Z. Kolláth

University of West Hungary, Sopron, Scarabantia, Győr-Moson-Sopron, Hungary

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Publications (90)240.78 Total impact

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    ABSTRACT: 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.
    09/2014; 445(3).
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    ABSTRACT: 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.
    The Astrophysical Journal Supplement Series 06/2014; 213(2). · 16.24 Impact Factor
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    ABSTRACT: We characterized the time intervals between the interchanges of the alternating high- and low-amplitude extrema of three RV Tauri and three RR Lyrae stars.
    01/2014;
  • Z. Kolláth, B. Kránicz
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    ABSTRACT: Multi-wavelength imaging luminance photometry of sky glow provides a huge amount of information on light pollution. However, the understanding of the measured data involves the combination of different processes and data of radiation transfer, atmospheric physics and atmospheric constitution. State of the art numerical radiation transfer models provide the possibility to define an inverse problem to obtain information on the emission intensity distribution of a city and perhaps the physical properties of the atmosphere. We provide numerical tests on the solvability and feasibility of such procedures.
    Journal of Quantitative Spectroscopy and Radiative Transfer 01/2014; · 2.38 Impact Factor
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    ABSTRACT: 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.
    The Astrophysical Journal 11/2013; 780(1). · 6.73 Impact Factor
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    ABSTRACT: 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.
    09/2013;
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    E. Plachy, Z. Kolláth, L. Molnár
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    ABSTRACT: 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.
    Monthly Notices of the Royal Astronomical Society 06/2013; 433(4). · 5.52 Impact Factor
  • E. Plachy, Z. Kolláth
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    ABSTRACT: 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.
    Astronomische Nachrichten 03/2013; · 1.40 Impact Factor
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    L. Molnár, Z. Kolláth, R. Szabó, E. Plachy
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    ABSTRACT: 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.
    Astronomische Nachrichten 10/2012; · 1.40 Impact Factor
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    ABSTRACT: 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.
    The Astrophysical Journal Letters 08/2012; 757(1). · 6.35 Impact Factor
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    ABSTRACT: Solar variability and its effects on the physical variability of our (space) environment produces complex signals. In the indicators of solar activity at least four independent cyclic components can be identified, all of them with temporal variations in their timescales. Time-frequency distributions (see Kolláth & Oláh 2009) are perfect tools to disclose the ``music scores'' in these complex time series. Special features in the time-frequency distributions, like frequency splitting, or modulations on different timescales provide clues, which can reveal similar trends among different indices like sunspot numbers, interplanetary magnetic field strength in the Earth's neighborhood and climate data. On the pseudo-Wigner Distribution (PWD) the frequency splitting of all the three main components (the Gleissberg and Schwabe cycles, and an ~5.5 year signal originating from cycle asymmetry, i.e. the Waldmeier effect) can be identified as a ``bubble'' shaped structure after 1950. The same frequency splitting feature can also be found in the heliospheric magnetic field data and the microwave radio flux.
    Proceedings of the International Astronomical Union 07/2012; 7(S286):423-426.
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    L. Molnár, Z. Kolláth, R. Szabó
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    ABSTRACT: 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.
    Monthly Notices of the Royal Astronomical Society 03/2012; 424(1). · 5.52 Impact Factor
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    E. Plachy, Z. Kolláth, L. Molnár
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    ABSTRACT: 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.
    02/2012;
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    L. Molnár, Z. Kolláth, R. Szabó
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    ABSTRACT: 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.
    01/2012;
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    ABSTRACT: 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.
    11/2011;
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    ABSTRACT: 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 data bases. The analysis of the first 322 d 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 ultraprecise, nearly uninterrupted Kepler photometry for non-radial 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.
    Monthly Notices of the Royal Astronomical Society 05/2011; 413(4):2709 - 2720. · 5.52 Impact Factor
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    Z. Kolláth, L. Molnár, R. Szabó
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    ABSTRACT: 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.
    Monthly Notices of the Royal Astronomical Society 02/2011; 414. · 5.52 Impact Factor
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    J. Robert Buchler, Zoltan Kollath
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    ABSTRACT: The Blazhko effect is a long term, generally irregular modulation of the light curves that occurs in a sizeable number of RR Lyrae stars. The physical origin of the effect has been a puzzle ever since its discovery over a hundred years ago. We build here upon the recent observational and theoretical work of Szabo et al. on RRab stars who found with hydrodynamical simulations that the fundamental pulsation mode can get destabilized by a 9:2 resonant interaction with the 9th overtone. Alternating pulsation cycles arise, although these remain periodic, i.e. not modulated as in the observations. Here we use the amplitude equation formalism to study this nonlinear, resonant interaction between the two modes. We show that not only does the fundamental pulsation mode break up into a period two cycle through the nonlinear, resonant interaction with the overtone, but that the amplitudes are modulated, and that in a broad range of parameters the modulations are irregular as in the observations. This irregular behavior is in fact chaotic and arises from a strange attractor in the dynamics.
    The Astrophysical Journal 01/2011; 731(1). · 6.73 Impact Factor
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    ABSTRACT: 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, additional frequencies beyond the well-known harmonics and Blazhko multiplets have been found. These frequencies are located around the half-integer multiples of the main pulsation frequency for at least three stars. In four stars, these frequencies are close to the first and/or second overtone modes. The amplitudes of these periodicities seem to vary over the Blazhko cycle. V350 Lyr, a non-Blazhko star in our sample, is the first example of a double mode RR Lyrae star that pulsates in its fundamental and second overtone modes. Comment: 9 pages, 7 figures 2 tables. Accepted for publication in MNRAS
    Monthly Notices of the Royal Astronomical Society 07/2010; · 5.52 Impact Factor
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    ABSTRACT: 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 bifurcation in our nonlinear RR Lyrae models computed by the Florida-Budapest hydrocode. This enabled us to trace the origin of this instability in RR Lyrae stars to a resonance, namely a 9:2 resonance between the fundamental mode and a high-order (9th) radial overtone showing strange-mode characteristics. We discuss the connection of this new type of variation to the mysterious Blazhko effect and argue that it may give us fresh insights to solve this century-old enigma. Comment: 10 pages, 12 figures and 1 table, accepted for publication in MNRAS
    Monthly Notices of the Royal Astronomical Society 07/2010; · 5.52 Impact Factor

Publication Stats

464 Citations
240.78 Total Impact Points

Institutions

  • 2013–2014
    • University of West Hungary, Sopron
      • Institute of Mathematics and Physics
      Scarabantia, Győr-Moson-Sopron, Hungary
  • 2001–2014
    • Hungarian Academy of Sciences
      • MTA Research Centre for Astronomy and Earth Sciences
      Budapeŝto, Budapest, Hungary
  • 1991–2012
    • Konkoly Observatory
      Budapeŝto, Budapest, Hungary
  • 1996–2006
    • University of Florida
      • Department of Physics
      Gainesville, FL, United States