J/A+A/390/585 Light curve of R Cygni (Kiss+, 2002)
Period-doubling events in the light curve of R Cygni:
Evidence for chaotic behaviour.
Kiss L.L., Szatmary K.
<Astron. Astrophys. 390, 585 (2002)>
=2002A&A...390..585K 2002A&A...390..585K
ADC_Keywords: Stars, variable ; Stars, late-type ; Photometry
Keywords: stars: variables: general - stars: late-type -
stars: AGB and post-AGB - stars: individual: R Cygni
Abstract:
A detailed analysis of the century long visual light curve of the
long-period Mira star R Cygni is presented and discussed. The data
were collected from the publicly available databases of the AFOEV, the
BAAVSS and the VSOLJ. The full light curve consists of 26655
individual points obtained between 1901 and 2001. The light curve and
its periodicity were analysed with help of the O-C diagram, Fourier
analysis and time-frequency analysis. The results demonstrate the
limitations of these linear methods. The next step was to investigate
the possible presence of low-dimensional chaos in the light curve. For
this, a smoothed and noise-filtered signal was created from the
averaged data and with the help of time delay embedding, we have tried
to reconstruct the attractor of the system. The main result is that R
Cygni shows such period-doubling events that can be interpreted as
being caused by a repetitive bifurcation of the chaotic attractor
between a period 2T orbit and chaos. The switch between these two
states occurs in a certain compact region of the phase space, where
the light curve is characterized by ∼1500-day long transients. The
Lyapunov spectrum was computed for various embedding parameters
confirming the chaotic attractor, although the exponents suffer from
quite high uncertainty because of the applied approximation. Finally,
the light curve is compared with a simple one zone model generated by
a third-order differential equation which exhibits well-expressed
period-doubling bifurcation. The strong resemblance is another
argument for chaotic behaviour. Further studies should address the
problem of global flow reconstruction, including the determination of
the accurate Lyapunov exponents and dimension.
Objects:
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RA (2000) DE Designation(s)
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19 36 49.4 +50 11 59 R Cygni = HD 185456
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File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
rcygall.dat 15 26655 Visual estimates (AFOEV, BAA, VSOLJ)
rcygavg.dat 15 2745 10-day bins
signal.dat 15 3668 Smoothed signal
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Byte-by-byte Description of file: rcygall.dat rcygavg.dat signal.dat
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Bytes Format Units Label Explanations
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1- 10 F10.2 d JD Julian Date of observation
12- 15 F4.1 mag mag Visual magnitude
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Acknowledgements: Laszlo Kiss ,
(End) Patricia Bauer [CDS] 17-Jul-2002