Automated nonlinear stellar pulsation calculations: Applications to RR Lyrae stars the slope of the fundamental blue edge and the first RRd model survey

R. Szabó, Z. Kolláth, J. R. Buchler

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40 Citations (Scopus)

Abstract

We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, Teff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.

Original languageEnglish
Pages (from-to)627-639
Number of pages13
JournalAstronomy and Astrophysics
Volume425
Issue number2
DOIs
Publication statusPublished - Oct 2004

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slopes
stars
strip
methodology
time series analysis
hysteresis
topology
simulation
hydrodynamics
diagram
calculation
astrophysics
diagrams
formalism
harmonics
parameter
effect

Keywords

  • Convection
  • Hydrodynamics
  • Stars: evolution
  • Stars: oscillations
  • Stars: variables: RR Lyr
  • Turbulence

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

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abstract = "We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, Teff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.",
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AU - Kolláth, Z.

AU - Buchler, J. R.

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N2 - We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, Teff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.

AB - We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, Teff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.

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