We analyse the OGLE-IV photometry of the first overtone and double-mode RR Lyrae stars (RRc/RRd) in the two fields towards the Galactic bulge observed with high cadence. In 27 per cent of RRc stars, ...we find additional non-radial mode, with characteristic period ratio, P
x/P
1O ∈ (0.6, 0.64). It strongly corroborates the conclusion arising from the analysis of space photometry of RRc stars, that this form of pulsation must be common. In the Petersen diagram the stars form three sequences. In 20 stars, we find two or three close secondary modes simultaneously. The additional modes are clearly non-stationary. Their amplitude and/or phase vary in time. As a result, the patterns observed in the frequency spectra of these stars may be very complex. In some stars, the additional modes split into doublets, triplets or appear as a more complex bands of increased power. Subharmonics of additional modes are detected in 20 per cent of stars. They also display a complex structure. Including our previous study of the OGLE-III Galactic bulge data, we have discovered 260 RRc and 2 RRd stars with the additional non-radial mode, which is the largest sample of these stars so far. The additional mode is also detected in two Blazhko RRc stars, which shows that the modulation and additional non-radial mode are not exclusive.
A detailed analysis is presented of 33 RR Lyrae stars in Pisces observed with the Kepler space telescope over the 8.9-d 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.
Non-radial modes are excited in classical pulsators, both in Cepheids and in RR Lyrae stars. Firm evidence comes from the first-overtone pulsators, in which an additional shorter period mode is ...detected with characteristic period ratio falling between 0.60 and 0.65. For first-overtone Cepheids, three separate sequences populated by nearly 200 stars are formed in the Petersen diagram, i.e. the diagram of period ratio versus longer period. For first-overtone RR Lyrae stars (RRc stars), the situation is less clear. A dozen or so such stars are known. They form a clump in the Petersen diagram without any obvious structure. Interestingly, all first-overtone RR Lyrae stars for which precise space-borne photometry is available, show the additional mode, which suggests that its excitation is common. Motivated by these results, we searched for non-radial modes in the OGLE-III photometry of RRc stars from the Galactic bulge. We report the discovery of 147 stars, members of a new group of double-mode, radial–non-radial-mode pulsators. They form a clear and tight sequence in the Petersen diagram, with period ratios clustering around 0.613 and a signature of a possible second sequence with higher period ratio (0.631). The scatter in period ratios of the already known stars is explained as due to population effects. Judging from the results of space observations, this still mysterious form of pulsation must be common among RRc stars and our analysis of the OGLE data just touches the tip of the iceberg.
Abstract
We present hydrodynamic BL Herculis type models which display a long-term modulation of pulsation amplitudes and phases. The modulation is either strictly periodic or quasi-periodic, with ...the modulation period and modulation pattern varying from one cycle to another. Such behaviour has not been observed in any BL Herculis variable so far; however, it is a common property of their lower luminosity siblings - RR Lyrae variables showing the Blazhko effect. These models provide support for the recent mechanism proposed by Buchler & Kolláth to explain this still mysterious phenomenon. In their model, a half-integer resonance that causes the period-doubling effect, discovered recently in Blazhko RR Lyrae stars, is responsible for the modulation of 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 that 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.
Chaos in hydrodynamic BL Herculis models Smolec, R; Moskalik, P
Monthly notices of the Royal Astronomical Society,
06/2014, Letnik:
441, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many ...phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars – RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.
We have performed a detailed systematic search for multiperiodicity in the Population I Cepheids of the Large Magellanic Cloud. In this process, we have identified for the first time several new ...types of Cepheid pulsational behaviour. We have found two triple-mode Cepheids pulsating simultaneously in the first three radial overtones. In 9 per cent of the first overtone (FO) Cepheids, we have detected weak but well-resolved secondary periodicities. They appear either very close to the primary pulsation frequency or at a much higher frequency with a characteristic period ratio of 0.60–0.64. In either case, the secondary periodicities must correspond to non-radial modes of oscillation. This result presents a major challenge to the theory of stellar pulsations, which predicts that such modes should not be excited in Cepheid variables. Non-radial modes have also been found in three of the fundamental first overtone (FU/FO) double-mode Cepheids, but no such oscillations have been detected in single-mode Cepheids pulsating in the FU mode. In 19 per cent of double-mode Cepheids pulsating in the first two radial overtones (FO/SO type), we have detected a Blazhko-type periodic modulation of amplitudes and phases. Both modes are modulated with a common period, which is always longer than 700 d. Variations of the two amplitudes are anticorrelated, and maximum of one amplitude always coincides with minimum of the other. We have compared observations of modulated FO/SO Cepheids with predictions of theoretical models of the Blazhko effect, showing that the currently most popular models cannot account for properties of these stars. We propose that the Blazhko effect in FO/SO Cepheids can be explained by a non-stationary resonant interaction of one of the radial modes with another, perhaps non-radial, mode of oscillations.
Context. Double-periodic (beat) Cepheids are important astrophysical objects which allow testing both the stellar evolution and stellar pulsation theories, as well as the physical properties of ...matter in stellar conditions. However, the phenomenon of double-periodic pulsation is still poorly understood. Recently we rediscussed the problem of modelling the double-periodic pulsation with non-linear hydrocodes. We showed that the published non-resonant double-mode models are incorrect, because they exclude the negative buoyancy effects. Aims. We continue our efforts to verify whether the Kuhfuß one-equation convection model with negative buoyancy included can reproduce the double-periodic Cepheid pulsation. Methods. Using the direct time integration hydrocode, which implements the Kuhfuß convection model, we search for stable double-periodic Cepheid models. We search for models pulsating in both fundamental and first overtone modes (F+1O), as well as in the two lowest order overtones (1O+2O). In the latter case, we focus on reproducing double-overtone Cepheids of the Large Magellanic Cloud (LMC). Results. We have found full amplitude non-linear beat Cepheid models of both types, F+1O and 1O+2O. In the case of F+1O models, the beat pulsation is most likely caused by the three-mode resonance, 2ω1 = ω0 + ω2, while in the double-overtone models the underlying mechanism (resonant or non-resonant) cannot be identified beyond doubt. Double-periodic models found in our survey exist, however, only in narrow period ranges and cannot explain the majority of the observed double-periodic objects. Conclusions. With only little doubt left, we conclude that current one dimensional one-equation convection models are incapable of reproducing the majority of the observed beat Cepheids. Among the shortcomings of current pulsation hydrocodes, the simple treatment of convection seems to be the most severe one. Growing evidence for the presence of non-radial modes in Cepheids suggests that the interaction between radial and non-radial modes should also be investigated.
We present the analysis of four first overtone RR Lyrae stars observed with the Kepler space telescope, based on data obtained over nearly 2.5 yr. All four stars are found to be multiperiodic. The ...strongest secondary mode with frequency f... has an amplitude of a few mmag, 20-45 times lower than the main radial mode with frequency f... The two oscillations have a period ratio of P.../P... = 0.612-0.632 that cannot be reproduced by any two radial modes. Thus, the secondary mode is non-radial. 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 P.../P... ~ 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 f... at ~1/2f... and at ~3/2f... 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 f... and its subharmonics are variable on a time-scale of 10-200 d. The dominant radial mode also shows variations on the same time-scale, but with much smaller amplitude. In three Kepler RRc stars we detect additional periodicities, with amplitudes below 1 mmag, that must correspond to non-radial g-modes. Such modes never before have been observed in RR Lyrae variables. (ProQuest: ... denotes formulae/symbols omitted.)
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 non-linear 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 (ninth) 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 into solving this century-old enigma.
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