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Period doubling bifurcation and high-order resonances in RR Lyrae hydrodynamical models
Solar and Stellar Astrophysics · Submitted 1 Feb 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigated period doubling, a well-known phenomenon in dynamical systems, for the first time in RR Lyrae models. | contribution 0.97 | 0.95 | 0.07 | asserted 1.00 |
| s1 | These studies provide theoretical background for the recent discovery of period doubling in some Blazhko RR Lyrae stars with the Kepler space telescope. | background 0.66 | 0.11 | 0.06 | asserted 0.92 |
| s2 | Since period doubling was observed only in Blazhko-modulated stars so far, the phenomenon can help in the understanding of the modulation as well. | background 0.58 | 0.07 | 0.05 | hedged possibility 0.88 |
| s3 | Utilising the Florida-Budapest turbulent convective hydrodynamical code, we identified the phenomenon in radiative and convective models as well. | method 0.65 | 0.96 | 0.06 | asserted 1.00 |
| s4 | 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. | result 0.98 | 0.95 | 0.14 | asserted 1.00 |
| s5 | Floquet stability roots were calculated to investigate the possible causes and occurrences of the phenomenon. | method 0.98 | 0.94 | 0.03 | asserted 0.93 |
| s6 | A two-dimensional diagnostic diagram was constructed to display the various resonances between the fundamental mode and the different overtones. | method 0.91 | 0.94 | 0.04 | asserted 1.00 |
| s7 | 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. | result 0.99 | 0.95 | 0.67 | asserted 1.00 |
| s8 | Destabilisation of the limit cycle by a resonance of a high-order mode is possible because the overtone is a strange mode. | interpretation 0.92 | 0.60 | 0.14 | hedged possibility 0.79 |
| s9 | The resonance is found to be sufficiently strong enough to shift the period of overtone with up to 10 percent. | result 1.00 | 0.94 | 0.08 | asserted 1.00 |
| s10 | 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. | interpretation 0.97 | 0.63 | 0.22 | hedged possibility 0.92 |
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Original 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.
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2 arXiv papers cite this in 3 sentences
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In their detailed analysis [ref] used the relaxation technique [ref] to determine the stability of the fundamental mode pulsation through the Floquet stability coefficients.
Variable turbulent convection as the cause of the Blazhko effect - testing the Stothers model · Period doubling phenomenon · 0.94
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