[vsnet 859] RT Cyg: Analysis of the AFOEV database

["Prof. Ivan ANDRONOV" <ila@auriga.ta3.sk>]

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{\Large\bf CYCLE--TO--CYCLE CHANGES\\ IN THE MIRA--TYPE STAR RT CYG}
\footnote{IAU Symposium 180 "Planetary Nebulae"  Poster III-4}\\[1mm]
V.I. Marsakova$^1,$    I.L. Andronov$^1,$    E. Schweitzer$^2$\\[1mm]
$^1$Department of Astronomy, Odessa State University,
 T.G.Shevchenko Park, Odessa 270014 Ukraine\\
$^2$AFOEV, Strasbourg, 11, rue de l'Universit\'e,
 67000 Strasbourg, France\\[2mm]
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{\bf Abstract}.
The moments of 82 maxima and 76 minima are used for the correlation
analysis of the characteristics of the individual cycles. 5 not trivial
correlations were found. The characteristic time of the secular decrease
of the period is $|P/\dot{P}|=(23.4\pm4.3)\cdot10^3$ yrs, but
decade--scale and cycle--to--cycle variations are also present.\\[2mm]

The observations were made by the members of the AFOEV (JD 2422897 --
50169). The AFOEV database was described by Schweitzer (1993). From all
data we deleted not sure values and estimates "fainter than". We also
have used our photographic data which were converted to the visual
magnitudes by using the characteristic curve $m_{vis}(m_{pg}).$ For
further analysis alltogether 7421 data points were used.

These data were smoothed by a multiharmonic fit by using the program by
Andronov (1994). The statistically significant number of harmonics is
$m=3,$ mean brightness at the maximum $7.40\pm0.02$ and minimum
$11.94\pm0.02.$ The estimates of the period $P=190.162\pm.003$ and
asymmetry $f=0.458\pm0.003.$

The individual cycles were fitted by the "asymptotic parabola" fit and
the time and brightness of the extrema was determined with corresponding
error estimates as described by Marsakova and Andronov (1996).

The moments of 82 maxima and 76 minima were fitted with weights inverse
proportional to the error estimate of the moment. The initial epoch for
the maximum is JD 2444589.6$\pm$0.9, for the minimum 24444499.8$\pm$0.7,
the period $P=190.13\pm0.01.$ The corresponding asymmetry is
$f=0.472\pm0.006.$

The value of the period has changed from $191.86\pm0.5$ days (JD
2423003--24340) to $189.4\pm0.1$ (46406--50089). Suggesting secular
period change one may obtain from the moments of extrema the
characteristic time of the period decrease
$|P/\dot{P}|=(23.4\pm4.3)\cdot10^3$ yrs. However, the period changes are
more complicated. High-order polynomial fits to the moments of extrema
argue for a statistically significant value of the degree of the
polynomial $n=4.$ This formal value argues for decade--scale period
variations. The asymmetry estimate is practically the same as for $n=1:$
$f=0.484\pm0.005.$

For the correlation analysis we have used the brightness $m$ and time
$t$ of the current (0), preceeding (1) and succeding (2) maximum,
preceeding (3) and succeding (4) minimum and their combinations. The
most prominent not trivial positive correlations were found for the
pairs $(m_3-m_4)-(m_0-m_2),$ $(m_2-m_0)-(t_4-t_3),$ $m_0-m_3$ (or
relative $m_2-m_4$,) $m_2-(m_4-m_0),$ $m_2-(m_4-m_3).$\\[2mm]

{\bf References}\\[2mm]
Andronov, I.L., 1994, Odessa Astron. Publ., 7, 49.\\
Marsakova, V.I., Andronov, I.L., 1996, Odessa Astron. Publ., 9, in press.\\
Schweitzer, E.: 1993,  Bull. AFOEV,  64, 14.
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