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The Astronomical Journal, 126:1933–1938, 2003 October # 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A BINARY STAR WITH A SCUTI COMPONENT: AB CASSIOPEIAE E. Soydugan,1 O. Demi_rcan,1 M. C. Akan,2 and F. Soydugan1 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 +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,
1. INTRODUCTION
AB Cassiopeiae (=HIP 12235, BD +70 193), discovered by Hoffmeister (1929), is an Algol-type binary system with an orbital period of Pb = 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 Pb = 0.0583 days and DV 0.05 mag (Rodrı´guez 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 Rodrı´guez et al. (1998), who gave M1 = 1.78 M and M2 = 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.
Min: I ¼ HJD 2;452;162:3596 þ 1:3668783E ;
ð1Þ
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
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 1C ¸ anakkale Onsekiz Mart University Observatory, TR-17100 C ¸ anakkale, Turkey;
[email protected]. 2 Ege University Observatory, TR-35100 Bornova, I˙zmir, Turkey.
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TABLE 1 Observational Log Date (UT)
Start (UT)
Start (HJD 2,452,130+)
Length (hr)
2001 Aug 11 .............. 2001 Aug 13 .............. 2001 Aug 25 .............. 2001 Sep 8 ................. 2001 Sep 9 ................. 2001 Sep 10 ............... 2001 Sep 13 ............... 2001 Oct 14 ............... 2001 Oct 18 ............... 2001 Oct 21 ............... 2001 Oct 23 ............... 2002 Jan 22 ............... 2002 Feb 6................. 2002 Feb 14............... 2002 Feb 16...............
23:04:24 23:38:26 21:15:51 20:11:24 18:15:13 17:54:18 19:03:43 17:10:04 16:48:39 19:26:01 18:33:44 20:23:09 18:11:56 17:58:03 17:23:14
3.463 5.484 17.386 31.342 32.261 33.247 36.295 67.218 71.203 74.313 76.276 167.352 182.260 190.250 192.225
1.8 1.5 4.8 5.8 7.0 7.6 6.2 6.3 5.0 0.7 4.1 2.1 4.8 1.7 3.8
secondary Tc, dimensionless potential of the primary h, phase shift, and fractional luminosity of the primary Lh were chosen as adjustable parameters during differential iterations. The linear limb-darkening coefficients xh and xc from Dı´az-Cordove´s, Claret, & Gime´nez (1995), the bolometric albedos Ah and Ac from Rucinski (1969), and the gravity-darkening exponents gh and gc 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, Th, was taken from Rodrı´guez et al. (1998) to be 8000 K. Ando (1980) estimated the mass ratio to be 0.22 using the approximate formula given by Plavec & Kratochvı´l (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, Tc, h, and Lh as adjustable parameters in the semidetached mode (mode 5). ThePvariation of the weighted sum of the squared residuals, W(OC)2, for the corresponding mass ratios is shown in Figure 2. As can be seen from the figP ure, the lowest value of W(OC)2 is around q = 0.19. In TABLE 2 B- and V-Band Observations of AB Cassiopeiae
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, l3, as a free parameter in the iterations, but it always becomes insignificantly small, indicating no third light in the system. Considering i, Tc, h, and Lh 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
HJD (2,452,100+)
DB
DV
33.4627 ...................... 33.4629 ...................... 33.4649 ...................... 33.4652 ...................... 33.4673 ...................... 33.4676 ...................... 33.4685 ...................... 33.4688 ...................... 33.4743 ...................... 33.4745 ......................
0.2410 ... 0.2480 ... 0.3450 ... 0.2730 ... 0.2980 ...
... 0.0890 ... 0.1370 ... 0.1070 ... 0.1170 ... 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.
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 pulsatTABLE 3 New Times of Minimum of AB Cassiopeiae HJD (2,400,000+)
Error
Min.
Filters
Meth.a
52,162.3596 ................ 52,166.4584 ................ 52,322.2834 ................
0.0002 0.0003 0.0007
I I I
B, V B, V B, V
pe pe pe
a
Method: (pe) photoelectric.
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TABLE 4 Photometric Solution for AB Cassiopeiae Parameter
B
V
i (deg)......................... Th (K) ........................ Tc (K)......................... h............................... c ............................... Phase shift.................. q................................. l3 ................................ e ................................. xh ............................... xc ............................... gh ............................... gc ............................... Lh/(Lh + Lc) .............. Lc/(Lh + Lc) .............. r1 (pole)...................... r1 (point) .................... r1 (side) ...................... r1 (back) ..................... r2 (pole)...................... r2 (point) .................... r2 (side) ...................... rP 2 (back) ..................... W(OC )2 .............
88.291 (0.170) 8000 4705 (44) 3.9574 (0.0099) 2.2077 0.0005 0.19 0.0 0.0 0.679 0.906 1.0 0.32 0.956 0.044 0.265 0.270 0.268 0.269 0.229 0.337 0.239 0.271 0.24979
88.260 (0.139) 8000 4729 (24) 3.9448 (0.0093) 2.2077 0.0005 0.19 0.0 0.0 0.607 0.820 1.0 0.32 0.921 0.079 0.266 0.271 0.269 0.270 0.229 0.337 0.239 0.271 0.18144
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 (Rodrı´guez et al. 1998; Frolov, Pastukhova, & Mironov 1982) and an adopted initial epoch T0,p = HJD 2,452,133.4876 (our first light maximum) and Pp = 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: T0,p = 2,452,133.4920 (0.0008) and Pp = 0.05828649 days (0.00000001). The OC 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 OC values does not show any
0.9
Σ
2
0.7
0.5
0.3
0.1 0.10
0.15
0.20
Fig. 2.—Behavior of
0.25
P
0.30
0.35
0.40
0.45
W(OC )2 as a function of mass ratio q
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.
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 OC analysis differs from the pulsation period derived by frequency analysis by only about 1.3 108 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)
OC (days)
Filters
52,133.4876................ 52,135.5289................ 52,147.4812................ 52,161.3600................ 52,161.4192................ 52,161.4715................ 52,161.5241................ 52,162.5215................ 52,163.2756................ 52,163.3334................ 52,163.3934................ 52,163.4571................ 52,163.5140................ 52,166.3096................ 52,197.3178................ 52,197.4259................ 52,201.2758................ 52,201.3328................ 52,201.3956................ 52,206.3415................ 52,206.4084................
0.0008 0.0011 0.0008 0.0008 0.0013 0.0019 0.0007 0.0012 0.0023 0.0013 0.0008 0.0009 0.0006 0.0009 0.0015 0.0004 0.0010 0.0006 0.0007 0.0008 0.0007
0 35 240 478 479 480 481 498 511 512 513 514 515 563 1095 1097 1163 1164 1165 1250 1251
0.0044 0.0031 0.0004 0.0071 0.0080 0.0020 0.0037 0.0028 0.0008 0.0013 0.0004 0.0058 0.0045 0.0023 0.0021 0.0064 0.0034 0.0047 0.0002 0.0086 0.0000
B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V B, V
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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 day1 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 Rodrı´guez et al. (1998), who found the pulsation frequency f to be 17.15637 and 17.1563 cycles day1, respectively. In the B and V bands, as seen in Table 6, the frequencies we obtained are 17.1564 and 17.1566 cycles day1, respectively. Also, we compared our amplitude obtained in the V band with that given by Rodrı´guez 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 X ð2Þ mðtÞ ¼ zero point þ ai sinð2fi t þ 2i Þ for V and plotted together with the observations (see Fig. 6). Here m(t) is the calculated magnitude and ai, i, and fi 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 Rodrı´guez et al. (1998), a value of Q = 0.036 0.006 days can be determined for the pulsation
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 0:5 log g þ 0:1Mbol þ log Teff : ð3Þ In this equation, P is the pulsation period and the remaining quantities have their usual meanings. The values of g, Mbol, and Teff were taken from Rodrı´guez et al. (1998). This value
TABLE 6 Pulsational Properties of the Primary Component of AB Cassiopeiae
Parameter
B (This Study)
V (This Study)
V (Rodrı´guez et al. 1998)
Frequency (cycles day1).............. Amplitude (mag).......................... Phase ...........................................
17.1564 (0.0004) 0.0222 (0.0010) 0.2471 (0.0067)
17.1566 (0.0004) 0.0196 (0.0009) 0.2904 (0.0071)
... 0.0219 (0.0009) ...
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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)
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Fig. 6.—Continued
compared with the literature value (q = 0.22; see, e.g., Ando 1980; Rodrı´guez 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 (Rodrı´guez 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 ¨ BI˙TAK). We Technical Research Council of Turkey (TU sincerely thank Professor Cafer I˙banog˘lu, Professor Edwin Budding, and Rafael Garrido Haba for their helpful discussions and suggestions. The research was also supported by the C ¸ anakkale 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.
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