A BINARY STAR WITH A SCUTI COMPONENT: AB CASSIOPEIAE E. Soydugan, 1 O. Dem_ircan, 1 M. C. Akan, 2 and F. Soydugan 1

The Astronomical Journal, 126:1933 1938, 2003 October # 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A. E A BINARY STAR WITH A SCUTI COMPONENT: AB CASSIOPEIAE E. Soydugan, 1 O. Dem_ircan, 1 M. C. Akan, 2 and F. Soydugan 1 Received 2002 November 19; accepted 2003 June 25 ABSTRACT New photometric observations of the Algol-type binary system AB Cassiopeiae were obtained in B and V filters during the 2001 2002 observing season at Ege University Observatory. As expected, the new light curves of the system, which were analyzed using the Wilson-Devinney code, exhibit short-period oscillations due to pulsation of the primary component. A photometric q-value search was performed, and the mass ratio of the system was found to be 0.19. The residuals from the observed-minus-computed light curves of the system reveal the pulsation light curves of the primary component. From the clear cycles of the pulsations in the light curves, we determined 21 new times of maximum light. The frequency content was investigated by using the Period98 program. Although the amplitude variation may suggest multiple periodicity in the pulsations, the power spectrum shows that only one frequency is significant; the remaining frequencies are probably not statistically significant. A multisite campaign is needed in order to study the reliability of the other pulsation modes. Key words: binaries: close binaries: eclipsing Scuti stars: individual: (AB Cassiopeiae) On-line material: machine-readable table 1. INTRODUCTION AB Cassiopeiae (=HIP 12235, BD +70 193), discovered by Hoffmeister (1929), is an Algol-type binary system with an orbital period of P b = 1.3668 days and the primary component being a Scuti type pulsating star. The pulsations were discovered by Tempesti (1971), who performed the first photoelectric photometry, using the Johnson V band. The pulsation period and amplitude of the primary component have been given as P b = 0.0583 days and DV 0.05 mag (Rodríguez et al. 1994, 1998), respectively, but at the phases of maximum the light amplitude appeared to vary from one night to another. An estimate of the mass of the component stars was made by Rodríguez et al. (1998), who gave M 1 = 1.78 M and M 2 = 0.39 M. AB Cas appears to have a semidetached configuration, in which the secondary component fills its Roche lobe; however, in the literature there is no spectroscopic evidence to prove the existence of mass transfer between the components. In order to understand the nature of the pulsation of the primary component and its possible connection to mass transfer through Roche lobe overflow in the system, we have included AB Cas in our observing program. 2. OBSERVATIONS New photometric observations of AB Cas were made over 15 nights during the 2001 2002 observing season with the 30 cm Schmidt-Cassegrain telescope of Ege University Observatory. The observational log is given in Table 1. All observations were made in Johnson B and V filters. An SSP-5A photometer (Optec, Inc.) was used, which contains a Hamamatsu R4457 photomultiplier tube. A total of 1329 and 1328 observational points were obtained in B and V, respectively. The B- and V-band data are listed in Table 2. As in previous work, BD +70 188 and BD 1 Çanakkale Onsekiz Mart University Observatory, TR-17100 Çanakkale, Turkey; esints@astronomy.sci.ege.edu.tr. 2 Ege University Observatory, TR-35100 Bornova, İzmir, Turkey. 1933 +70 186 were chosen as comparison and check stars, respectively. No light variations were found for these comparison and check stars. The atmospheric extinction coefficients in each color for each observational night were calculated by using observations of the comparison star. Then all the instrumental B and V magnitudes were corrected for atmospheric extinction, and the corresponding magnitude differences (in the sense variable or check star minus comparison) were calculated. Standard errors are 0.014 and 0.012 mag in B and V, respectively. The resulting light curves for AB Cas minus C1 (comparison star) are shown in Figure 1 plotted against orbital phase, where the oscillations originating from the primary component are clearly seen outside primary eclipse and also through the secondary minimum. Our calculated ephemeris, Min: I ¼ HJD 2;452;162:3596 þ 1:3668783E ; was used to create Figure 1. New times of minimum light obtained by using the method of Kwee & van Woerden (1956) are given in Table 3. 3. PHOTOMETRIC ANALYSIS In the Wilson-Devinney (W-D) solutions (Wilson 1992), we used normal points obtained from the individual observational points. Because we could see the pulsations in the maximum and in the secondary minimum of the light curves, none of the data points were averaged. In order to obtain normalized values of the system light, we used zeropoint values of 0.204 and 0.079 mag, which correspond to the magnitudes at about phase 0.25, for B and V, respectively, and B and V light curves normalized to unity. A total of 842 and 892 data points in the B and V filters, respectively, were used in the new light-curve solution of the system with the W-D code. Each data point was given the same weight. In the W-D solution, some parameters were kept free and others were fixed to their known values during all iterations. The orbital inclination i, surface temperature of the ð1þ

1934 SOYDUGAN ET AL. Vol. 126 TABLE 1 Observational Log Date (UT) Start (UT) Start (HJD 2,452,130+) Length (hr) 2001 Aug 11... 23:04:24 3.463 1.8 2001 Aug 13... 23:38:26 5.484 1.5 2001 Aug 25... 21:15:51 17.386 4.8 2001 Sep 8... 20:11:24 31.342 5.8 2001 Sep 9... 18:15:13 32.261 7.0 2001 Sep 10... 17:54:18 33.247 7.6 2001 Sep 13... 19:03:43 36.295 6.2 2001 Oct 14... 17:10:04 67.218 6.3 2001 Oct 18... 16:48:39 71.203 5.0 2001 Oct 21... 19:26:01 74.313 0.7 2001 Oct 23... 18:33:44 76.276 4.1 2002 Jan 22... 20:23:09 167.352 2.1 2002 Feb 6... 18:11:56 182.260 4.8 2002 Feb 14... 17:58:03 190.250 1.7 2002 Feb 16... 17:23:14 192.225 3.8 secondary T c, dimensionless potential of the primary h, phase shift, and fractional luminosity of the primary L h were chosen as adjustable parameters during differential iterations. The linear limb-darkening coefficients x h and x c from Díaz-Cordovés, Claret, & Giménez (1995), the bolometric albedos A h and A c from Rucinski (1969), and the gravity-darkening exponents g h and g c from von Zeipel (1924) for radiative atmospheres (primary component) and from Lucy (1967) for convective atmospheres (secondary component) were all fixed (see Table 4). The surface temperature of the primary star, T h, was taken from Rodríguez et al. (1998) to be 8000 K. Ando (1980) estimated the mass ratio to be 0.22 using the approximate formula given by Plavec & Kratochvíl (1964). To obtain the photometric mass ratio, we decided to make a photometric q-value search using the W-D code. The search was made in the B light curve by choosing i, T c, h,andl h as adjustable parameters in the semidetached mode (mode 5). TheP variation of the weighted sum of the squared residuals, W(O C) 2, for the corresponding mass ratios is shown in Figure 2. As can be seen from the figure, the lowest value of P W(O C) 2 is around q = 0.19. In TABLE 2 B-andV-Band Observations of AB Cassiopeiae HJD (2,452,100+) DB DV 33.4627... 0.2410... 33.4629...... 0.0890 33.4649... 0.2480... 33.4652...... 0.1370 33.4673... 0.3450... 33.4676...... 0.1070 33.4685... 0.2730... 33.4688...... 0.1170 33.4743... 0.2980... 33.4745...... 0.1180 Note. Table 2 is presented in its entirety in the electronic edition of the Astronomical Journal. A portion is shown here for guidance regarding its form and content. Fig. 1. Differential B (top) and V (bottom) light curves of AB Cas all subsequent iterations, q was taken as a constant parameter with the value of 0.19. In the light-curve solution, we also applied a third light, l 3, as a free parameter in the iterations, but it always becomes insignificantly small, indicating no third light in the system. Considering i, T c, h, and L h as adjustable parameters, the iterations were carried on until the corrections to the parameters became smaller than the corresponding probable errors. Using the final parameters, the computed light curve was obtained, and it is shown along with the V observations in Figure 3. With the obtained computed light curves, proximity effects often known as the reflection and ellipticity effects were subtracted from the light curves. Thus, only the pulsations remained in the light curves. The results of the photometric solution are listed in Table 4. The residual (observed minus computed) light curve, displaying only the pulsations, is shown in Figure 4 for V. 4. FREQUENCY ANALYSIS OF THE PHOTOMETRIC DATA FOR PULSATIONS In order to study the pulsation of the primary component, we had to exclude the eclipses and proximity effects from the observed light curves of the system. To accomplish this task, we used the W-D code to produce theoretical light curves. Then we had to exclude the primary eclipse, since the pulsat- TABLE 3 NewTimesofMinimumofABCassiopeiae HJD (2,400,000+) Error Min. Filters Meth. a 52,162.3596... 0.0002 I B, V pe 52,166.4584... 0.0003 I B, V pe 52,322.2834... 0.0007 I B, V pe a Method: (pe) photoelectric.

No. 4, 2003 AB CASSIOPEIAE 1935 TABLE 4 Photometric Solution for AB Cassiopeiae Parameter B V i (deg)... 88.291 (0.170) 88.260 (0.139) T h (K)... 8000 8000 T c (K)... 4705 (44) 4729 (24) h... 3.9574 (0.0099) 3.9448 (0.0093) c... 2.2077 2.2077 Phase shift... 0.0005 0.0005 q... 0.19 0.19 l 3... 0.0 0.0 e... 0.0 0.0 x h... 0.679 0.607 x c... 0.906 0.820 g h... 1.0 1.0 g c... 0.32 0.32 L h /(L h + L c )... 0.956 0.921 L c /(L h + L c )... 0.044 0.079 r 1 (pole)... 0.265 0.266 r 1 (point)... 0.270 0.271 r 1 (side)... 0.268 0.269 r 1 (back)... 0.269 0.270 r 2 (pole)... 0.229 0.229 r 2 (point)... 0.337 0.337 r 2 (side)... 0.239 0.239 r P 2 (back)... 0.271 0.271 W(O C) 2... 0.24979 0.18144 Fig. 3. Normal points of AB Cas in the V band and the computed light curve (solid line) corresponding to the parameters from the solution of the V light curve. ing component is eclipsed during these phases. Finally, the residuals from the computed light curves should display only the light changes that originate from pulsations (see Fig. 4). By considering only the clear cycles of the residual light curves, we estimated 21 times of maximum light for AB Cas, obtained using the well-known method of Kwee & van Woerden (1956) as averages over the two (B and V ) bands. The new times of maximum light and their errors are given in Table 5. With the pulsational times of maximum obtained by us, combined with other times of maximum from previous studies (Rodríguez et al. 1998; Frolov, Pastukhova, & Mironov 1982) and an adopted initial epoch T 0,p = HJD 2,452,133.4876 (our first light maximum) and P p = 0.058286477 days (our pulsation period found by frequency analysis in V ), a least-squares fit of a linear ephemeris leads to the following elements: T 0,p = 2,452,133.4920 (0.0008) and P p = 0.05828649 days (0.00000001). The O C residuals and cycle numbers (E) computed using these light elements are also listed in Table 5. As can be seen from the table, the distribution of O C values does not show any 0.9 0.7 0.5 0.3 Σ 2 0.1 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Fig. 2. Behavior of P W(O C) 2 as a function of mass ratio q change, and they can be represented by using linear regression, which is the best method for these data. Consequently, in the pulsation period there is no variation with time. The pulsation period found from O C analysis differs from the pulsation period derived by frequency analysis by only about 1.3 10 8 days. The frequency analysis was performed on the residual light curves using a package of computer programs called Period98 (Sperl 1996). The results in each band are given in TABLE 5 Pulsational Times of Maximum of the Primary Component of AB Cassiopeiae HJD (2,400,000+) Error E (cycles) O C (days) Filters 52,133.4876... 0.0008 0 0.0044 B, V 52,135.5289... 0.0011 35 0.0031 B, V 52,147.4812... 0.0008 240 0.0004 B, V 52,161.3600... 0.0008 478 0.0071 B, V 52,161.4192... 0.0013 479 0.0080 B, V 52,161.4715... 0.0019 480 0.0020 B, V 52,161.5241... 0.0007 481 0.0037 B, V 52,162.5215... 0.0012 498 0.0028 B, V 52,163.2756... 0.0023 511 0.0008 B, V 52,163.3334... 0.0013 512 0.0013 B, V 52,163.3934... 0.0008 513 0.0004 B, V 52,163.4571... 0.0009 514 0.0058 B, V 52,163.5140... 0.0006 515 0.0045 B, V 52,166.3096... 0.0009 563 0.0023 B, V 52,197.3178... 0.0015 1095 0.0021 B, V 52,197.4259... 0.0004 1097 0.0064 B, V 52,201.2758... 0.0010 1163 0.0034 B, V 52,201.3328... 0.0006 1164 0.0047 B, V 52,201.3956... 0.0007 1165 0.0002 B, V 52,206.3415... 0.0008 1250 0.0086 B, V 52,206.4084... 0.0007 1251 0.0000 B, V

1936 SOYDUGAN ET AL. Vol. 126 Fig. 4. Residuals between observed and computed light curves in V Table 6. The spectral window pattern of the data, power spectrum, and the residual power spectrum after removing the main peak (including the significance limit for V ) are shown in Figures 5a, 5b, and 5c, respectively. Since the observations were done from a single site, the 1 cycle day 1 alias is very strong, as expected. The pulsation frequency obtained in both B and V confirms the earlier results of Frolov et al. (1982) and Rodríguez et al. (1998), who found the pulsation frequency f to be 17.15637 and 17.1563 cycles day 1, respectively. In the B and V bands, as seen in Table 6, the frequencies we obtained are 17.1564 and 17.1566 cycles day 1, respectively. Also, we compared our amplitude obtained in the V band with that given by Rodríguez et al. (1998) and did not see any meaningful difference (Table 6). After prewhitening for the first frequency, we obtained the second highest peak, which resides in the noise and is lower than the significance level. So, the existence of a secondary frequency with such a small amplitude cannot be accepted. Breger et al. (1993) gave a good criterion for the reality of a peak, which is a signal-to-noise ratio S/N of 4.0 for the amplitude. In our case the S/N was calculated to be 10.51 for the power. The night-by-night pulsation observations were represented as mðtþ ¼zero point þ X a i sinð2f i t þ 2 i Þ for V and plotted together with the observations (see Fig. 6). Here m(t) is the calculated magnitude and a i, i,and f i are the amplitude, phase, and frequency of the ith frequency. In the theoretical representation and for the remaining residuals in each band, we used the time of the first observational point as the origin, which are HJD 2,452,133.4627 and HJD 2,452,133.4629 for B and V, respectively. As can be seen from Figure 6, the agreement between the computed and the observed curves is quite good. The amplitude of the pulsation changes from one cycle to another, suggesting multiple periodicity. Following Rodríguez et al. (1998), a value of Q = 0.036 0.006 days can be determined for the pulsation ð2þ Fig. 5. (a) Spectral window pattern of the data, (b) power spectrum, and (c) resulting power spectrum after removing the main peak, wth the significance cutoff in V indicated (horizontal line). constant by using the well-known relation of Petersen & Jørgensen (1972), log Q ¼ 6:454 þ log P þ 0:5logg þ 0:1M bol þ log T eff : ð3þ In this equation, P is the pulsation period and the remaining quantities have their usual meanings. The values of g, M bol, and T eff were taken from Rodríguez et al. (1998). This value TABLE 6 Pulsational Properties of the Primary Component of AB Cassiopeiae Parameter B (This Study) V (This Study) V (Rodríguez et al. 1998) Frequency (cycles day 1 )... 17.1564 (0.0004) 17.1566 (0.0004)... Amplitude (mag)... 0.0222 (0.0010) 0.0196 (0.0009) 0.0219 (0.0009) Phase... 0.2471 (0.0067) 0.2904 (0.0071)...

No. 4, 2003 AB CASSIOPEIAE 1937 Fig. 6. Pulsational behavior of the primary component of AB Cas, together with the Fourier solution in the V filter of Q suggests that the pulsation is in the fundamental mode. We thought that there may be a real secondary peak in AB Cas: First, after prewhitening for the first frequency, we obtained the second highest peak, which resides in the noise. Secondly, the differential magnitudes C2 C1 were compared with the reliability of the secondary peak. We saw that the secondary peak was much lower than the scattering of the differential magnitude between two comparison stars, which was about 0.01 mag. Thus, the secondary peak cannot be accepted as significant at the present time. In order to overcome this situation, multisite observations of AB Cas are needed. It may be expected that mass accretion by the primary component could cause similar changes in the pulsational character of this star. 5. CONCLUSION We have used new photoelectric observations of AB Cassiopeiae to refine the geometric and physical parameters of this binary system, including the pulsational properties of the primary component. A mass ratio search resulted in a slightly different value (q = 0.19)

1938 SOYDUGAN ET AL. Fig. 6. Continued compared with the literature value (q = 0.22; see, e.g., Ando 1980; Rodríguez et al. 1998). The amplitude of the pulsations in the observations seems to vary from cycle to cycle, indicating the probable existence of other pulsation modes (see Fig. 4). Although the amplitude variation may indicate multiple periodicity in pulsation, the power spectrum shows that only one frequency is significant according to the Breger et al. (1993) criterion, and in addition, the value of the pulsational constant suggests that this is the radial fundamental mode (Rodríguez et al. 1998). The origin of this kind of variability may be one pulsation frequency plus additional variation that is not cyclic in character (disturbances in the light curves due to scatter in the observations, mass accretion by the primary component, etc.). A future multisite campaign would help overcome this problem. This work was partly supported by the Scientific and Technical Research Council of Turkey (TÜBİTAK). We sincerely thank Professor Cafer İbanoğlu, Professor Edwin Budding, and Rafael Garrido Haba for their helpful discussions and suggestions. The research was also supported by the Çanakkale Onsekiz Mart University Research Foundation. This article is a part of the Ph.D. thesis of E. S. The authors thank the referee for helpful discussions and suggestions. Ando, H. 1980, Ap&SS, 71, 249 Breger, M., et al. 1993, A&A, 271, 482 Díaz-Cordovés, J., Claret, A., & Giménez, A. 1995, A&AS, 110, 329 Frolov, M. S., Pastukhova, E. N., & Mironov, A. V. 1982, Inf. Bull. Variable Stars, No. 2179 Hoffmeister, C. 1929, Astron. Nachr., 234, 33 Kwee, K. K., & van Woerden, H. 1956, Bull. Astron. Inst. Netherlands, 12, 327 Lucy, L. B. 1967, Z. Astrophys., 65, 89 Plavec, M., & Kratochvíl, P. 1964, Bull. Astron. Inst. Czechoslovakia, 15, 156 REFERENCES Petersen, J. O., & Jørgensen, H. E. 1972, A&A, 17, 367 Rodríguez, E., Claret, A., Sedano, J. L., García, J. M., & Garrido, R. 1998, A&A, 340, 196 Rodríguez, E., López de Coca, P., Rolland, A., Garrido, R., & Costa, V. 1994, A&AS, 106, 21 Rucinski, S. M. 1969, Acta Astron. 19, 245 Sperl, M. 1996, Commun. Asteroseismol., No. 111, 5 Tempesti, P. 1971, Inf. Bull. Variable Stars, No. 596 Wilson, R. E. 1992, Documentation of Eclipsing Binary Computer Model (rev. ed.; Gainesville: Dept. Astron., Univ. Florida) von Zeipel, H. 1924, MNRAS, 84, 665