The Be Star Newsletter, Volume 36 - August 2002

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Hunting for Beta Cephei Stars using Self-Correlation Analysis John R. Percy, Matthew Coulter, & Farisa Mohammed Department of Astronomy & Astrophysics, University of Toronto, Toronto ON Canada M5S 3H8 email:  jpercy@utm.utoronto.ca Received: August 22, 2002

ABSTRACT We describe a largely-unsuccessful hunt for new Cephei stars among bright stars, and binary stars, using self-correlation analysis.

1. Introduction Beta Cephei (also known as Beta Canis Majoris) stars are early-type stars (generally B0.5-B2 III or IV) stars which are pulsating in low-order radial modes with periods of 3 to 6 hours. The first Beta Cephei star was discovered almost a century ago. Many more were discovered -- primarily among the bright stars -- during the early and mid-20th century, but the rate of discovery has decreased substantially in the last three decades. On the other hand, slowly-pulsating B stars (SPB) have been discovered in large numbers; these stars are pulsating in low-order non-radial modes with periods of typically 1 to 2 days. The pulsation mechanism for both types of variables has been identified; it is the effect of the opacity of iron-peak elements, deep in the envelopes of the stars. A study of the variability of early-type stars using the Hipparcos photometry database (Waelkens et al. 1998) yielded 72 SPB stars and only 4 new Beta Cephei stars. We have recently found that self-correlation analysis is a useful tool for identifying short-period variables in the Hipparcos photometry database (Percy et al. 2002 and references therein). Here, we use this tool to hunt for new Beta Cephei stars among two important populations, using the Hipparcos epoch photometry: (1) bright B0.5-B2 II or IV stars suspected of variability; and (2) B0.5-B2 III or IV stars in binary systems. 2. Self-Correlation Analysis Self-correlation analysis is complementary to other forms of variable star analysis. It can detect characteristic time scales in the data. It determines the cycle-to-cycle behavior of the star, averaged over all the data. The measurements do not have to be equally-spaced. Our algorithm works as follows (Percy et al. 1993): for all pairs of measurements, the difference in magnitude (mag) and the difference in time (t) are calculated. We plot mag against t in a "self-correlation diagram", from zero up to some appropriate upper limit (which if possible should be a few times greater than the expected time scales, but less than the total time span of the data); the mag are binned in t so that, if possible, there are at least a few values in each bin; the mag in each bin are then averaged. The average mag will be a minimum at multiples of . Each minimum can be used to estimate . The height of the maxima is a measure of the average amplitude of the variability. If the variability were perfectly periodic, and the magnitudes had no error, then the minima would fall to zero; in fact, the height of the minima is determined by the average error of the measurements, and by the degree of irregularity, if any. The range in the self-correlation diagram (maximum to minimum) is about 0.5 times the range in magnitude (maximum to minimum) in the light curve or phase diagram. The persistence of the minima to large t is also determined by the degree of irregularity. Our method differs from autocorrelation analysis; it is more akin to the "variogram" method described by Eyer & Genton (1999). 3. The Hipparcos Epoch Photometry Because of the specific observing schedule of the Hipparcos satellite, the times of the photometric observations are distributed in a highly non-random way: observations are made 0.0143 day apart, then 0.0746, then 0.0143 and so forth. The length of these clusters of observations can be a few tenths of a day up to several days. The clusters are then normally separated by 25±5 days, the exact amount depending on the ecliptic latitude of the star. This means that there is no t between 0.0143 and 0.0746 day, 0.1032 and 0.1635 day etc., and there may be no t between a few hours and 25 days. This places some constraints on our method of analysis, since some bins may be empty. The Hipparcos magnitude is wide-band, and the standard error of a measurement ranges from a few millimagnitudes to about 0.02 magnitude at magnitude 10. Because of the long gaps between clusters, and because self-correlation analysis compares only measurements which are t apart (where t is from zero up to the maximum length of the clusters), and because Fourier analysis requires the star to be strictly periodic, self-correlation analysis can be well suited for studying short-period variability in Hipparcos photometry. Note that it uses only the clusters of measurements to form the self-correlation diagram; it does not have to bridge the long gaps between them. Since the minima in the self-correlation diagram should recur at multiples of the period, we Fourier-analyzed the data in the self-correlation diagram for a few stars, and determined a "self-correlation phase diagram" for these stars. This was useful, in a few cases, for putting more stringent upper limits on the amplitude of any variability. 4. Results The self-correlation method was first applied to Hipparcos photometry of all known Beta Cephei stars, to see if the "known" period and amplitude could be recovered. This was the case, except for a few stars whose range was 0.010, and whose period was 0.1 day or less. In this case, the combination of observational error, and the gaps in the self-correlation diagram, made the determination of the parameters problematic. The method was then applied to our two samples of possible new Beta Cephei stars. In the following sections, is the amplitude of the self-correlation diagram; the light curve range is approximately 2.0 times this. SPV refers to short-term variability. Bright Beta Cephei Candidates. HIP 28237 (139 Tau; B0.5II): = 0.002 on time scale 0.26 day?; HIP 31190 (HR 2397; B2IV): 0.007; HIP 32385 (HR 2501; B2III): 0.007; HIP 32782 (HR 2537; B2IV): ~ 0.02, ellipsoidal variable?; HIP 33579 (HR 2618; B2II): 0.002; HIP 34940 (HR 2733; B2IV): 0.003; HIP 39961 (HR 3204; B2IV-V): 0.002; HIP 40932 (HR 3293; B1.5III): 0.004; HIP 42568 (V343 Car; B1.5III): 0.004; HIP 42828 ( Pyx; B1.5III): 0.002; HIP 42923 (HR 3479; B2III): = 0.005, time scale 0.9 day?; HIP 43575 (HR 3521; B1-2III): 0.005; HIP 43937 (V376 Car; B2IV-V): 0.003; HIP 48527 (HR 3924; B2III): 0.003; HIP 59747 ( Cru; B2IV): 0.003; HIP 61585 ( Mus; B2IV-V): 0.003; HIP 66925 (HR 5151; B0.5III): = 0.0175, time scale 0.9 day (?), Waelkens et al. (1998) class this as an Cyg variable; HIP 67464 (HR 5190; B2IV): 0.002; HIP 70270 (HR 5375; B1III): = 0.025, time scale ~ 0.9 day (?), a 1.54-day ellipsoidal variable according to Jerzykiewicz & Sterken (1992); HIP 73273 ( Lup; B2III): = 0.003, time scale 0.45 day?; HIP 78401 ( Sco; B0.3IV): = 0.004, time scale 0.8 day?; HIP 85696 ( Sco; B2IV): 0.005; HIP 88947 (HR 6772; B1II): = 0.005, time scale 0.4 day?; HIP 97634 (V380 Cyg; B1III): ~ 0.015, time scale 0.4 day?; HIP 96483 ( Aql; B0.5III): 0.003; HIP 100751 ( Pav; B2IV): 0.005; HIP 117957 (V373 Cas; B0.5II): 0.005. Beta Cephei Candidates in Binary Systems. HIP 3346 (V486 Cas; B1III): 0.002, binary period 5.5 days; HIP 17448 (o Per; B1III): 0.005, binary period 4.42 days; HIP 22797 (5 Ori; B2III): 3.7-day ellipsoidal variable, SPV 0.005; HIP 25044 (22 Ori; B2IV-V): 0.001, binary period 9.3 days (?); HIP 25473 ( Ori; B1III): 2.52-day ellipsoidal variable, SPV 0.005; HIP 29276 ( Pic; B0.5III): 1.67-day ellipsoidal variable, SPV 0.005; HIP 45080 (V357 Car; a Car; B2IVe): 0.001, binary period 6.74 days; HIP 45941 ( Vel; B2IV): 0.001; HIP 64004 (2 Cen; B2IV): 0.003, binary period 7.6 days (?); HIP 68002 ( Cen; B2IV): 8.024-day ellipsoidal variable, SPV 0.005; HIP 76297 ( Lup; B2IV): 0.002, binary period 2.85 days; HIP 84573 (u Her; B2IVp): 2.05-day ellipsoidal variable, SPV 0.005; HIP 102999 (Y Cyg; B0IVx2): 3.00-day ellipsoidal variable, SPV 0.005; HIP 103968 (V1898 Cyg; B1IVp): 2.93-day ellipsoidal variable, SPV 0.005; HIP 105091 (HD 203025; B2III): 0.005; HIP 113461 (NY Cep; B0IVx2): 0.005, binary period 15.27 days; HIP 113825 (CW Cep; B0.5III): = 0.010, time scale 0.45 day (see Fig. 1 below; note the minima at multiples of this value); Han et al. (2002) note photometric "complexities" in the light curve of this 17.4-day eclipsing binary. Figure 1. Self-correlation diagram for CW Cep. 5. Conclusions The most remarkable conclusion is the lack of Beta Cephei candidates among these two samples -- down to a limit of mag = 0.01. This is consistent with the findings of Waelkens et al. (1998) who found very few Beta Cephei candidates in the Hipparcos photometric database, using another method of analysis. There are some suggestions of very low amplitude variations on a time scale of 0.5-1.0 day in a few stars. Potential Beta Cephei stars may vary on such time scales, due to non-radial pulsation or to rotation. Most of the early searches for Beta Cephei stars were based on several hours of observations on single nights, and these are not well suited for identifying variability on longer time scales. The possibility that many stars, previously searched for Beta Cephei variability, might vary on time scales of a day should not be overlooked. Acknowledgements. Matthew Coulter was a participant in the University of Toronto Mentorship Program, which enables outstanding senior high school students to work on research projects at the university. We thank JoAnne Hosick for Fourier-analyzing some of the self-correlation diagrams. We also acknowledge the Ontario Work-Study Program, and NSERC Canada which provided a research grant. REFERENCES Eyer, L. & Genton, M.G. 1999, A&AS, 136, 421 Han, W., Kim, C.H., Lee, W.B. & Koch, R.H. 2002, AJ, 123, 2724 Jerzykiewicz, M. & Sterken, C. 1992, A&A, 261, 477 Percy, J.R., Ralli, J. & Sen, L.V. 1993, PASP, 105, 287 Percy, J.R., Hosick, J., Kincaide, H. & Pang, C. 2002, PASP, 114, 551 Waelkens, C., Aerts, C., Kestens, E., Grenon, M. & Eyer, L. 1998, A&A, 330, 215