We present the result of the analysis of the FI Sge individual light curves constructed on Transiting Exoplanet Survey Satellite (TESS) observations. FI Sge the RR Lyrae pulsating variable star with bicyclicity effects and possible Blazhko effect. In the present study, we analyzed 3603 photometric data obtained by the Transiting Exoplanet Survey Satellite (TESS) in the special TESS IR bandpass with a time resolution of about 10 minutes. The observations covered a 27-day interval (BJD 2459769.90 − 2459796.12) with a small gap of about a day. The full data set contains 52 minima and 51 maxima of the seasonal light curve. We suppose that for this data set, the analysis of the light curve shapes in minima provides more reliable results. We studied the variations of the minima’ shapes of the individual light curves at common and for the separate affinity groups. The last one allowed us to detect not only classical bicyclicity, but also secondary bicyclicity for FI Sge. This result was obtained at first and it is atypical behavior of light curves for pulsating variable stars.

Recent studies have shown that the irregular O-C variations observed in many non-Blazhko RR Lyrae stars may result from random, cycle-to-cycle (C2C) variations in their light curves. However, centuries-long data series reveal that the O-C diagrams of Blazhko stars exhibit particularly large-amplitude, irregular variations. In this letter, we extend the previous investigation of non-Blazhko stars to Blazhko stars to explore the role of C2C variations in the O-C diagrams. Kepler We derived the O-C diagrams from space telescope light curves using a precise template-fitting method. Based on their Fourier analyses, we also constructed residual O-C diagrams that were pre-whitened for frequencies associated with the Blazhko effect. We then fitted the same statistical models to both types of O-Cs that we had previously applied to non-Blazhko stars. Kepler The optimal statistical model includes the C2C variation for 74% of the O-C curves in our Blazhko sample, and the parameter describing the strength of the C2C variation is significantly larger than that obtained for non-Blazhko stars. This may explain the strong irregular O-C variations previously observed in Blazhko stars. Furthermore, we found a strong positive correlation between the C2C variation strength and the amplitude of the frequency-modulation component of the Blazhko effect, indicating a connection between the two phenomena.

Context. The lack of RR Lyr stars in binary systems is an atypical fact when we consider other classes of variables. Therefore, it has become a challenge for observers to detect an RR Lyr variable in a binary system. Aims. The RR Lyr variable KIC 2831097 was one of the most promising candidates. The phases of maximum brightness in the Kepler photometry showed a regular variation superimposed on a parabolic trend. These variations in the times of maximum brightness (T max s) were interpreted as a possible light-time travel effect (LTTE) in a wide binary and a fast evolutionary change in the period. Methods. We planned two spectroscopic runs with the FIES instrument mounted at the Nordic Optical Telescope to test the hypothesis of binarity. The observations were programmed at the predicted quadratures of the orbit, when the two mean radial velocities are expected to differ by about 100 km s −1 . The GEOS collaboration complemented the spectroscopic survey by a photometric one. We also analysed Gaia time series and intensive TESS photometry. Results. The radial velocity curves obtained at the quadratures show the same mean radial velocity (-203 km s −1 ), which rules the possibility of an LTTE out. The constant mean radial velocity, the [Fe/H] content determined from ground-based CCD observations, and the astrometric parameters supplied by Gaia allow us to infer that KIC 2831097 is a single high-velocity metal-poor RRc star belonging to the Galactic halo. We revisited Kepler photometry and detected a weak Blazhko effect consisting of an oscillation of only 1.1% of the period in about 50 d. We also analysed the TESS photometry of Kepler -1601, whose photometry is contaminated by KIC 2831097. We collected 116 T max s, from the ground-based campaign, 103 T max s from TESS, and 4 T max s from Gaia . In total, we have 3624 T max s. Linear ephemerides cannot fit the whole dataset, but only parts of them. The period shows a tendency to decrease in value, as if it were an evolutionary effect, but not at a constant rate. Conclusions. The spectroscopic and photometric campaigns performed in the framework of a professional-amateur project failed to confirm that KIC 2831097 belongs to a binary system: the chase remains open. As an RR Lyr variable, KIC 2831097 shows an intriguing evolution of the period.

Abstract We analyzed the incidence and properties of RR Lyrae stars that show evidence for amplitude and phase modulation (the so-called Blazhko Effect) in a sample of ∼3000 stars with LINEAR and ZTF light curve data collected during the periods of 2002–2008 and 2018–2023, respectively. A preliminary subsample of about ∼500 stars was algorithmically preselected using various data quality and light curve statistics, and then 228 stars were confirmed visually as displaying the Blazhko effect. This sample increases the number of field RR Lyrae stars displaying the Blazhko effect by more than 50% and places a lower limit of (11.4 ± 0.8)% for their incidence rate. We find that ab type RR Lyrae that show the Blazhko effect have about 5% (0.030 day) shorter periods than starting sample, a 7.1σ statistically significant difference. We find no significant differences in their light curve amplitudes and apparent magnitude (essentially, signal-to-noise ratio) distributions. No period or other differences are found for c type RR Lyrae. We find convincing examples of stars where the Blazhko effect can appear and disappear on timescales of several years. With time-resolved photometry expected from the Legacy Survey of Space and Time, a similar analysis will be performed for even larger samples of field RR Lyrae stars in the southern sky and we anticipate a higher fraction of discovered Blazhko stars due to better sampling and superior photometric quality.

Abstract In this study, we conduct a comparative analysis of the properties of Blazhko and non-Blazhko RRab stars. We identified 1054 non-Blazhko and 785 Blazhko RRab stars in the photometric data observed by the K2 mission, which, combined with those 37 stars observed in the original Kepler field, constituted our study sample. Using the Fourier decomposition method, we calculated the pulsation parameters, including phase differences and amplitude ratios, for these RRab stars, revealing significant discrepancies in the pulsation parameters between Blazhko and non-Blazhko RRab stars. However, distinguishing between Blazhko and non-Blazhko RRab stars based on Fourier parameters remains challenging due to the significant overlap in their distributions. By crossmatching our sample with the low-resolution spectra of LAMOST Data Release (DR) 12, we identified 147 Blazhko and 111 non-Blazhko RRab stars, which exhibit similar metallicity distributions. Furthermore, crossmatching with Gaia DR3 data yielded 766 Blazhko and 950 non-Blazhko RRab stars, showing differences in color indices but not in absolute magnitudes. Our findings suggest that the Blazhko effect is linked to pulsation parameters and colors rather than metallicities or absolute magnitude.

The physical origin of the Blazhko effect (BL), a phenomenon of a single or multiple periodic modulation(s) of the light curve, is under debate. Efficiently identifying and characterizing the BL is essential in understanding its origins and accounting for its effect on numerous applications of RRabs in the era of large time-domain surveys. In this study, we make use of Resnet 34, a well-known convolutional neural network (CNN) architecture, to identify RRab stars with BL from phased light curves collected from OGLE. Using reliably classified RRabs from frequency analysis to train, validate, and test our model, we show that our CNN method reaches accuracies up to 94%. We then applied our CNN method to some additional RRabs located in the Magellanic Cloud (MC) and the Galactic Bulge (GB), leading to the discovery of 113 and 2496 BL candidates, respectively. The identification accuracy for the MC Sample is estimated to be 91% after cross-matching the CNN classification results with those from frequency analysis. Similarly, the light-curve parameters of these classified BL/non-BL candidates by our CNN method from the GB region resemble those observed in the literature, confirming the reliability of our CNN classifications. Our CNN method is subject to issues related to light-curve quality and sampling, but its overall reliance on light-curve quality is comparable to that of frequency analysis. Furthermore, we find that BL modulation could be primarily characterized by variations in light-curve structure.

We report a δ Scuti star, KIC 10407873, exhibiting significant amplitude modulation. Fourier analysis of Kepler long-cadence data (i.e., Q0-Q17, spanning 1471 days) reveals two distinct features: harmonic series of frequencies in the low-frequency region and the frequencies of the split triplet lines in the high-frequency region. Using the Hilbert transform method, we separated the amplitude modulation signals, obtaining precise parameters for the two modulation frequencies. For the harmonic series of frequencies in the low-frequency region, we isolated them through a prewhitening process. Based on the residual segmented spectrum and the phase-folding diagram, we propose that these harmonic series of frequencies may be caused by temperature inhomogeneity on the stellar surface and stellar rotation. The subsequent phase evolution diagrams we generated, combined with LAMOST’s vsini data, further support this hypothesis. Consequently, this suggests that the cause of amplitude modulation in the high-frequency region is unrelated to stellar rotation. Finally, we discussed the information potentially carried by the isolated modulation signals, as well as the similarities between the star’s dual-amplitude modulation and the periodically modulated Tseraskaya–Blazhko effect.

We present the result of the processing of our observations of the FI Sge, the pulsating RR Lyrae type variable with the Blazhko effect in the R-band. The data were obtained during 36 nights in 2018 as well as during 13 nights in 2021. We used the period and initial epoch obtained from our observations in V-band. We confirmed the presence of the Blazhko effect, the bi-cyclicity effect, and also the effect of discrete displacement of the light curves along the phase curve detected firstly in the V-band. We detect some differences in the dynamic of the light curve variability in different photometrical bands, possibly related to the Blazhko effect.

Context. To date, puzzlingly few bona fide RR Lyrae stars have been identified in binaries. Binarity in pulsating stars can be revealed through well-timed photometric data over sufficiently long time bases because of the light travel time effect (LTTE) on the pulsations, which manifests as variation in the timings of maximum light in the O−C (observed minus calculated) diagram. However, O−C variations can also have other causes, such as the Blazhko effect or a sudden or gradual change in the main pulsation period. Aims. We approach this challenge by disentangling the Blazhko effect and period changes from the potential LTTE on V1109 Cas, an RR Lyrae star suspected to be part of a binary system based on its O−C data in the GEOS database. In doing so, we aim to uncover the subtler signals indicative of a companion (LTTE). Methods. We analysed nine years of ground-based photometric data, using Fourier analysis to model the pulsation modulated by the Blazhko effect. From the fit to the observed light curves, we constructed a refined O−C diagram without the scatter caused by Blazhko modulation. Subsequently, we considered different possible scenarios, because distinguishing intrinsic period changes or breaks from the LTTE is challenging. Results. If the remaining O−C variation is due to a period break, refining the O−C diagram can almost entirely remove the trends. If we interpret the variation as an LTTE, we can consider possible configurations. While we currently favour a period break as the explanation for the residual O−C variations, more data on the star in the forthcoming years will help reveal whether the O−C variations are due to the LTTE or intrinsic period changes. Conclusions. Our study, based on a detailed light-curve fitting of V1109 Cas, offers insights into the discernment between Blazhko modulation, intrinsic period breaks, and the LTTE in binary systems. Our results highlight the complexity of determining binarity from O−C data traditionally used for detecting binary motion, calling for caution in this process.

IX Del is a variable star that was classified as uncertain E/SD at the Variable Star Index. The SSV-UAI-GRAV (Unione Astrofili Italiani, Variable Star Section) suggested a campaign to observe the star in order to understand its true nature. The Štefánik and Ďáblice observatories in Prague also collaborated in the observing campaign of the Italian section. From 2024 August to 2024 September, 10 observing sessions were obtained with terrestrial telescopes and V-band CCDs. From the analysis of the data thus obtained, combined with the Zwicky Transient Facility data, the star IX Del has been reclassified as an RRab-type variable with a pulsation period of 0.540914 day and a range of 1.36 mag g. The Blazhko effect from the result of this work is evident.

RRd stars are a subclass of RR Lyrae stars that pulsate simultaneously in the fundamental and the first-overtone radial modes. We report the analysis of 10 RRd stars discovered in the Sloan Digital Sky Survey (SDSS) Stripe 82 region of the Galactic halo using SDSS and Zwicky Transient Facility data. By combining the two data sets, we constructed ∼23 yr long lightcurves in gri bands, and conclude that out of 10, 9 were the classical RRd stars and 1 was the anomalous RRd star. We also observed the long-term variation, the Blazhko effect, in 3 classical RRd stars out of 10 stars, giving an incidence rate of 30%. The shortest Blazhko period observed was 226.4 ± 0.8 days and the longest was 2799 ± 75 days.

We derived additional pulsation frequencies in the HADS star V965 Cep from the frequency analysis of the O − C diagram built with the TESS Quick-Look Pipeline (QLP) data and from the TESS QLP light curve. Thus, the star appeared to be a multi-mode pulsator with a modulated light curve, similar to RR Stars with the Blazhko effect.

The Van Hoof effect is a phase shift existing between the radial velocity curves of hydrogen and metallic lines within the atmosphere of pulsating stars. In this article, we present a study of this phenomenon through the spectra of the brightest pulsating star RR Lyr of RR Lyrae stars recorded for 22 yr. We based ourselves, on the one hand, on 1268 spectra (41 nights of observation) recorded between the years 1994 and 1997 at the Observatory of Haute Provence (OHP, France) previously observed by Chadid and Gillet, and on the other hand on 1569 spectra (46 nights of observation) recorded at our Oukaimeden Observatory (Morocco) between 2015 and 2016. Through this study, we have detected information on atmospheric dynamics that had not previously been detected. Indeed, the Van Hoof effect which results in a clear correlation between the radial velocities of hydrogen and those of the metallic lines has been observed and analyzed at different Blazhko phases. A correlation between the radial velocities of different metallic lines located in the lower atmosphere has been observed as well. For the first time, we were able to show that the amplitude of the radial velocity curves deduced from the lines of hydrogen and that of Fe ii (λ4923.921 Å) increases toward the minimum of the Blazhko cycle and decreases toward the maximum of the same Blazhko cycle. Furthermore, we found that the Van Hoof effect is also modulated by the Blazhko effect. Thus, toward the minimum of the Blazhko cycle the Van Hoof effect is more visible and at the maximum of the Blazhko cycle, this effect is minimal. We also observed the temporal evolution of the amplitudes of the radial velocities of the lower and upper atmosphere. When observed over a long time, we can interpret it as a function of the Blazhko phases.

RR Lyrae stars (RRLs) are pulsating stars, many of which also show a long-term variation called the Blazhko effect which is a modulation of amplitude and phase of the lightcurve. In this work, we searched for the incidence rate of the Blazhko effect in the first-overtone pulsating RR Lyrae (RRc) stars of the Galactic halo. The focus was on the Stripe 82 region in the Galactic halo which was studied by Sesar et al. using the Sloan Digital Sky Survey (SDSS) data. In their work, 104 RRLs were classified as RRc type. We combined their SDSS light curves with Zwicky Transient Facility (ZTF) data, and used them to document the Blazhko properties of these RRc stars. Our analysis showed that among the 104 RRc stars, eight were rather RRd stars, and were excluded from the study. Out of the remaining 96, 34 were Blazhko type, 62 were non-Blazhko type, giving the incidence rate of 35.42% for Blazhko RRc stars. The shortest Blazhko period found was 12.808 ± 0.001 days for SDSS 747380, while the longest was 3088 ± 126 days for SDSS 3585856. Combining SDSS and ZTF data sets increased the probability of detecting the small variations due to the Blazhko effect, and thus provided a unique opportunity to find longer Blazhko periods. We found that 85% of RRc stars had the Blazhko period longer than 200 days.

We discuss the new approach for the analysis of the long-term dense series of observations of RR Lyr-type pulsating stars with the Blazhko effect. The standard way, namely The frequency analysis of the O–C values for the times of maxima does not allow for to detection of the complex nature of the periodic changes in the shape of the light curves, including bi-cyclicity. We have shown the perspectives of a new approach on the example of the analysis of FISge variable observations containing a total of 55 observational nights during a period of five years (AZT-3 Telescope, Mayaki Observational Station, SRI “Astronomical Observatory”, I. I. Mechnikov ONU). The study is based on the data obtained by S. N. Udovichenko during the 2013 and 2014 observational seasons as well as on data obtained by S. N. Udovichenko and the author during the 2018 observational season. Our results show that in order to understand the features in the shape of the light curve variations for RR Lyr type pulsating stars with the Blazhko effect, it is necessary to have data for full cycles of variability over a long time, and not just the moments of maxima.

Context. Until now, it has been accepted that the additional frequencies in the fundamental-(RRab) and overtone-mode pulsating (RRc and RRd) RR Lyrae stars are of a different nature. RRab stars show frequencies associated with periodic doubling, as well as frequencies at the first and second radial overtones, and linear combinations of these. RRc stars show frequencies with specific ratios (f1/fx ∼ 0.61 or ∼0.63), which are explained by non-radial modes, and frequencies with a ratio of fx/f1 ∼ 0.68, for which there is currently no accepted explanation. Aims. To search for similarities in spectral content, we compared the recently published Fourier spectra of TESS and K2 RRc stars with the spectra of Kepler RRab stars that do not show the Blazhko effect but contain additional frequencies. Methods. We analysed the time series data using standard Fourier methods, and also investigated the possibility of excitation of the second radial overtone mode in RRab stars using numerical hydrodynamical codes. Results. We show that the additional frequencies appear in non-Blazhko RRab stars at the position of the second radial overtone mode, and the pattern they create is very similar to that caused by the additional frequencies with the period ratio of ∼0.68 in RRc stars. The formerly raised hypothesis that the additional frequencies of these RRab stars are due to a second radial overtone is unlikely.

Context. Although spectroscopic observations of RR Lyrae stars have been underway for almost a century, the fact that the hydrogen line exhibits three successive emissions in each pulsation cycle is still a very recent discovery. Aims. The purpose of the present study is to clarify the physical origin of these three emissions and their connection to atmospheric dynamics and to examine the influence of Blazhko modulation on their intensity. Methods. We used 2437 high-resolution spectra over a total of 81 nights taken by the ELODIE spectrograph (Haute Provence Observatory, France) in the years 1994–1997, rounded out with a 2015 run from Oukaïmeden Observatory (Morocco). We performed a detailed analysis of the line profile variations over the whole pulsation cycle. Results. Based on the blueshift of the main Hα emission, the velocity of the hypersonic shock front was estimated at between 100 and 150 ± 10 km s−1 (Mach number between 10 and 15). It has been established that the shock velocity increases from the minimum Blazhko to its maximum and afterward, it gradually decreases to the Blazhko minimum to start growing again. This observational result is consistent with the shock model proposed in 2013 to explain the Blazhko effect. The intensity of the Hα emission increases with the shock velocity up to a maximum value around 137 km s−1 and then decreases as the shock velocity increases further. This effect would be the consequence of the increasingly important ionization of the atoms in the radiative shock wake. The second (blueshifted) Hα emission is the consequence of an approximately constant supersonic compression (Mach number between 2 and 3) of the upper atmosphere falling onto the photospheric layers, during 3 to 16% of the pulsation period. Finally, the third Hα emission (P-Cygni profile) would be the consequence of the expansion of the high atmosphere induced by the shock wave during its final weakening.

In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 9845907. Using the data from Kepler, we detected 85 significant frequencies, including the first overtone f 1 = 17.597 day−1 as the dominant frequency, the non-radial independent frequency f 3 = 31.428 day−1 (ℓ = 1), as well as two modulation terms f m1 = 0.065 day−1 and f m2 = 1.693 day−1. We found fourteen pairs of triplet structures with f m1 or f m2, four pairs of which can further form quintuplet structures. We note these are the most intriguing features discovered in this study and they were recognized for the first time in δ Scuti stars. We discussed several possible explanations, i.e., beating, the Blazhko effect, combination mode hypothesis, nonlinear mode coupling, large separation, and stellar rotational splitting for these equidistant structures. Our asteroseismic models indicate this modulation with f m1 might be related to the rotational splitting. The study of more δ Scuti stars with triplet and/or quintuplet structures using high-precision space photometry would be helpful to further explore its origin.

Context. Additional low-amplitude signals have been observed in many RR Lyrae stars separate from pulsations in radial modes. The most common of these are short-period signals forming a period ratio of around 0.60–0.65 with the first overtone and long-period signals forming a period ratio of around 0.68. The RR Lyrae stars may also exhibit quasi-periodic modulation in their light curves, the so-called Blazhko effect. Aims. We used the extensive sample of the first-overtone RR Lyrae stars observed by the Kepler telescope during the K2 mission to search for and characterize additional low-amplitude signals. The K2 data provides space-based photometry for a statistically significant sample. Hence, this data is excellent for studying the pulsation properties of RR Lyrae stars in detail. Methods. We used K2 space-based photometry for RR Lyrae candidates from Campaigns 0–19. We selected RR Lyrae stars pulsating in the first overtone and performed a frequency analysis for each star to characterize their frequency contents. Results. We classified 452 stars as first-overtone RR Lyrae. From that sample, we selected 281 RR0.61 stars, 67 RR0.68 stars, and 68 Blazhko stars. We found particularly interesting stars that show all of the above phenomena simultaneously. We detected signals in RR0.61 stars that form period ratios lower than those observed for the majority of stars of this type. These signals likely form a new sequence in the Petersen diagram, around a period ratio of 0.60. In 32 stars, we detected additional signals that form a period ratio close to that expected in RRd stars, but the classification of these stars as RRd is uncertain. We also report a discovery of additional signals in eight stars that form a new group in the Petersen diagram around the period ratio of 0.465–0.490. The nature of this periodicity remains unknown.

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.