L. Molnár

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 has been observed only in Blazhko-modulated stars so far, the phenomenon can help in understanding the modulation as well. Utilizing the Florida–Budapest turbulent convective hydrodynamical code, we have identified the phenomenon in both radiative and convective models. A period-doubling cascade was also followed up to an eight-period solution, confirming that destabilization 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 illustrate 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 ninth overtone and the fundamental mode. Destabilization 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 strong enough to shift the period of overtone by up to 10 per cent. 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.

Kepler photometry of RRc stars: peculiar double-mode pulsations and period doubling

We present the analysis of four first overtone RR Lyrae stars observed with the Kepler space telescope, based on data obtained over nearly 2.5yr. All four stars are found to be multiperiodic. The strongest secondary mode with frequency f2 has an amplitude of a few mmag, 20 45 times lower than the main radial mode with frequency f1. The two oscillations have a period ratio of P2/P1 = 0.612 0.632 that cannot be reproduced by any two radial modes. Thus, the secondary mode is nonradial. Modes yielding similar period ratios have also recently been discovered in other variables of the RRc and RRd types. These objects form a homogenous group and constitute a new class of multimode RR Lyrae pulsators, analogous to a similar class of multimode classical Cepheids in the Magellanic Clouds. Because a secondary mode with P2/P1 �0.61 is found in almost every RRc and RRd star observed from space, this form of multiperiodicity must be common. In all four Kepler RRc stars studied, we find subharmonics of f2 at �1/2f2 and at �3/2f2. This is a signature of period doubling of the secondary oscillation, and is the first detection of period doubling in RRc stars. The amplitudes and phases of f2 and its subharmonics are variable on a timescale of 10 200d. The dominant radial mode also shows variations on the same timescale, but with much smaller amplitude. In three Kepler RRc stars we detect additional periodicities, with amplitudes below 1mmag, that must correspond to nonradial g-modes. Such modes never before have been observed in RR Lyrae variables.

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.

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 PX/P1 � 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.

V473 Lyrae, a unique second-overtone Cepheid with two modulation cycles

V473 Lyrae is the only Galactic Cepheid with confirmed periodic amplitude and phase variations similar to the Blazhko effect observed in RR Lyrae stars. We collected all available photometric data and some radial velocity measurements to investigate the nature of the modulation. The comparison of the photometric and radial velocity amplitudes confirmed that the star pulsates in the second overtone. The extensive data set, spanning more than 40 years, allowed us to detect a secondary modulation cycle with a period of approximately 5300 days or 14.5 years. The secondary variations can be detected in the period of the primary modulation, as well. Phenomenologically, the light variations are analogous to the Blazhko effect. To find a physical link, we calculated linear hydrodynamic models to search for potential mode resonances that could drive the modulation and found two viable half-integer (n:2) and three n:4 resonances between the second overtone and other modes. If any of these resonances will be confirmed by non-linear models, it may confirm the mode resonance model, a common mechanism that can drive modulations both in RR Lyrae and Cepheid stars.

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 100 d, 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 stand-alone mechanism behind the Blazhko effect.

First observations of W Virginis stars with K2: detection of period doubling

We present the first analysis of W Vir stars observed by the Kepler space telescope in the K2 mission. Clear cycle-to-cycle variation were detected in the light curves of KT Sco and the globular cluster member M80-V1. While the variations in the former star seems to be irregular on the short time scale of the K2 data, the latter appears to experience period doubling in its pulsation. Ground-based colour data confirmed that both stars are W Vir-type pulsators, while a comparison with historical photometric time-series data revealed drastic period changes in both stars. For comparison we reexamine ground-based observations of W Vir, the prototype of the class, and conclude that it shows period doubling instead of mode beating. These results support the notion that nonlinear dynamics plays an important role in the pulsation of W Virginis-type stars.

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% 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.

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.

On the interchange of alternating-amplitude pulsation cycles

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.