DEEP, LOW MASS RATIO OVERCONTACT BINARY SYSTEMS. III. CU TAURI AND TV MUSCAE

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1 The Astronomical Journal, 130: , 2005 July # The American Astronomical Society. All rights reserved. Printed in U.S.A. DEEP, LOW MASS RATIO OVERCONTACT BINARY SYSTEMS. III. CU TAURI AND TV MUSCAE S.-B. Qian, 1,2,3 Y.-G. Yang, 1,2 B. Soonthornthum, 4 L.-Y. Zhu, 1,2 J.-J. He, 1,2 and J.-Z. Yuan 1,2 Received 2005 January 13; accepted 2005 March 26 ABSTRACT New CCD photometric light curves in the B and V bands of the neglected W UMa type eclipsing variable star CU Tauri are presented. The O Connell effect in the V light curve obtained in 2001 by Yang and Liu was about V ¼þ0:015, but it vanished in our 2004 observations. The variations in the levels of both minima were seen. Our two epochs of light minimum and others compiled from the literature were used for the period study. It is shown that the types of some eclipse times were incorrect and the values of the period obtained by previous investigators were aliases that prevented formation of a plausible O C curve. A new linear ephemeris was derived, and it is discovered that the orbital period of CU Tau shows a continuous decrease at a rate of dp/dt ¼ 1:81 ; 10 6 days yr 1. The present symmetric light curves were solved with the 2003 version of the Wilson-Devinney (W-D) code. Both our solutions and those derived by Yang and Liu reveal that CU Tau is a deep ( f ¼ 50:1% 3:2%), low mass ratio (q ¼ 0:1770 0:0017) overcontact binary system. Meanwhile, the photoelectric light curves in the B, V, R, andi bands of TV Muscae published by Hilditch and coworkers were reanalyzed with the 2003 version of the W-D code. It is shown that the low mass ratio binary turns out to be a deep overcontact system with f ¼ 74:3% 11:3%. A period analysis with all collected times of light minimum revealed a combination of a long-term period decrease (dp/dt ¼ 2:16 ; 10 7 days yr 1 ) and a possible cyclic change with a period of 29.1 yr. The rapid long-term period decreases of both systems can be explained as a combination of the mass transfer from the more massive component to the less massive one and the angular momentum loss due to mass outflow from the L2 point. In that way, the overcontact degrees of the two systems will become deeper as their periods decrease, and finally they will evolve into a single rapid-rotation star. However, for CU Tau, the rate of the secular period decrease is very large when compared with the other systems of the same type. This suggests that the long-term period decrease may be part of a long-period periodic change, which we need more data to check. Key words: binaries: close binaries: eclipsing stars: evolution stars: individual (CU Tauri, TV Muscae) 1. INTRODUCTION The phenomena of the blue straggler stars and the FK Com type stars are not well-understood problems in stellar astrophysics. One of the possibilities for their formation is from the coalescence of W UMa type overcontact binary systems. The most popular evolutionary scenario for this type of binary star is that they are formed from initially detached systems by angular momentum loss (AML) via magnetic stellar wind (Vilhu 1982; Guinan & Bradstreet 1988; Eggen & Iben 1989). This scenario was strongly supported by the results of a systematic search for short-period close binaries in open and globular clusters (e.g., Kaluzny & Shara 1988; Kaluzny et al. 1993; Mazur et al. 1995). At the overcontact phase, a combination of thermal relaxation oscillation (TRO; e.g., Lucy 1976; Flannery 1976; Robertson & Eggleton 1977) and variable AML via the change of the degree of overcontact may cause them to oscillate around a critical mass ratio (Qian 2003a), which indicates that a broken overcontact stage cannot be met for cool, short-period objects and can increase the lifetime in the overcontact phase. However, the gradual decrease of the mass ratio will make them finally evolve into rapidly rotating single stars (e.g., van t Veer 1997) when the distribution of the angular momentum meets the more familiar criterion (Hut 1980) that the orbital angular momentum is less than 3 times the total spin angular momentum, i.e., J rot > 1 3 J orb. On the other hand, if the degree of overcontact is rather high, a dynamical instability will be encountered, and the merging of an overcontact binary star is also inevitable (Rasio & Shapiro 1995). Therefore, deep ( f 50:0%), low mass ratio (q 0:25) overcontact binary stars may be the progenitors of blue straggler/ FK Com type stars. Table 1 contains 24 such overcontact binary systems. For those sample stars, the range of orbital period is from days (FG Hya) to days (KN Per). The system GSC has the highest degree of overcontact ( f ¼ 93:4%). The sample binary star, AH Cnc, is a member of the old open cluster M67. Detail photometric analyses and orbital period studies of those systems can provide invaluable information for the coalescence of binary systems. The light variability of CU Tauri was discovered by Binnendijk (1950) from photographic observations. According to the fourth edition of the General Catalogue of Variable Stars (GCVS; Kholopov et al. 1987, p. 242), it is an EW/KW-type binary with a spectral type of G0. The linear ephemeris given in the GCVS was 1 National Astronomical Observatories/ Yunnan Observatory, Chinese Academy of Sciences, P.O. Box 110, Kunming, China; qsb@netease.com. 2 United Laboratory of Optical Astronomy, Chinese Academy of Sciences, Beijing, China. 3 Visiting Astronomer, Astrophysics Research Institute, Liverpool John Moores University. 4 Department of Physics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand; boonraks@chiangmai.ac.cn. 224 Min: I ¼ 2;440;969:2328 þ 0:41222E days; while the orbital period given in the Finding List for Observers of Interacting Binary Stars catalog (Wood et al. 1980) is days. Yang & Liu (2004) published the first complete B and V light curves, which showed that the light curves of CU Tau are typical EW type, in which the light variation is ð1þ

2 TABLE 1 Deep, Low Mass Ratio Overcontact Binary Systems DEEP OVERCONTACT BINARY SYSTEMS. III. 225 Star Name q f (percent) P References AH Aur , 2 AP Aur DN Aur XY Boo , 6 FN Cam , 8 AH Cnc YY CrB , 11 V728 Her V857 Her FG Hya , 15 UZ Leo TV Mus V2388 Oph , 19 MW Pav KN Per IK Per Y Sex CU Tau , 24 AW UMa HV UMa BU Vel GR Vir GSC GSC References. (1) Rucinski & Lu 1999; (2) Vanko et al. 2001; (3) Li et al. 2001; (4) Goderya et al. 1997a; (5) McLean & Hilditch 1983; (6) Winkler 1977; (7) Lu et al. 2001; (8) Pribulla & Vanko 2002; (9) Sandquist & Shetrone 2003; (10) Rucinski et al. 2000; (11) Pribulla et al. 2002; (12) Nelson et al. 1995; (13) Gomez-Forrellad & Garcia-Melendo 1996; (14) Lu & Rucinski 1999; (15) Qian & Yang 2005; (16) Vinkó et al. 1996; (17) this paper; (18) Rucinski et al. 2002; (19) Yakut et al. 2004; (20) Lapasset 1980; (21) Goderya et al. 1997b; (22) Zhu et al. 2005; (23) Yang & Liu 2003; (24) Yang & Liu 2004; (25) Pribulla et al. 1999; (26) Csák et al. 2000; (27) Twigg 1979; (28) Qian & Yang 2004; (29) Yang et al. 2005; (30) Maciejewski et al continuous and the primary and the secondary minima both are nearly in the same depth. The photometric analysis by Yang & Liu (2004) indicated that CU Tau is an A-type overcontact binary system with a small mass ratio of q ¼ 0:18. The linear ephemerides, given in the fourth edition of GCVS (Kholopov et al. 1987, p. 242) and in the catalog of Wood et al. (1980), were used to compute the O C values of some photoelectric and CCD (PC) times of light minimum by Yang & Liu (2004), but those O C values (listed in Table II of the paper by Yang & Liu) showed large scatters (up to 0.2 days). Therefore, they derived a new one Min: I ¼ 2;452;251:1098 þ 0: E days; which was used to calculate the O C values of the PC data. The residuals plotted in Figure 1 of their paper also displayed large scatters (up to 0.05 days), which were attributed to irregular period changes by them. However, such a large period jump with a very short timescale is less likely for overcontact binary stars. In order to understand the properties of the orbital period variation and the evolutionary state of the system, we intended to observe it in 2004 January and give a detailed photometric study in the present paper. The other system, TV Muscae, was reported to be a W UMa type eclipsing binary of rather small amplitude (0.4 mag) and an orbital period of days by Hertzsprung (1928). It is a ð2þ Fig. 1. Comparison between the light curve in V band obtained on 2004 January 15 and 16 and that obtained by Yang & Liu in 2001 January for CU Tau. Phases of those observations were computed with eq. (3). The variable O Connell effect and changes of the light levels at both minima are seen. poorly studied binary because it can only be observed in the Southern Hemisphere. The first spectroscopic and photometric investigations were published by Hilditch et al. (1989) in the final paper of their series of papers on contact and near-contact binary systems. It was shown that TV Mus is an overcontact binary star with a rather extreme mass ratio of q ¼ 0:135 and a degree of overcontact of f ¼ 13%. The value of f shows that it is a shallow overcontact binary system. However, as shown in Table 1, many low mass ratio overcontact binaries usually have a high degree of overcontact ( f > 50%). This may indicate that this system needs further analysis. On the other hand, most W UMa type binaries are observed to have a variable orbital period (e.g., Qian 2001, 2003a). To search for period changes in TV Mus, we intended to analyze all available times of light minimum of the system. 2. NEW CCD PHOTOMETRIC OBSERVATIONS FOR CU TAURI CU Tau was observed in two nights in 2004 January (January 15 and 16) with the PI1024 TKB CCD photometric system attached to the 1.0 m reflecting telescope at the Yunnan Observatory. The effective field of view of the CCD photometric system is about 6A5 ; 6A5 at the Cassegrain focus. During the observation, B and V filters were used that are close to the standard Johnson UBV system (Yang & Li 1999). The integration time for each image is 120 s. The comparison and the check stars are the same as those used by Yang & Liu (2004). The task phot (measure magnitudes for a list of stars) of the aperture photometry package of IRAF was used to reduce the observed images. The B and V photometric data are listed in Tables 2 and 3 with their Heliocentric Julian Dates, phases, and magnitude differences between CU Tau and the comparison star. The phases of those observations were computed with the new period determined in x 3. Two epochs of light minimum were derived with a least-squares solution and are shown in Table 4. Since the light curves near both minima are symmetric, a parabolic fitting method was used to determine those eclipse times. The complete V light curve is plotted in Figure 1. It is shown in the figure that the data are quality and the light variations at both minima are transit, indicating that the eclipses are partial ones. In Figure 1 the light curve in the V band obtained by Yang

3 226 QIAN ET AL. Vol. 130 TABLE 2 CCD Photometric Data of CU Tauri in V Band Observed in 2004 January & Liu (2004) in 2001 January is also plotted. It can be seen that the light curve of Yang & Liu (2004) shows a positive O Connell effect, with Max: I Max: II ¼ 0:015 mag, whereas it disappeared when we observed in 2004 January. The changes at the levels of two light minima are also seen. This type of variation was not unusual for W UMa type binary stars, e.g., BX Peg (Lee et al. 2004), FG Hya (Qian & Yang 2005), and CE Leo (Kang et al. 2004). 3. ORBITAL PERIOD CHANGE AND PHOTOMETRIC SOLUTIONS FOR CU TAURI 3.1. Revised on the Orbital Period and Orbital Period Variation Although several values of orbital periods of CU Tau have been determined, Yang & Liu (2004) showed that none can be used to form a plausible O C curve. In order to investigate the orbital period variation of the system in detail, all available PC times of light minimum were compiled and are listed in Table 5. Those shown in column (3) are the observational methods, where pe refers to photoelectric photometry and CCD to chargecoupled device photometry. The O C diagram with respect to the ephemeris given by Yang & Liu (2004) is displayed in Figure 2. Strange variations (irregular jumps) and a large scatter of the O C values can be seen from this figure. This type of change is impossible for W UMa type binary stars, indicating that the orbital period of CU Tau needs to be revised. The situation of CU Tau resembles those of GW Cep (Qian 2003a) and VW Boo (Qian & Zhu 2002). If the orbital period in an ephemeris is not correct, the accumulative effect can produce an O C larger than P e /2 (P e is the period in the ephemeris), and thus one cannot correctly calculate the values of E and O C. For CU Tau, based on all PC times of light minimum, a new linear ephemeris, Min: I ¼ 2;453;020:0760(0:0027) þ 0: (0: )E days; was derived. Of the three values of the orbital period, given by Kholopov et al. (1987, p. 242), Wood et al. (1980), and Yang & Liu (2004), the value derived by Yang & Liu is closest to the present one. However, when comparing the ephemeris (eq. [3]) with that determined by Yang & Liu (2004; eq. [2] in their paper), a period difference of P ¼ 0: days is obtained. The O C values of all PC data from the new linear ephemeris were calculated and are shown in column (5) of Table 5. As listed in the column, the absolute values of all O C values are no larger than days, suggesting that this ephemeris is plausible. The corresponding O C diagram is plotted in Figure 3. A continuous period decrease is clearly seen in the figure. A leastsquares solution leads to the following quadratic ephemeris Min: I ¼ 2;453;020:06737(0:00006) þ 0: (0: ) E 1:02(0:01) ; 10 9 E 2 days; which can fit all PC data well (Fig. 3, solid line). During the calculation of equation (4), the O C values of the two times of ð3þ ð4þ

4 No. 1, 2005 DEEP OVERCONTACT BINARY SYSTEMS. III. 227 TABLE 3 CCD Photometric Data of CU Tauri in B Band Observed in 2004 January light minimum, 2,449, and 2,450, , were not used because their O C values show a larger scatter when compared with the general trend formed by the other data points. The residuals of all PC data from equation (4) are displayed in Figure 4, and no variations can be seen there. The scatter of all residuals is less than days, which is a typical value for W UMa type binary stars, suggesting that equation (4) can give a good description of all the PC data. The solid line in Figure 3 indicates that the period of CU Tau is decreasing continuously. With the quadratic term in equation (4), a continuous period decrease rate, dp/dt ¼ 1:81 ; 10 6 days yr 1, was determined, which corresponds to a period decrease of 15.6 s (100 yr) 1. During the analysis of the period change, we found that the types of some times of light minimum, e.g., 2,449, , 2,450, , 2,450, , 2,450, , 2,450, , 2,450, , 2,450, , 2,451, , 2,451, , and 2,452, , were incorrect in the original references and were corrected. The right types of these eclipse times are TABLE 4 New CCD Times of Light Minimum for CU Tauri Error Minimum Filter 2,453, I B 2,453, I V 2,453, II B 2,453, II V shown in Table 5. Since both of the depths of the primary and secondary minima are nearly the same for W UMa type binary stars, when a system is observed only near the epoch of minimum light, it is very difficult to distinguish the minimum as primary or secondary. Therefore, in that case, the types of the light minima are usually given incorrectly for W UMa type binary systems Photometric Solutions with the Wilson-Devinney Method The first complete photometric light curves in B and V bands and solutions for CU Tau were published by Yang & Liu (2004). However, their light curves showed peculiarities with a typical positive O Connell effect with Max: I Max: II ¼ 0:015 in V band, but the light curve in B band was symmetric. This may affect their photometric solutions. Day-to-day variations in the light curves of a few W UMa type binaries have been reported, e.g., VW Cep (Pustylnik & Niarchos 2000) and CE Leo (Kang et al. 2004). Therefore, symmetric light curves are very useful in determining the photometric parameters of this kind of binary star. In order to check the photometric elements given by Yang & Liu (2004) and to derive geometrical and astrophysical parameters of the system, we intended to analyze the present observations by using the 2003 version of the Wilson-Devinney (W-D) program (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & Van Hamme 2003). The same value of temperature for star 1 (star eclipsed at primary light minimum) as that taken by Yang & Liu (2004) (T 1 ¼ 5900 K) was used, which corresponds to the spectral type of G0 (Kholopov et al. 1987, p. 242). The bolometric

5 228 QIAN ET AL. Vol. 130 TABLE 5 Photoelectric and CCD Times of Light Minimum for CU Tau (+2,400,000) (1) Min. (2) Methods (3) E (4) O C (5) Residuals (6) Ref. (7) 49, I pe Discarded 1 49, I pe , II pe , I pe , I pe , II pe , II pe , II pe , I pe , I pe , II pe , II pe , I pe , II CCD , II CCD Discarded 4 51, I pe , II pe , I CCD , II CCD , II pe , I CCD , I CCD , I CCD , II CCD References. (1) Agerer & Hübscher 1998; (2) Agerer & Hübscher 1997; (3) Agerer et al. 1999; (4) Yang & Liu 2004; (5) Agerer & Hübscher 2000; (6) Agerer & Hübscher 2003; (7) Nelson 2003; (8) Nelson 2004; (9) this paper. albedos A 1 ¼ A 2 ¼ 0:5 were from Rucinski (1969), and the values of the gravity-darkening coefficients g 1 ¼ g 2 ¼ 0:32 were from Lucy (1967). These correspond to the common convective envelope of the binary star. The limb-darkening coefficients of in B and in V were used according to Claret & Gimenez (1990). The adjustable parameters were the orbital inclination, i; the mean temperature of star 2, T 2 ;the monochromatic luminosity of star 1, L 1B and L 1V ; and the dimensionless potential of star 1 ( 1 ¼ 2, mode 3 for overcontact configuration). A q-search method was used to determine a reliable mass ratio of the system. Solutions were carried out for various values of the mass ratio q ¼ M 2 /M 1 (q ¼ 0:1, 0.2, 0.3, 0.4, 0.6, 0.8, and 1.0). For each q value, the computation started at mode 2 (detached mode), and we found that the solutions usually converged to mode 3 (overcontact configuration). The relation between the resulting sum of weighted square deviations and q is displayed in Figure 5. A minimum of was obtained at q ¼ 0:2. Therefore, we chose the initial q valuetobe0.2and made it an adjustable parameter. Then we performed a differential Fig. 2. O C diagram of CU Tau computed with the linear ephemeris obtained by Yang & Liu (2004). The large scatter of the O C values (up to 0.2 days) indicates that the orbital period of the system is incorrect. Fig. 3. O C curve of CU Tau formed by all available photoelectric and CCD data. Those O C values were calculated with the new derived linear ephemeris (eq. [3]). The solid line represents the fit by the quadratic ephemeris (eq. [4]), which suggests a continuous period decrease.

6 No. 1, 2005 DEEP OVERCONTACT BINARY SYSTEMS. III. 229 TABLE 6 Photometric Solutions for CU Tauri Parameters Photometric Elements Errors Fig. 4. Residuals of CU Tau from the quadratic ephemeris (eq. [4]). No changes can be seen. correction until it converged, and thus final solutions were derived. It is found that the solution converged at q ¼ 0:1770 (0:0017). The photometric solutions are listed in Table 6, and the theoretical light curves computed with those photometric elements are plotted in Figure 6. Our solutions suggest that CU Tau is a deep overcontact binary system with a high degree of overcontact of f ¼ 50:1% 3:2%. The derived mass ratio, q ¼ 0:1770(0:0017), reveals that it is a low mass ratio system. Despite the asymmetry of the light curve, the present solutions are close to those derived by Yang & Liu (1994). Both sets of solutions indicate that CU Tau is a deep, low mass ratio overcontact binary system. The light curves displayed in Figure 6 and the photometric solutions listed in Table 6 both indicate that CU Tau is an A-type overcontact binary system. However, we derived a secondary temperature of 5938 K, which is 38 K higher than that of the primary component. This situation was also met in the other three low mass ratio systems, i.e., V802 Aql (Samec et al. 2004), FG Hya (Qian & Yang 2005), and V902 Sgr (Samec & Corbin 2002). With the statistical relation given by Qian (2003a), M 1 ¼ 0:391(0:059) þ 1:96(0:17)P; ð5þ g 1 = g Assumed A 1 = A Assumed x 1B = x 2B Assumed x 1V = x 2V Assumed T 1 ( K) Assumed q in out T 2 ( K) i L 1 /(L 1 + L 2 )(B) L 1 /(L 1 + L 2 )(V) = r 1 (pole) r 1 (side) r 1 ( back) r 2 ( pole) r 2 (side) r 2 ( back) The degree of overcontact ( f ) (%) ! (O C) M 2 should be M 2 ¼ 0:21 0:02 M because of q ph ¼ 0:1770 0: ORBITAL PERIOD CHANGES AND PHOTOMETRIC SOLUTIONS FOR TV MUSCAE 4.1. Orbital Period Variations All available times of light minimum of TV Mus are listed in Table 7. Up to now, only three sets of eclipsing times were published. The first linear ephemeris was given by Hertzsprung (1928): Min: I ¼ 2;424;161:9711 þ 0:445701E days: ð6þ Hilditch et al. (1989) later published three photoelectric times of light minimum and obtained a revised ephemeris, the value of M 1 was estimated to be M 1 ¼ 1:20 0:09 M, which is consistent with the spectral type of G0, and therefore Min: I ¼ 2;445;089:3963 þ 0: E days: ð7þ Fig. 5. Relation between and q for CU Tau. Fig. 6. Observed (triangles and circles) andtheoretical(solid lines) light curves in B and V bands for CU Tau.

7 230 QIAN ET AL. Vol. 130 TABLE 7 Available Times of Light Minimum for TV Muscae (+2,400,000) (1) Min. (2) Methods (3) E (4) (O C) 1 (5) Residuals (6) Reference (7) 24, I Mean epoch , I pe , II pe , I pe , I CCD , I CCD , II CCD , I CCD , I CCD , II CCD References. (1) Hertzsprung 1928; (2) Hilditch et al. 1989; (3) Ogloza & Zakrzewski The O C curve computed with equation (7) is displayed in Figure 7, which shows that the orbital period of TV Mus is variable. However, since no data were published in the two time intervals between 2,424,161 and 2,445, and between 2,445, and 2,450, , the properties of the orbital period changes are not clear. By assuming a secular period decrease, the following quadratic equation, Min: I ¼ 2;445;089:3997(0:0012) þ 0: (0: )E 1:32(0:08) ; E 2 days; was derived. The quadratic term in this equation reveals a period decrease with a rate of dp/dt ¼ 2:16 ; 10 7 days yr 1. After the long-term period variation was removed from the O C curve, the residuals are shown in column (6) of Table 7 and are displayed in the bottom panel of Figure 7. As listed in Table 7, the scatter of those residuals is up to days, which is a large value for photoelectric and CCD data, indicating the possibility of the presence of an additional change in the ð8þ orbital period of TV Mus. A least-squares solution yields the following ephemeris, R e ¼þ0:0032(0:0003) þ 0:0240(0:0022) sin ½0N0151E þ 342N0(1N7)Š; which suggests a cyclic change with an amplitude of days. With the relation! ¼ 360 P e /T, the period of the periodic variation is determined to be 29.1 yr. However, as aforementioned, since the eclipse times of TV Mus are scarce, in order to check the period change of TV Mus, new times of light minimum are needed. After the period changes described in equations (8) and (9) were removed, the residuals are displayed in Figure Photometric Solutions with the W-D Method The first complete photoelectric light curves in the B, V, R, andi bands and solutions for TV Mus were published by Hilditch et al. (1989) with the method of Rucinski (1976). However, only the V light curve was analyzed in their solution. The derived degree of overcontact ( f ¼ 13%) is very small when compared with those of the other low mass ratio systems listed in Table 1. To understand the geometric structure and evolutionary state of the system, we intended to reanalyze the four-band ð9þ Fig. 7. O C diagram of TV Mus computed with the linear ephemeris obtained by Hilditch et al. (1989). The solid line refers to a long-term period decrease with a rate of dp/dt ¼ 2:16 ; 10 7 days yr 1.Afterthelong-term period decrease is removed, the residuals are displayed in the bottom panel, which may reveal a cyclic variation in the orbital period. Fig. 8. Residuals of TV Mus after period changes described in eqs. (7) and (8) were removed. No changes can be seen.

8 No. 1, 2005 DEEP OVERCONTACT BINARY SYSTEMS. III. 231 TABLE 8 Photometric Solutions for TV Muscae Parameters Photometric Elements Errors g 1 = g Assumed A 1 = A Assumed x 1B = x 2B Assumed x 1V = x 2V Assumed x 1R = x 2R Assumed x 1I = x 2I Assumed T 1 ( K) Assumed q in out T 2 ( K) i L 1 /(L 1 + L 2 )(B) L 1 /(L 1 + L 2 )(V) L 1 /(L 1 + L 2 )(R) L 1 /(L 1 + L 2 )(I) = r 1 (pole) r 1 (side) r 1 (back) r 2 (pole) r 2 (side) r 2 (back) The degree of overcontact ( f ) (%) !(O C) light curves obtained by Hilditch et al. (1989) with the 2003 version of the W-D program (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & Van Hamme 2003). WetakethesamevalueofT 1 as that used by Hilditch et al. (1989). The same values of A 1, A 2, g 1,andg 2 used for CU Tau were fixed. The limb-darkening coefficients in the B and V bands were taken according to Claret & Gimenez (1990), and those in the R and I bands were from Claret et al. (1995). First, we fixed the mass ratio at the value q ¼ 0:135 adopted by Hilditch et al. (1989), and the adjustable parameters were the orbital inclination, i; the mean temperature of star 2, T 2 ;the monochromatic luminosity of star 1, L 1B, L 1V, L 1R,andL 1I ;and Fig. 9. Photoelectric light curves of TV Mus in B, V, R, andi bands obtained by Hilditch et al. (1989). Solid lines represent theoretical light curves derived by using the W-D method. Stars refer to B, circles to V, diamondstor, and triangles to I bands. TABLE 9 Absolute Parameters for TV Muscae Parameters Values Units M M M M R R R R L L L L A R the dimensionless potential of star 1 ( 1 ¼ 2, mode 3 for overcontact configuration). However, we found that the solution does not converge. Then we made q an adjustable parameter and choose q ¼ 0:135 as the initial value. A photometric solution with the differential correction code suggests that those solutions converged at q ¼ 0:1659(0:0028). The photometric parameters are listed in Table 8, and the theoretical light curves computed with those photometric elements are plotted in Figure 9 where corrections of , , and mag wereappliedtotheb, V, andi light curves, respectively. The present solutions indicate that TV Mus is a deep overcontact binary system with a high degree of overcontact of f ¼ 74:3% 11:3%. Combining our photometric parameters with the value of M 1 sin 3 i ¼ 1:25 derived by Hilditch et al. (1989), the absolute parameters of TV Mus were determined and are shown in Table 9. Our photometric parameters, especially the degree of overcontact ( f ), are different from those derived by Hilditch et al. (1989). This may be caused by the fact that we use their four-band light curves (BVRI), while only the V light curve was used by them in their analysis. We think the present solutions aremorereliable. 5. DISCUSSION AND CONCLUSIONS Our two epochs of light minimum obtained with the 1.0 m telescope at the Yunnan Observatory and others collected from the literature were used for period study of CU Tau. As with GW Cep (Qian 2003a) and VW Boo (Qian & Zhu 2002), we discovered that the values of the orbital period derived by previous investigators are not correct. A new linear ephemeris was derived, and a plausible O C curve was formed for this binary star. The orbital period was found to be decreasing continuously with a rate of dp/dt ¼ 1:81 ; 10 6 days yr 1.ForTVMus, its orbital period is also decreasing, and a possible cyclic change is found to be superposed on the long-term decrease. This kind of period change, a cyclic variation superposed on a long-term period change, is usually encountered for W UMa type binary stars, for example, V417 Aql (Qian 2003b), BX Peg (Lee et al. 2004), FG Hya (Qian & Yang 2004a), CE Leo (Kang et al. 2004), GR Vir (Qian & Yang 2004), AK Her (Awadalla et al. 2004), ER Ori (Kim et al. 2003), and XY Leo (Yakut et al. 2003). If the continuous period decrease is caused by a conservative mass transfer from the primary to the secondary, then by using the following well-known equation (assuming conservative mass loss), Ṗ 1 P ¼ 3Ṁ 1 1 ; ð10þ M 1 M 2 the mass transfer rates can be estimated to be dm 1 /dt ¼ 3:7 ; 10 7 and 4:2 ; 10 8 M yr 1 for CU Tau and TV Mus, respectively.

9 232 QIAN ET AL. Vol. 130 TABLE 10 Physical Properties for Deep, Low Mass Ratio Overcontact Binaries CU Tauri and TV Muscae Parameters CU Tauri TV Muscae Spectral type... G0 G0 G1 P dp/dt (days yr 1 ) ; ; 10 7 Cyclic period change... Maybe Yes Variation of the light curve... Yes Yes f (%) q M 1 (M ) M 2 (M ) dm 1 /dt (M yr 1 ) ; ; 10 8 The photometric solutions given in xx 3 and 4 indicate that CU Tau and TV Mus are deep, low mass ratio overcontact binary systems. The observational properties of both systems are summarized in Table 10. As shown in this table, the physical properties of the two binary stars are nearly the same. The high degrees of overcontact of both systems indicate that their fluid surfaces are so close to the outer critical Roche lobe that mass outflow from the outer Lagrangian point L2 is inevitable. The continuous period decrease may be caused by the mass transfer from the more massive component to the less massive one, accompanied by AML due to mass outflow from L2. In that way, the situations of CU Tau and TV Mus resemble those of AW UMa (Pribulla et al. 1999), FG Hya (Qian & Yang 2005), IK Per (Zhu et al. 2005), and GR Vir (Qian & Yang 2004). All of them are deep ( f > 50%), low mass ratio (q < 0:25) overcontact binary stars with a secular decreasing period. The decreases of the orbital periods will result in the shrinking of inner and outer critical Roche lobes and thus will cause f to increase. Finally, they will evolve into a single rapid-rotation star before the fluid surface reaching the outer critical Roche lobe (Rasio & Shapiro 1995). However, when comparing the decrease rate of CU Tau (dp/dt ¼ 1:81 ; 10 6 days yr 1 ) with those of the other W UMa type binary stars (e.g., BX Peg, V714 Mon, and V417 Aql) listed by Qian (2001) and Qian et al. (2004), this value is larger than the others by 1 order of magnitude. This may be caused by the short time interval of the observations (only 9.2 yr), and the present period decrease may be a part of a long-period cyclic variation or a combination of a cyclic change and a long-term variation, as has been observed in other W UMa type binaries (e.g., V417 Aql). For TV Mus, the period changes presented here are only based on three sets of times of light minimum. Since the period changes of both binary systems are very important to understanding their evolutionary states, more accurate epochs of minimum light are required in the future. This work is partly supported by the Science and Technology Department of Yunnan Province (2003RC19), the Yunnan Natural Science Foundation (2003A0072M), the National Key Fundamental Research Project through grant G , the Chinese Natural Science Foundation ( ), and the Chinese Academy of Sciences (KJCXZ-SW-T06). S.-B. 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