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AH Draconis--a tale of two periods.

Introduction and history

AH Dra, under the name AG8994, was first suspected to be variable by Schilt & Hill (1) in the 1930s. They noted it as possibly variable from 14 measurements and gave a range of 8.51-9.29. This caused it to be added to the Catalogue of Suspected Variable Stars (2) as CSV2829, and to be observed by Nikulina (3) during the years 1941-1959. His analysis resulted in a period of 158 days, which was the basis for the value quoted in the GCVS. (4) Strangely enough Nikulina gave no magnitudes for maximum and minimum (in the paper he used values ranging from -1 to 17.6 which he called 'st', presumably for 'step value'), so the values for these (8.5-9.3) in the GCVS are taken straight from Schilt & Hill. The spectrum is of type M7, and it is classfied as an SRb star. (An SRb is characterised by a late-type spectrum and a light curve which is more irregular than an SRa. Interestingly enough, in this context, they are often found to have two periods.)

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Using AAVSO observations Kiss et al. (5) found two periods for AH Dra (189 days and 107 days). Mizser et al. (6) published a plot showing no fewer than four different periods which appear to be 110, 190, 200 and 6660 days.

In 1971 the star was added to the BAA VSS binocular list and has been regularly observed by the Association since then up until the present day.

Observations and analysis

A total of 3501 observations of the star from the BAA VSS database, by 71 different observers (the most prolific of which are shown in Table 1), have been collected over a period of 37 years (1971 2007). These observations are plotted as 10-day means in Figure 1.

The observations were binned with a bin size of 10 days, and Fourier analyis was performed using a program provided by John Howarth. (7) The results can be seen in Figure 2. Frequencies of up to 0.1 cycles per day (cpd) (i.e. periods down to 10 days) were examined in increments of 0.0001 cpd. The two main peaks can be seen at 0.0053 cpd (corresponding to 188.68 days) and 0.0095 cpd (corresponding to 105.26 days). Nothing else appears to raise its head above the level of background noise.

To check for stability in these periods the observations were divided into 7 sections of 5 years each (though the last section consisted of 7 years) starting in 1971. The two periods can be clearly seen in Figure 3. In most cases the statistical errors are less than 0.2 days. (For the observations between 1975 and 1980 the error is 0.34 days.) Assuming that the observations have a standard error of 0.2 magnitudes, then the expected statistical error, assuming one constant period, given by the software for the period is 0.018 days. However, as this paper has found, there is more than one period and they are not entirely constant. This results in the much higher statistical error as seen in Figure 4.

A quick glance at Figure 3 suggests that the two periods have been stable since 1975, but plotting the errors for the 105-day period it can be seen in Figure 4 that the period has varied by considerably more than the statistical error. Tantalisingly, the 189-day period is not seen in the data from 19711975, suggesting that it may be a relatively new development. Instead a 67-day period is seen. The 105-day period, on the other hand, seems to be more long-lived and less variable. The periods are also listed in Table 2.

The semi-amplitudes for both periods can be seen in Figure 5. Both sets of semi-amplitudes have increased during the time-period covered by the BAA observations, so AH Dra seems to be varying more dramatically in amplitude now than it has in the past. Whether the 189-day period is now decreasing in amplitude permanently or only temporarily is something that only future observations will be able to show.

Discussion

To check if the 105-day or 189-day periods were visible in the data used for the GCVS, the same analysis was performed on Nikulina's original photographic data (3) from the 1940s and 1950s (almost 400 observations). It came as a surprise to find that the 105-day period (corresponding to 0.096 cpd) was by far the most prominent period visible there, far stronger than the period of 158-days (0.0063 cpd) which was the one decided upon for the GCVS (see Figure 6) (This has a semi-amplitude of 1.11 st). A slightly smaller peak at 0.0054 cpd (185 days) can perhaps be discerned, but is certainly not as clear as the 189-day period in the BAA data.

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This analysis suggests that the 105-day period has remained reasonably constant since observations started in 1941, but the 189-day period is more variable and possibly temporary.

The extreme limits of variability found in the raw BAA observations are from 6.7 to 9.4, though 99.5% of the observations lie between 7.0 and 8.9. This seems to imply a range about twice that mentioned in the GCVS (8.5-9.3).

In a separate study of semiregular variables (not using BAA observations but using, amongst others, AAVSO & AFOEV observations) Kiss et al. (5) found the following two periods for AH Dra: 189 days and 107 days, though nothing was said about their stability. Their results seem to support the conclusions of this paper, which is reassuring, though not surprising considering that there is considerable time overlap of the AAVSO & BAA observations.

In an infrared study of several variables using data from the COBE satellite, Smith, Price & Moffett (8) postulate that the IR light curves for AH Dra correlate with the visible light curve, with a negligible lag, which is quite consistent with other SRs and in contrast to Miras which have a significant IR lag. They adopted a period of 156 days by finding the maxima, calculating the separations between them and then taking an average over these periods. (9) The optical data they used for this analysis was actually from the Kiss et al. paper which produced the two periods of 189 and 107 days, so perhaps this gives a clue as to how the GCVS value of 158 days was arrived at. Interestingly enough, their 3.5um observations seem to show a regular period of around 100 days, though the shorter wavelength graphs appear more irregular.

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Percy & Polano (10) in their study of M giant stars (including both Miras and SRb stars) found that the biperiodic variables can be divided into two classes: those with secondary periods of 10-15 times the primary period, and those with a period ratio of between 1.5 and 2. AH Dra, with a ratio of 189/105 = 1.8, fits nicely into this latter category. The authors suggest that this may indicate that that these variables are pulsating in the fundamental and the first overtone.

Conclusions

It is clear that the period given in the GCVS is (and has always been) incorrect. AH Dra has one period of around 105 days which has been there since the very first observations. This period is, however, not constant but varies slightly by a couple of days. Currently it also has another, less well defined but higher amplitude, period of around 190 days. This has varied between 188 and 203 days during the time covered by the BAA observations. Only future observations will be able to show if this other period will continue, or disappear to be replaced by a different one.

The extreme limits of variability found in the BAA observations are from 6.7 to 9.4 with 99.5% of the observations lying between 7.0 and 8.9, a greater range than that given in the GCVS.

Acknowledgments

I would like to extend my grateful thanks to John Howarth for not only providing the software for analysing the observations, but also for a lot of help and support in using it and in interpreting the results. Thanks are also due to Prof Roger Griffin (no relation) for ferreting out several obscure articles concerning the original observations of this star. I would also like to thank the referees for comments which have led to substantial improvements in the paper.

Address: Tamburingr 3, 175 48 Jarfalla, Sweden [davidgr1200@yahoo.se]

References

(1) Schilt J. & Hill S. J., Contributions from the Rutherford Observatory, Observatory of Columbia University No. 30, 1937

(2) Kukarkin et al., Catalogue of Suspected Variable Stars, 1951

(3) Nikulina T. G., Tadz Byull 43-44, 1966

(4) Kholopov et al., General Catalogue of Variable Stars (4th edn.), 1985-1988

(5) Kiss L. et al., Astron. Astrophys. 346, 542-555 (1999)

(6) Mizser et al., JAAVSO, 19, 47 (1990)

(7) Howarth J. & Greaves J., MNRAS 325, 1383-1388 (2001)

(8) Smith B., Price S. & Moffett A., 'Phase lags in the optical-infrared light curves of asymptotic giant branch stars', AJ 131, 612-620 (2006)

(9) Smith B., private communication (2009)

(10) Percy J. R. & Polano S., 'Pulsation modes in M Giants' in A half century of stellar pulsation interpretation: a tribute to Arthur N. Cox, Paul A. Bradley and Joyce A. Guzik (eds.), Proceedings of a conference held in Los Alamos, NM 16-20 June 1997, ASP Conference Series 135, p.249 (1998)

Received 2009 February 7; accepted 2009 September 2
Table 1. BAA observers with more than 50
observations of AH Dra

J Toone          591   G Ramsey        101
I A Middlemist   518   I P Nartowicz   89
T Markham        205   R A Kendall     75
J S Day          196   D Stott         73
S W Albrighton   182   D M Swain       70
R B I Fraser     159   S Allmand       66
J S Smith        125   D Gavine        57
D Hufton         123   D Griffin       53

Table 2. The calculated periods
of AH Dra for intervals of 5
years

5-year      Period 1   Period 2
interval     (days)     (days)

1971-1975    102.7       67.0
1976-1980    104.2      202.5
1981-1985    104.1      188.5
1986-1990    106.6      188.8
1991-1995    105.7      185.8
1996-2000    103.6      192.9
2001-2007    104.9      193.6
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Author:Griffin, David
Publication:Journal of the British Astronomical Association
Geographic Code:4EUUK
Date:Apr 1, 2010
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