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Z. Kolláth

Publications and source records attributed to Z. Kolláth.

At least 19 recordsLinked to original sources
arXiv2018

Chaotic dynamics in the pulsation of DF Cygni, as observed by Kepler

Pulsations of RV Tauri-type variable stars can be governed by chaotic dynamics. However, observational evidence for this happening is usually hard to come by. Here we use the continuous, 4-year-long observations of the Kepler space telescope to search for the signs of chaos in the RVb-type pulsating supergiant, DF Cygni. We use the Global Flow Reconstruction method to estimate the quantitative properties of the dynamics driving the pulsations of the star. The secondary, long-term light variation, i.e., the RVb phenomenon was removed in the analysis with the Empirical Mode Decomposition method. Our analysis revealed that the pulsation of DF Cyg could be described as a chaotic signal with a Lyapunov dimension of ~2.8. DF Cyg is only the third RV Tau star, and the first of the RVb subtype, where the nonlinear analysis indicates that low-dimensional chaos may explain the peculiarities of the pulsation.

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arXiv2016

Magnetic cycles at different ages of stars

We study the different patterns of interannual magnetic variability in stars on or near the lower main sequence, approximately solar-type (G-K dwarf) stars in time series of 36 years from the Mount Wilson Observatory Ca\,{\sc ii}\,H\&K survey. Our main aim is to search for correlations between cycles, activity measures and ages. Time-frequency analysis has been used to discern and reveal patterns and morphology of stellar activity cycles, including multiple and changing cycles, in the datasets. Both the results from short-term Fourier transform and its refinement using the Choi-Williams distribution, with better frequency resolution, are presented in this study. Rotational periods of the stars were derived using multi-frequency Fourier analysis.From the studied 29 stars we found at least one activity cycle on 28 of them. Twelve stars, with longer rotational periods ($39.7\pm6.0$ days) have simple, smooth cycles, and the rest of the stars, with on-average much faster rotation ($18.1\pm12.2$ days) show complex and sometimes vigorously changing, multiple cycles. The cycles are longer and quite uniform in the first group ($9.7\pm1.9$ years), while are generally shorter and with greater variety in the second one ($7.6\pm4.9$). There is a clear age division between stars with smooth and complex cycles that follows the known separation between the older and younger stars at around 2 to 3~Gyr of age.

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arXiv2015

An RR Lyrae family portrait: 33 stars observed in Pisces with K2-E2

A detailed analysis is presented of 33 RR Lyrae stars in Pisces observed with the Kepler space telescope over the 8.9-day long K2 Two-Wheel Concept Engineering Test. The sample includes not only fundamental-mode and first overtone (RRab and RRc) stars but the first two double-mode (RRd) stars that Kepler detected and the only modulated first-overtone star ever observed from space so far. The precision of the extracted K2 light curves made it possible to detect low-amplitude additional modes in all subtypes. All RRd and non-modulated RRc stars show the additional mode at P_X/P_1~0.61 that was detected in previous space-based photometric measurements. A periodicity longer than the fundamental mode was tentatively identified in one RRab star that might belong to a gravity mode. We determined the photometric [Fe/H] values for all fundamental-mode stars and provide the preliminary results of our efforts to fit the double-mode stars with non-linear hydrodynamic pulsation models. The results from this short test run indicate that the K2 mission will be, and has started to be, an ideal tool to expand our knowledge about RR Lyrae stars. As a by-product of the target search and analysis, we identified 165 bona-fide double-mode RR Lyrae stars from the Catalina Sky Survey observations throughout the sky, 130 of which are new discoveries.

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arXiv2014

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.

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arXiv2014

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.

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arXiv2013

High-precision 2MASS JHKs light curves and other data for RR Lyrae star SDSS J015450+001501: strong constraints for non-linear pulsation models

We present and discuss an extensive data set for the non-Blazhko ab-type RR Lyrae star SDSSJ015450+001501, including optical SDSS ugriz light curves and spectroscopic data, LINEAR and CSS unfiltered optical light curves, and infrared 2MASS JHKs and WISE W1 and W2 light curves. Most notably, light curves obtained by 2MASS include close to 9000 photometric measures collected over 3.3 years and provide exceedingly precise view of near-IR variability. These data demonstrate that static atmosphere models are insufficient to explain multi-band photometric light curve behavior and present strong constraints for non-linear pulsation models for RR Lyrae stars. It is a challenge to modelers to produce theoretical light curves that can explain data presented here, which we make publicly available.

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arXiv2013

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.

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arXiv2013

Low-dimensional chaos in RR Lyrae models

The recent precise photometric observations and successes of the modelling efforts transformed our picture of the pulsation of RR Lyrae stars. The discovery of additional frequencies and the period doubling phenomenon revealed that a significant interaction may occur between pulsational modes. The signs of irregularities were detected both in observed light curves and hydrodynamic calculations. In this paper we present the analysis of four peculiar hydrodynamic model solutions. All four solutions were found to be chaotic. The fractal (Lyapunov) dimensions of their attractors were calculated to be ~2.2. We also investigated possible resonances between the fundamental mode and the first overtone in the dynamical neighbourhood of these models. The most important is the 6:8 resonance that was also detected in the Kepler observations of RR Lyrae itself. These results reveal that the investigation of chaotic models is important in discovering and understanding resonances in RR Lyrae stars.

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arXiv2013

Elimination of long-term variation from chaotic light curves

We performed a comparative dynamical investigation of chaotic test data using the global flow reconstruction method. We demonstrate that large-amplitude, long-term variations may have a disturbing effect in the analysis. The Empirical Mode Decomposition method (EMD) and the Fourier filtering were tested to remove the additional variations. Test results show that the elimination of these variations significantly increased the robustness of the reconstructions.

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arXiv2012

New results in RR Lyrae modeling: convective cycles, additional modes and more

Recent theoretical and observational findings breathed new life into the field of RR Lyrae stars. The ever more precise and complete measurements of the space asteroseismology missions revealed new details, such as the period doubling and the presence of the additional modes in the stars. Theoretical work also flourished: period doubling was explained and an additional mode has been detected in hydrodynamic models as well. Although the most intriguing mystery, the Blazhko-effect has remained unsolved, new findings indicate that the convective cycle model can be effectively ruled out for short- and medium-period modulations. On the other hand, the plausibility of the radial resonance model is increasing, as more and more resonances are detected both in models and stars.

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arXiv2012

Nonlinear asteroseismology of RR Lyrae

The observations of the Kepler space telescope revealed that fundamental-mode RR Lyrae stars may show various radial overtones. The presence of multiple radial modes may allow us to conduct nonlinear asteroseismology: comparison of mode amplitudes and frequency shifts between observations and models. Here we report the detection of three radial modes in the star RR Lyr, the eponym of the class, using the Kepler short cadence data: besides the fundamental mode, both the first and the ninth overtones can be derived from the data set. RR Lyrae shows period doubling, but switches occasionally to a state where a pattern of six pulsation cycles repeats instead of two. We found hydrodynamic models that show the same three modes and the period-six state, allowing for comparison with the observations.

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arXiv2012

Can turbulent convective variations drive the Blazhko cycle? Dynamical investigation of the Stothers idea

The Blazhko-phenomenon, the modulation of the pulsation of RR Lyrae stars remains one of the most stubborn unsolved problems of stellar pulsation. The recent idea of Stothers proposes that periodic variations in the properties of the convective envelope may be behind the amplitude and phase modulation. In this work we approximated the mechanism by introducing variations in the convective parameters of the Florida-Budapest hydrodynamic code and also by means of amplitude equations. We found that the process is only effective for long modulation periods, typically for more than hundred days, in agreement with the thermal time scales of the pulsation in RR Lyrae stars. Due to the slow response of the pulsation to the structure changes, short period, high amplitude Blazhko-modulation cannot be reproduced with this mechanism or would require implausible variations in the convective parameters on short time scales. We also found that the modulation of the mixing length results in strong differences between both the luminosity and radius variations and the respective phase modulations of the two quantities, suggesting notable differences between the energy output of the photosphere and the mechanical variations of the layers. The findings suggest that the convective cycle model is not well suited as a standalone mechanism behind the Blazhko-effect.

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arXiv2012

Detection of chaos in RR Lyrae models

The period doubling phenomenon was recently discovered in RR Lyrae stars with the Kepler space telescope and has been theoretically explained by hydrodynamic calculations. However, peculiar solutions of the Florida-Budapest turbulent convective hydrodynamic code suggest that bifurcation cascade may evolve to chaos in these dynamical systems. We show that chaotic behaviour may be recovered from the radius variations of the model using the global flow reconstruction method. The fractal (Lyapunov) dimension of the underlying dynamical attractor is calculated to be ~2.2. Compared to the radius, the luminosity variations proved to be less suitable for such investigations due to their complexity. That suggest that even the continuous Kepler data would require transformation before conducting a similar analysis.

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arXiv2012

Uncovering hidden modes in RR Lyrae stars

The Kepler space telescope revealed new, unexpected phenomena in RR Lyrae stars: period doubling and the possible presence of additional modes. Identifying these modes is complicated because they blend in the rich features of the Fourier-spectrum. Our hydrodynamic calculations uncovered that a 'hidden' mode, the 9th overtone is involved in the period doubling phenomenon. The period of the overtone changes by up to 10 per cent compared to the linear value, indicating a very significant nonlinear period shift caused by its resonance with the fundamental mode. The observations also revealed weak peaks that may correspond to the first or second overtones. These additional modes are often coupled with period doubling. We investigated the possibilities and occurrences of mutual resonances between the fundamental mode and multiple overtones in our models. These theoretical findings can help interpreting the origin and nature of the 'hidden' modes may be found in the high quality light curves of space observatories.

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arXiv2011

Period doubling in Kepler RR Lyrae stars

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 the root cause of this effect is a high order resonance (9:2) between the fundamental mode and the 9th radial overtone, which is a strange mode. We discuss the implications of these recent findings on our understanding of the century-old Blazhko problem.

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arXiv2011

Period doubling bifurcation and high-order resonances in RR Lyrae hydrodynamical models

We investigated period doubling, a well-known phenomenon in dynamical systems, for the first time in RR Lyrae models. These studies provide theoretical background for the recent discovery of period doubling in some Blazhko RR Lyrae stars with the Kepler space telescope. Since period doubling was observed only in Blazhko-modulated stars so far, the phenomenon can help in the understanding of the modulation as well. Utilising the Florida-Budapest turbulent convective hydrodynamical code, we identified the phenomenon in radiative and convective models as well. A period-doubling cascade was also followed up to an eight-period solution confirming that the destabilisation of the limit cycle is indeed the underlying phenomenon. Floquet stability roots were calculated to investigate the possible causes and occurrences of the phenomenon. A two-dimensional diagnostic diagram was constructed to display the various resonances between the fundamental mode and the different overtones. Combining the two tools, we confirmed that the period-doubling instability is caused by a 9:2 resonance between the 9th overtone and the fundamental mode. Destabilisation of the limit cycle by a resonance of a high-order mode is possible because the overtone is a strange mode. The resonance is found to be sufficiently strong enough to shift the period of overtone with up to 10 percent. Our investigations suggest that a more complex interplay of radial (and presumably non-radial) modes could happen in RR Lyrae stars that might have connections with the Blazhko effect as well.

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arXiv2011

Cepheid investigations using the Kepler space telescope

We report results of initial work done on selected candidate Cepheids to be observed with the Kepler space telescope. Prior to the launch 40 candidates were selected from previous surveys and databases. The analysis of the first 322 days of Kepler photometry, and recent ground-based follow-up multicolour photometry and spectroscopy allowed us to confirm that one of these stars, V1154 Cyg (KIC 7548061), is indeed a 4.9-d Cepheid. Using the phase lag method we show that this star pulsates in the fundamental mode. New radial velocity data are consistent with previous measurements, suggesting that a long-period binary component is unlikely. No evidence is seen in the ultra-precise, nearly uninterrupted Kepler photometry for nonradial or stochastically excited modes at the micromagnitude level. The other candidates are not Cepheids but an interesting mix of possible spotted stars, eclipsing systems and flare stars.

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