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\IBVShead{5483}{1 December 2003}

\IBVStitle{A Revised Period for the Mira Variable AW Aurigae}

\IBVSauth{Templeton, M. R.}

\IBVSinsto{American Association of Variable Star Observers (AAVSO), 25 Birch Street, Cambridge, MA 02138, USA; email: aavso@aavso.org}

\SIMBADobj{AW Aur}
\IBVStyp{  M  }
\IBVSkey{Miras: time-series}
\IBVSabs{AW Aurigae is listed in the GCVS as a Mira variable with a period}
\IBVSabs{of 695 days, one of the longest among the Miras.  However, the period}
\IBVSabs{was considered preliminary when first determined by Kurochkin (1951)}
\IBVSabs{and the original ephemeris of Max = JD 2429200 + 695 X E}
\IBVSabs{produced very large (O-C) residuals.  Analysis of visual}
\IBVSabs{and V-band data from the AAVSO International Database and}
\IBVSabs{photometry from the Harvard College Observatory plate collection}
\IBVSabs{yields a best-fitting period of 449.3 +/- 0.7 days.}

\begintext

AW Aurigae -- $\alpha$:5\hr 40\mm 00\fsec7; $\delta$:+28\deg 42\arcm 49\farcs0 
(J2000) -- is listed in the GCVS as a Mira variable with a period of 695 days.
The published period is one of the longest among the Miras, making 
AW Aurigae an object of some astrophysical interest.  However, this period 
was considered preliminary by Kurochkin (1951), and the quoted $(O-C)$ values 
are very large.  The star was among the 58 Mira variables studied by Whitney 
(1960) at the request of B.V. Kukarkin, to better determine their elements.
Whitney did not revise the 695-day period for
this star, though like Kurochkin he also noted very large residuals in his 
$(O-C)$ analysis.  Although the star has been mentioned as part of several Mira
population studies since then, no discussion or refinement
of its period appears in the literature.  As part of a larger project to study
secular changes in Mira variable pulsations, I analyzed visual and CCD data 
from the American Association of Variable Star Observers (AAVSO) International 
Database (ID), along with Harvard College Observatory (HCO) photographic plate 
data for AW Aurigae, and compared the period determined using these data to 
the period given in the GCVS.  I find that the period quoted in the GCVS is 
incorrect,  and that the best-fitting period to the available data is 449.3 
$\pm$ 0.7 days.

I used three separate data sets to determine the correct period: visual 
observations from the AAVSO ID (380 total observations,
148 positive observations), CCD $V$-band observations from the AAVSO ID (27
total observations, 24 positive), and blue-sensitive photographic plate 
observations from HCO (197 total observations, 46
positive).  The visual observations span the longest period of time of the
three data sets (JD 2439851 to 2452904; December 1967 to September 2003), and 
so were used for the Fourier analysis.  I used the CLEANest program
(Foster, 1996) to compute the Fourier transform shown in Figure 1.  The
strongest peak is centered on a period of $449.3 \pm 0.7$ days
($\nu = 2.225 \times 10^{-3}$~cyc/d).  Although the data is noisy, the
449.3-day peak and its Fourier harmonic at 224.7~days are both stronger than
any other peak in the spectrum.  There is a weak signal at about 720 days, but
given the noise level it may be spurious.

Based upon Fourier analysis of the visual data alone, the best ephemeris of 
AW Aurigae appears to be 
\begin{equation}
{\rm Max} = {\rm JD} 2445320 + 449.3 \cdot E.
\end{equation}
The post-1967 HCO plates agree with this ephemeris, as do the AAVSO $V$-band 
CCD observations.  However, there is a significant phase shift between the 
maxima predicted by this ephemeris and the maxima obtained from the HCO 
photographic plate data from 1928 to 1952.  Table 1 gives previously published
dates of maximum for AW Aurigae as well as dates derived from the AAVSO and HCO
data, and Figure 2 shows the resulting $(O-C)$ diagram.  While the HCO and 
AAVSO visual data seem to be well-fit by a period of 449.3 days, the maxima 
derived from the 1928-1952 HCO plate data are offset in phase by nearly 150 
days from the ephemeris given above.


\begin{table}
\caption{Dates of maxima of AW Aurigae.  Dates taken from Kurochkin (1951) and
Whitney (1960) are given without error bars.  Dates derived from HCO plate
data and AAVSO observations should be considered accurate to $\pm 20$ days.}
\begin{center}
\begin{tabular}{ccccccccccc}
\hline
JD Max & E & Source & & JD Max & E & Source & & JD Max & E & Source \\
\hline
2419447 & $-$58 & Kurochkin & &  2431540 & $-$31 & HCO & &  2445320 &   0 & AAVSO\\
2424448 & $-$47 & Kurochkin & &  2432010 & $-$30 & HCO & &  2445790 &   1 & AAVSO\\
2424857 & $-$46 & Kurochkin & &  2432440 & $-$29 & HCO & &  2446220 &   2 & AAVSO\\
2425250 & $-$45 & HCO & &  2434712 & $-$24 & Whitney & &  2446670 &   3 & AAVSO\\
2425700 & $-$44 & HCO & &  2435095 & $-$23 & Whitney & &  2447130 &   4 & AAVSO\\
2426150 & $-$43 & HCO & &  2439920 & $-$12 & AAVSO & &  2447610 &   5 & AAVSO\\
2426580 & $-$42 & HCO & &  2440360 & $-$11 & AAVSO & &  2448010 &   6 & AAVSO\\
2427041 & $-$41 & Kurochkin & &  2440820 & $-$10 & AAVSO & &  2448470 &   7 & AAVSO\\
2427490 & $-$40 & HCO & &  2441240 &  $-$9 & AAVSO & &  2448900 &   8 & AAVSO\\
2427960 & $-$39 & HCO & &  2441730 &  $-$8 & AAVSO & &  2449370 &   9 & AAVSO\\
2428380 & $-$38 & HCO & &  2442210 &  $-$7 & AAVSO & &  2449850 &  10 & AAVSO\\
2428820 & $-$37 & HCO & &  2442630 &  $-$6 & AAVSO & &  2450270 &  11 & AAVSO\\
2429283 & $-$36 & Kurochkin & &  2443090 &  $-$5 & AAVSO & &  2450720 &  12 & AAVSO\\
2429760 & $-$35 & HCO & &  2443540 &  $-$4 & AAVSO & &  2451170 &  13 & AAVSO\\
2430220 & $-$34 & HCO & &  2443960 &  $-$3 & AAVSO & &  2451610 &  14 & AAVSO\\
2430640 & $-$33 & HCO & &  2444450 &  $-$2 & AAVSO & &  2452080 &  15 & AAVSO\\
2431110 & $-$32 & HCO & &  2444900 &  $-$1 & AAVSO & &  2452530 &  16 & AAVSO\\
\hline
\end{tabular}
\end{center}
\end{table}

The best-defined maximum of the HCO plate data lies at JD 2427490, and although
we detected few maxima with the plate data, Kurochkin (1951) gives a date of
maximum ($m = 12.3$) of JD 2427041 obtained by Shajn (1933).  Assuming these
two dates are actually maxima, then the period is 449 days, consistent
with the 449.3-day period given the uncertainty of the maxima dates.  Kurochkin
lists another date of maximum of JD~2419447, and the time difference between
these two maxima corresponds to 16.9 cycles of 449.3 days or exactly 17 cycles
of 446.7 days, both results being reasonable given the measurement errors.

Figure 3 shows the AAVSO visual and $V$-band data and the 1928-1952 HCO 
photographic plate data folded with a period of 449.3 days.  This folding 
period is an excellent fit to the data, though both the visual and plate data
show significant scatter.  All three data sets were folded with the GCVS 
period of 695 days, and the resulting folded light curves (not shown) were 
clearly incoherent.  Therefore, it appears that the 449.3-day period matches
all available data, with the only uncertainty being the reason for the
discontinuity in $(O-C)$.  There are only two data points in the 1952-1967 gap,
published by Whitney (1960).  The latter of these two points has a residual
of around 100 days, much lower than the points preceeding it.  While it
suggests a possible trend downward in $(O-C)$, it may also be a random 
fluctuation.  Analysis of other data archives besides the Harvard plate 
archives will be necessary to understand AW Aurigae's behavior during this 
time.

Though the revised period is likely the correct one, there is still substantial
scatter in the $(O-C)$ residuals and in the folded visual light curve.  In
the case of the $(O-C)$ residuals, this may be due in large part to the
scarcity of data and subsequent poor fitting of a mean curve to individual
cycles.  However, given the scatter in the folded visual data, it may also be
due in part to intrinsic, cycle-to-cycle variations.  Such behavior is observed
in some other long-period Miras like Z Tau (Zijlstra \& Bedding, 2003), 
and may indicate that AW Aurigae has a ``meandering'' period.  Furthermore,
the large jump in $(O-C)$ suggests that the star may not have
maintained the 449.3-day period throughout the span of observations. 
Unfortunately, the data coverage is not sufficient to enable a more thorough 
analysis such as wavelet transformation, and it is difficult to more precisely 
determine the dates of maximum with the available data.

In summary, the period of the Mira variable AW Aurigae appears to be 
about 449.3~days, rather than the very long period of 695 days given in 
the GCVS.  This period is still long relative to most Mira variables,
but is not otherwise noteworthy.  A discontinuity in the $(O-C)$ diagram
suggests a possible temporary change in period or phase shift in pulsation,
but both the 1967-2003 visual data and the 1928-1952 HCO plate data are both
well-fit by a 449.3-day period.  The $(O-C)$ residuals show some scatter,
which could be attributed to poor determination of the dates of maxima
or to real variations.  The latter is observed in other Mira variables with
similarly long periods, and better time-series coverage in future observations
would be valuable in determining whether the period truly varies.  Furthermore,
the search for and analysis of archival data spanning the time between 1952 
and 1967 will be necessary to understand the behavior of this star, and are
encouraged.


\IBVSfig{6.0cm}{5483-f1.eps}{Fourier transform of AAVSO visual data for
AW Aurigae.  The strongest peak is centered on 449.3 days.  The peak at
224.7 days ($\sim 0.00445$~cyc/d) is the second Fourier harmonic of the main
peak.  There is a much weaker peak around 720 days, but this may be 
spurious.}
%%\IBVSfigKey{5483-f1.eps}{AW Aur}{periodogram}

I would like to thank Dr.~Janet Mattei and Aaron Price for their assistance 
in the preparation of this paper, along with the 45 visual and 4 CCD observers
of the AAVSO whose observations made this work possible.  Thanks also to 
Alison Doane and the Harvard College Observatory for access to the Harvard
photographic plate collection.

\clearpage

\IBVSfig{5.5cm}{5483-f2.eps}{(O-C) diagram showing the dates of 
maximum derived from both the visual and HCO patrol plate data.  There is
a very large jump in (O-C) values between 1952 and 1967, suggesting either
a temporary period change or a phase shift in the pulsations.}
%%\IBVSfigKey{5483-f2.eps}{AW Aur}{O-C diagram}

\IBVSfig{5.5cm}{5483-f3.eps}{AAVSO visual data (left panel), 
AAVSO $V$-band CCD 
data (center panel), and HCO photographic plate data (right panel) of
AW Aurigae, folded with a period of 449.3 days.  The folding period is an
excellent fit to the observations.  Diamonds: positive
observations; triangles: fainter-than observations.}
%%\IBVSfigKey{5483-f3.eps}{AW Aur}{light curve}

\references

Foster, G., 1996, {\it AJ}, {\bf 112}, 1709

Kurochkin, N. E., 1951, {\it Perem. Zvezdy}, {\bf 8}, No. 5, 351

Shajn, P., 1933, {\it Perem. Zvezdy}, {\bf 4}, No. 4, 119

Whitney, B. S., 1960, {\it AJ}, {\bf 65}, 381

Zijlstra, A. A. \& Bedding, T. R., 2003, {\it JAVSO}, {\bf 31}, 2

\endreferences

\end{document}
