplet components are studied in detail. Most of the epoch-independent phase differences show a slight, systematic colour dependence, however, these trends have the opposite sign in the two stars. The mean values of the global physical parameters and their changes with Blazhko phase are determined utilizing the Inverse Photometric Method (IPM). The modulation properties and the IPM results are compared for the two variables. The pulsation period of XY And is the shortest when its pulsation amplitude is the highest, while UZ Vir has the longest pulsation period at this phase of the modulation. Despite this opposite behaviour, the phase relations of their mean-physical-parameter variations are similar. These results are not in accord with the predictions of the Blazhko model of Stothers (2006, ApJ, 652, 643).

Period doubling and Blazhko modulation in BL Herculis hydrodynamic models

We present the hydrodynamic BL Herculis-type models which display a long-term modulation of pulsation amplitudes and phases. The modulation is either strictly periodic or it is quasi-periodic, with the modulation period and modulation pattern varying from one cycle to the other. Such behaviour has not been observed in any BL Her variable so far, however, it is a common property of their lower luminosity siblings - RR Lyrae variables showing the Blazhko effect. These models provide a support for the recent mechanism proposed by Buchler & Kollath to explain this still mysterious phenomenon. In their model, a half-integer resonance that causes the period doubling effect, discovered recently in the Blazhko RR Lyrae stars, is responsible for the modulation of the pulsation as well. Although our models are more luminous than is appropriate for RR Lyrae stars, they clearly demonstrate, through direct hydrodynamic computation, that the mechanism can indeed be operational. Of great importance are models which show quasi-periodic modulation - a phenomenon observed in Blazhko RR Lyrae stars. Our models coupled with the analysis of the amplitude equations show that such behaviour may be caused by the dynamical evolution occurring in the close proximity of the unstable single periodic saddle point.

Search for high-amplitude δ Scuti and RR Lyrae stars in Sloan Digital Sky Survey Stripe 82 using principal component analysis

We propose a robust principal component analysis framework for the exploitation of multiband photometric measurements in large surveys. Period search results are improved using the time-series of the first principal component due to its optimized signal-to-noise ratio. The presence of correlated excess variations in the multivariate time-series enables the detection of weaker variability. Furthermore, the direction of the largest variance differs for certain types of variable stars. This can be used as an efficient attribute for classification. The application of the method to a subsample of Sloan Digital Sky Survey Stripe 82 data yielded 132 high-amplitude δ Scuti variables. We also found 129 new RR Lyrae variables, complementary to the catalogue of Sesar et al., extending the halo area mapped by Stripe 82 RR Lyrae stars towards the Galactic bulge. The sample also comprises 25 multiperiodic or Blazhko RR Lyrae stars.

Blazhko RR Lyrae light curves as modulated signals

We present an analytical formalism for the description of Blazhko RR Lyrae light curves. In this formalism the amplitude and frequency modulations are treated in a manner similar to the theory of electronic signal transmission. We consider monoperiodic RR Lyrae light curves to be carrier waves, and modulate their amplitude (AM), frequency (FM) and phase (PM); as a general case we discuss simultaneous AM and FM. The main advantages of this method are the following: (i) the mathematical formalism naturally explains numerous light-curve characteristics found in the Blazhko RR Lyrae stars such as mean brightness variations, complicated envelope curves and non-sinusoidal frequency variations; (ii) our elucidation also explains the properties of the Fourier spectra such as apparent higher order multiplets, amplitude distribution of the sidepeaks, the appearance of the modulation frequency itself and its harmonics. In addition, compared to the traditional methods, our light-curve solutions reduce the number of necessary parameters. This formalism can be applied to any type of modulated light curves, not just to Blazhko RR Lyrae star light curves.

The CoRoT star 105288363: strong cycle-to-cycle changes of the Blazhko modulation

We present the analysis of the CoRoT star 105288363, a new Blazhko RR Lyrae star of type RRab (f0 = 1.7623 c/d), observed with the CoRoT space craft during the second long run in direction of the galactic center (LRc02, time base 145 d). The CoRoT data are characterized by an excellent time sampling and a low noise amplitude of 0.07 mmag in the 2-12 c/d range and allow us to study not only the fine details of the variability of the star but also long-term changes in the pulsation behaviour and the stability of the Blazhko cycle. We use, among other methods, standard Fourier analysis techniques and O-C diagrams to investigate the pulsational behavior of the Blazhko star 105288363. In addition to the frequency pattern expected for a Blazhko RR Lyrae star, we find an independent mode (f1 = 2.984 c/d) showing a f0/f1 ratio of 0.59 which is similar to that observed in other Blazhko RR Lyrae stars. The bump and hump phenomena are also analysed, with their variations over the Blazhko cycle. We carefully investigated the strong cycle-to-cycle changes in the Blazhko modulation (PB = 35.6 d), which seem to happen independently and partly diametrically in the amplitude and the phase modulation. Furthermore, the phasing between the two types of modulation is found to change during the course of the observations.