Analysis of the irregular pulsations of AC Herculis

Z. Kolláth, J. R. Buchler, T. Serre, J. Mattei

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The AAVSO lightcurve data of the irregularly pulsating star AC Herculis of the RV Tau class are analysed. The lightcurve is shown not to be compatible with a periodic, or even multiperiodic pulsation, even if allowance is made for evolution. Instead the best explanation is that the irregularly alternating cycles are a manifestation of low dimensional chaos. Our flow reconstruction suggests that the dynamics can be successfully embedded in 3 dimensions. Further, the (Lyapunov) fractal dimension of the underlying dynamic attractor is computed to be 2.05 ≲ dL ≲ 2.45, independent of the dimension of the reconstruction space. It is smaller than the value of dL ≈ 3.1 found for the more irregular lightcurve of R Sct. From these results we are led to conclude that the lightcurve is likely to have been generated by a 3 dimensional dynamics, i.e. by 3 first order ODEs. In simpler language, it expresses the remarkable fact that the observational value at any time s(tn) is a unique function h of the values at only three preceding observations, viz. s(tn+1) = h(s(tn), s(tn-1), s(tn-2)).

Original languageEnglish
Pages (from-to)147-154
Number of pages8
JournalAstronomy and Astrophysics
Volume329
Issue number1
Publication statusPublished - Jan 1 1998

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alternating current
chaotic dynamics
allowances
chaos
fractals
stars
cycles
analysis
allowance

Keywords

  • Chaos
  • Methods: data analysis
  • Methods: numerical
  • Stars: individual: AC Her
  • Stars: oscillations

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

Kolláth, Z., Buchler, J. R., Serre, T., & Mattei, J. (1998). Analysis of the irregular pulsations of AC Herculis. Astronomy and Astrophysics, 329(1), 147-154.

Analysis of the irregular pulsations of AC Herculis. / Kolláth, Z.; Buchler, J. R.; Serre, T.; Mattei, J.

In: Astronomy and Astrophysics, Vol. 329, No. 1, 01.01.1998, p. 147-154.

Research output: Contribution to journalArticle

Kolláth, Z, Buchler, JR, Serre, T & Mattei, J 1998, 'Analysis of the irregular pulsations of AC Herculis', Astronomy and Astrophysics, vol. 329, no. 1, pp. 147-154.
Kolláth Z, Buchler JR, Serre T, Mattei J. Analysis of the irregular pulsations of AC Herculis. Astronomy and Astrophysics. 1998 Jan 1;329(1):147-154.
Kolláth, Z. ; Buchler, J. R. ; Serre, T. ; Mattei, J. / Analysis of the irregular pulsations of AC Herculis. In: Astronomy and Astrophysics. 1998 ; Vol. 329, No. 1. pp. 147-154.
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