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\IBVShead{5383}{26 February 2003}

\IBVStitle{A Revised Period For AY~A\lowercase{ur}}

\IBVSauth{Price, A.; Templeton, M. R.; Mattei, J. A.}

\IBVSinsto{American Association of Variable Star Observers (AAVSO), Clinton B. Ford Astronomical Data \& Research Center, 25 Birch St., Cambridge, MA 02138, USA; email: aavso@aavso.org}

\SIMBADobj{AY Aur}
\IBVStyp{ M }
\IBVSkey{Miras - photometry, Stars - variables - Miras}

\IBVSabs{The period of the Mira variable AY Aur has been determined to be}
\IBVSabs{longer than that published in the GCVS 4th Edition.}
\IBVSabs{Fourier and CLEANEST analysis of AAVSO data determines the period}
\IBVSabs{to be 389.8 days. The discrepancy may have been caused by the effects}
\IBVSabs{of large gaps in observational data magnified by the close proximity}
\IBVSabs{of the star's period in relation to the length of the solar cycle. }

\begintext

AY Aur,  $\alpha$:05\hr 56\mm 06\sec; $\delta$:+32\day 08\fmm5, (J2000 -- FK5) is a Mira-type
variable with a visual  magnitude range of 10.0 -- 16.0.
The period according to the 4th
edition of the {\it General Catalog of Variable
Stars} (GCVS) (Kholopov et al., 1985)  is 186.6 days,
changed from the period of 373.6 days in the 3rd edition of
the GCVS (Kukarkin et al., 1971). 

In 1960, AY Aur was included as a survey of stars needing
more observations commissioned by B. V. Kukarkin, who was
then President of IAU Commission 27. That survey was
performed by the University of Oklahoma Observatory under
Balfour S. Whitney. Whitney determined the period to be 186.8
days (Whitney 1960). Regrettably, Mr.~Whitney is
deceased and no more information on the survey is available
through the observatory.

The Third Edition of the GCVS references this survey 
but continues to list AY Aur with a period of 373.6
days in the tables. This was the mean value for the total
number of observations available at the time (Samus, 2000).  
The period determined by Whitney was later used in the 
Fourth Edition of the GCVS.

372 visual observations covering 22 years from 
the AAVSO International Database were put through a 
Fourier analysis routine developed at AAVSO. The {\tt CLEANEST} and {\tt SLICK}
 algorithms (Foster, 1995) utilize
a date compensated discrete fourier transform (Ferraz-Mello, 1981), and were
developed specifically to deal with unevenly-spaced time-series measurements. A 
CLEANest analysis of long term visual data gives a revised period of 389.8 
days. Theoretical error is  $\pm$0.3 days
but experience shows it to be underestimated by a factor of 2 because it assumes a 
true sinusoid. A DCDFT analysis of 54 CCD {\it V}-band observations covering 3 years from
the AAVSO International Database gives a period of 390.0 days.


Figure 1 shows the spectrum of the DCDFT analysis.  The strongest peak is
located at 389.8 days, with two higher-order Fourier harmonics at 195.4  
and 129.5 days indicating a non-sinusoidal light curve.  The theoretical
errors of the latter two periods are both 0.3~days, though
as with the dominant period, these are probably a factor of two too low.

We believe that the current GCVS period is incorrect, and is due to the
window function of the data dominated by a one cycle per year alias.  The
GCVS period of 186.8~days is very close to the inverse sum of the 389.8 day
period and one cycle per year:

\begin{displaymath}
\Pi_{\tt GCVS} \simeq { {1}\over{(1/389.8\,{\tt d}) + (1/365.25\,{\tt d})}} =
188.6\,{\tt days}
\end{displaymath}

This suggests that earlier Fourier analysis were confused by the large
annual data gaps.  This is particularly important here, given that the
intrinsic period is very close to one year.  Visual inspection of the
earliest AAVSO data shows large gaps of six months or more, and often the
minima are sparsely sampled if at all.  The most recent data has much
smaller annual gaps, and the shorter GCVS period is clearly ruled out.

Figure 2 is a plot of AAVSO visual and CCD {\it V}-band observations with calculated maxima and minima beginning on JD~2452272.758
and going backward using the 389.8~day period. The maxima was derived by 
applying a 3rd degree polynomial fit to the last cycle in the light curve.

A weighted wavelet transform (Foster, 1996) of all AAVSO optical and CCD data
reveals no significant period change over the span of 1969 -- 2002.
Figure 3 shows a  plot of the results of wavelet analysis. Error is estimated 
to be $\pm$0.0008 days based on the length of observational data. 

In addition to these visual and CCD {\it V}-band observations, we conducted
a survey of the Damon Series  blue photographic plates at the Harvard College Observatory.
Only observations near maximum were possible due to the
interference of GSC~2410~799, a nearby star with a $V$ mag of
12.5. 38 photographic observations were made from \hbox{1968 -- 1989}. They are plotted 
in Figure~2 as different symbols along with visual and CCD {\it V}-band observations. Their fit with our
calculated maxima and minima acts as an independent data set confirming our new period.

We thank 72 observers worldwide for their observations which made this 
study possible. We would also like to thank Ronald Zissell,
Stephen O' Connor, Robert James, and Thomas Michalik for
their CCD {\it V}-band observations.
We acknowledge Alison Doane and
the Harvard College Observatory for access to their
Astronomical Photograph Collection. Finally, we thank Nikolai N.
Samus, George Hawkins, Emily Lu and Elizabeth Waagen
for assistance in preparation of this work. 





\IBVSfig{6.0cm}{5383-f1.eps}{ CLEANest Fourier transform of AY Aur visual data spanning JD 2440949.8 - 2452605.9 (December 29, 1970 -- November 27, 2002).The dominant period is 389.8d. The 195.4 day period is an Fourier 
harmonic. We 
believe the source of the 188.5 day period to be an artifact of annual data gaps, but more data is needed.}
%\IBVSfigKey{5383-f1.eps}{AY Aur}{periodogram}

\IBVSfig{18.5cm}{5383-f2.eps}{ AAVSO Visual, CCD {\it V}-band, and Harvard photographic observations 
plotted with the 389.8 day period. }
%\IBVSfigKey{5383-f2.eps}{AY Aur}{light curve}

\IBVSfig{10.0cm}{5383-f3.eps}{ Contour plot of weighted wavelet transform analysis. The new period 
is the solid line between 350 and 450 days. The contour between 175 and 225 days is the Fourier harmonic.
}
%\IBVSfigKey{5383-f3.eps}{AY Aur}{periodogram}

\newpage


\references

Ferraz-Mello, S. 1981, {\it Astron. J.}, {\bf 86}, 619
%%\BIBCODE{1981AJ.....86..619F}

Foster, G. 1995, {\it Astron. J.}, {\bf 109}, 1889
%%\BIBCODE{1995AJ....109.1889F}

Foster, G. 1996, {\it Astron. J.}, {\bf 111}, 541
%%\BIBCODE{1996AJ....111..541F}

Foster, G. 1996, {\it Astron. J.}, {\bf 112}, 1709
%%\BIBCODE{1996AJ....112.1709F}

Kholopov, P. N., et al., 1985, {\it General Catalog of Variable Stars, 4th edition}, Moscow

Kukarkin, B. V., et al., 1971, {\it General Catalog of Variable Stars, 3rd edition}, Moscow

Samus, N. 2000, {\it Private communication}

Whitney, B. S., 1960, {\it Astron. J.}, {\bf 65}, 381
%%\BIBCODE{1960AJ.....65..381W}

\endreferences

\end{document}

