### Abstract

It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multiperiodic and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time series analysis, the global flow reconstruction technique, to probe the properties of the irregular pulsation cycles. We show in particular that the chaotic dynamics of this star's complicated light curve is captured by a simple four-dimensional polynomial map or flow (four first-order ordinary differential equations). Another important feature is that the method allows us to quantify an irregular signal that has the potential benefit for extracting novel stellar constraints from an irregular light curve. Finally, from the low dimensionality (four) of the flow we can infer a simple physical picture of the pulsations, and arguments are presented that the pulsations of R Set are the result of the nonlinear interaction of two vibrational normal modes of the star.

Original language | English |
---|---|

Pages (from-to) | 489-501 |

Number of pages | 13 |

Journal | Astrophysical Journal |

Volume | 462 |

Issue number | 1 PART I |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Chaos
- Methods: data analysis
- Stars: individual (R Scuti)
- Stars: oscillations
- Stars: variables: other (RV Tauri)

### ASJC Scopus subject areas

- Space and Planetary Science
- Nuclear and High Energy Physics

### Cite this

*Astrophysical Journal*,

*462*(1 PART I), 489-501.

**Nonlinear analysis of the light curve of the variable star R scuti.** / Buchler, J. R.; Kolláth, Z.; Serre, T.; Mattei, J.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 462, no. 1 PART I, pp. 489-501.

}

TY - JOUR

T1 - Nonlinear analysis of the light curve of the variable star R scuti

AU - Buchler, J. R.

AU - Kolláth, Z.

AU - Serre, T.

AU - Mattei, J.

PY - 1996

Y1 - 1996

N2 - It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multiperiodic and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time series analysis, the global flow reconstruction technique, to probe the properties of the irregular pulsation cycles. We show in particular that the chaotic dynamics of this star's complicated light curve is captured by a simple four-dimensional polynomial map or flow (four first-order ordinary differential equations). Another important feature is that the method allows us to quantify an irregular signal that has the potential benefit for extracting novel stellar constraints from an irregular light curve. Finally, from the low dimensionality (four) of the flow we can infer a simple physical picture of the pulsations, and arguments are presented that the pulsations of R Set are the result of the nonlinear interaction of two vibrational normal modes of the star.

AB - It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multiperiodic and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time series analysis, the global flow reconstruction technique, to probe the properties of the irregular pulsation cycles. We show in particular that the chaotic dynamics of this star's complicated light curve is captured by a simple four-dimensional polynomial map or flow (four first-order ordinary differential equations). Another important feature is that the method allows us to quantify an irregular signal that has the potential benefit for extracting novel stellar constraints from an irregular light curve. Finally, from the low dimensionality (four) of the flow we can infer a simple physical picture of the pulsations, and arguments are presented that the pulsations of R Set are the result of the nonlinear interaction of two vibrational normal modes of the star.

KW - Chaos

KW - Methods: data analysis

KW - Stars: individual (R Scuti)

KW - Stars: oscillations

KW - Stars: variables: other (RV Tauri)

UR - http://www.scopus.com/inward/record.url?scp=23544440523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23544440523&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23544440523

VL - 462

SP - 489

EP - 501

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 PART I

ER -