GR VIRGINIS: A DEEP OVERCONTACT BINARY

The Astronomical Journal, 128:2430 2434, 2004 November # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A. GR VIRGINIS: A DEEP OVERCONTACT BINARY S.-B. Qian and Y.-G. Yang National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming; and United Laboratory of Optical Astronomy, Chinese Academy of Sciences, 100012 Beijing, China; qsb@livjm.ac.uk Received 2004 June 3; accepted 2004 August 10 ABSTRACT Orbital period variations of the low-mass ratio (q ¼ 0:122) overcontact binary system, GR Vir, were investigated by using two new CCD times of minimum light and other photoelectric data compiled from literatures. It is found that the O C residuals of GR Vir show a cyclic variation with a period of 19.3 yr and an amplitude of 0.0140 days while they are undergoing a long-term decrease (dp=dt ¼ 4:32 ; 10 7 days yr 1 ). Meanwhile, the 1988 photoelectric observations from Cereda et al. were analyzed using the Wilson-Devinney method. Like some low-mass ratio overcontact binary stars (e.g., AW UMa), GR Vir is an A-type overcontact binary with a high degree of overcontact ( f ¼ 78:6%). By combining the spectroscopic solutions with the photometric elements, the absolute parameters of the system are determined as follows: M 1 ¼ 1:36 M, M 2 ¼ 0:17 M, a ¼ 2:40 R, R 1 ¼ 1:42 R, R 2 ¼ 0:61 R, L 1 ¼ 2:87 L,andL 2 ¼ 0:48 L. The long-term period decrease is interpreted as the result of mass transfer from the more massive component to the less massive one in combination with the angular momentum loss due to mass outflow from the L 2 point. The conditions in GR Vir resemble those in AW UMa. Both systems show a high degree of overcontact, low mass ratios, and secular shrinking of their orbits. As their orbital periods decrease, the shrinking of the inner and outer critical Roche lobes will cause the common convective envelope to become deeper, until finally the formation of single, rapid-rotation stars is inevitable. The period oscillation may by caused either by the presence of an unseen tertiary component (e.g., a white dwarf ) or by magnetic activity on the part of the primary component. Key words: binaries: close binaries: eclipsing stars: evolution stars: individual (GR Virginis) 1. INTRODUCTION Observatory in China. The PI1024 TKB CCD photometric The light variability of GRVir (=SAO 140120, BD 6 system attached to this telescope was used. Its effective field 4068, of view at the Cassegrain focus is about 6:5 ; 6:5 arcmin HD 129903) was discovered by Strohmeier et al. (1965) and. During observations the integration time for each image was independently by Harris (1979). The latter made photoelectric 100 s. PHOT (which measures magnitudes for a list of stars) observations of the system, which revealed that it is an eclipsing binary with a short period (8 h 30 m from the aperture photometry package IRAF was used to reduce the observed images. Two times of light minimum were ). Complete light curves in the B and V bandpass were obtained by Cereda et al. (1988) and derived from the observations. Halbedel (1988), but no photometric solutions of the system were published. The first radial velocity curves for both components of the binary star were recently published by Rucinski & All available photoelectric and CCD times of light minimum for GR Vir were compiled and are listed in Table 1. As shown in the table, the errors of most data are less than 0.001 days. Lu (1999). The derived mass ratio (q sp ¼ 0:122) indicates that Therefore, details of period investigation can be done with GR Vir is one of the smallest known W UMa type binary stars. those eclipse times. The (O C ) The color indices b y ¼ 0:37 (Olsen 1983) and B V ¼ 0:55 1 residuals in the table were calculated with the linear ephemeris given by Cereda et al. (Cereda et al. 1988) led to the object being classified as spectral (1988), type F9 G0, while Rucinski & Lu (1999) classified it as F7/F8. Although epochs and orbital periods were derived by several authors (e.g., Cereda et al. 1988 and Halbedel 1988), the investigation of the period of this eclipsing binary star has been I ¼ 2445665:6415 þ 0A3469788E: ð1þ neglected. It is well known that orbital period variations are While calculating the (O C ) 1 values, we noticed that the types very common for W UMa type binary stars (e.g., Qian 2001, of the eclipse times published by Müyesseroglu et al. (2003) are 2003a, 2003b; Kreiner et al. 2001). To look for period changes not in agreement with the cycles E computed with equation (1). in GR Vir, we observed the system at epochs of light minimum. We suspect that this may be caused by the change of the light In the present paper, the O C variation and photoelectric curve of GR Vir. When Cereda et al. (1988) observed the system, its light curve was type A, but as Müyesseroglu et al. observations obtained by Cereda et al. (1988) are analyzed. Then, on the basis of orbital period changes and the photometric (2003) observed, it may have changed from type A to type W, solutions of the binary system, its triplicity, structure, and evolutionary state are all discussed. as has been observed in several W UMa type binary systems (e.g., AM Leo; Binnendijk 1969; Hoffmann & Hopp 1982; Derman et al. 1991). 2. NEW OBSERVATIONS AND PERIOD VARIATIONS The corresponding O C curve for GR Vir is shown in FOR GR VIRGINIS Figure 1. The (O C ) 1 value of the eclipse time, HJD GR Vir was observed in the V bandpass on 2004 January 15 and 16 with the 1 m reflecting telescope at the Yunnan 2,452,782.428, published by Müyesseroglu et al. (2003) was not shown in this figure and not used in the following period 2430

GR VIRGINIS 2431 TABLE 1 Photoelectric and CCD Times of Light Minimum for GR Virginis HJD 2,400,000+ Errors Min. Method E (O C ) 1 (O C ) 2 Residuals Ref. 44,020.7852...... II Pe 4740.5 0.0033 +0.0141 +0.0001 1 45,095.3870...... II Pe 1643.5 +0.0052 +0.0086 0.0004 1 46,560.8501...... I Pe 2580 +0.0033 0.0061 +0.0020 2 46,924.4799...... I Pe 3628 0.0007 0.0121 0.0008 1 46,939.3998...... I Pe 3671 0.0009 0.0124 0.0009 1 50,947.3710... 0.0010 I Pe 15222 +0.0182 +0.0143 +0.0004 3 52,375.5126... 0.0001 I Pe 19338 0.0050 +0.0069 +0.0005 4 52,399.4499... 0.0003 I Pe 19407 0.0092 +0.0031 0.0031 4 52,440.3970... 0.0002 I Pe 19525 0.0056 +0.0072 +0.0015 4 52,443.3443... 0.0003 II Pe 19533.5 0.0076 +0.0053 0.0004 4 52,460.3464... 0.0002 II Pe 19582.5 0.0075 +0.0056 +0.0001 4 52,464.3366... 0.0003 I Pe 19594 0.0075 +0.0057 +0.0002 4 52,761.3401... 0.0008 II Pe 20450 0.0179 0.0005 0.0023 5 52,761.5185... 0.0011 I Pe 20450.5 0.0129 +0.0045 +0.0027 5 52,769.3237... 0.0004 I Pe 20473 0.0148 +0.0027 +0.0010 6 52,769.4964... 0.0004 II Pe 20473.5 0.0156 +0.0019 +0.0002 6 52,796.3861... 0.0006 II Pe 20551 0.0167 +0.0012 0.0002 5 52,797.4277... 0.0005 I Pe 20554 0.0161 +0.0019 +0.0004 6 52,805.4052... 0.0008 I Pe 20557 0.0191 0.0010 0.0023 6 52,824.3191... 0.0006 I Pe 20631.5 0.0155 +0.0029 +0.0018 5 53,020.3518... 0.0016 II CCD 21196.5 0.0258 +0.0014 +0.0028 7 53,021.3986... 0.0005 II CCD 21199.5 0.2000 0.0044 0.0030 7 References. (1) Cereda et al. 1988; (2) Halbedel 1988; (3) Agerer et al. 1999; (4) Albayrak et al. 2002; (5) Müyesseroglu et al. 2003; (6) Selam et al. 2003; (7) the present paper. analysis, because it shows large scatter when compared with the general trend indicated by other data points. As can be seen from Figure 1, the O C residuals recently decreased rapidly, and the period variation of GR Vir is very complex. There may exist a period oscillation superposed on a secular decrease. This type of period variation is commonly encountered in W UMa type binary stars, e.g., V417 Aql (Qian 2003b). Therefore, by considering continuous O C variation, a sinusoidal term is added to a quadratic ephemeris to give a good description of the (O C ) 1 curve (solid line, Fig.1).Usinga least-squares method, the following equation (O C ) 1 ¼ 0:0024(0:0010) þ 0A00000321(0:00000020)E 2:05(0:10) ; 10 10 E 2 þ 0:0140(0:0008)sin½0N0178 ; E þ 169A3(0A5)Š ð2þ was determined. The quadratic term in this equation indicates a long-term period decrease with a rate of dp=dt ¼ 4:32 ; 10 7 days yr 1, which corresponds to a period decrease of 3.9 s century 1. After the long-term period was removed, the (O C ) 2 residuals plotted in Figure 2 clearly show a cyclic change. With the sinusoidal term in the equation (2), a period of Fig. 1. The (O C ) 1 curve of GR Vir based on the linear ephemeris given by Cereda et al. (1988). The solid line represents a combination of a secular decrease and a cyclic variation. Also represented by the dashed line is the quadratic fit given in eq. (2). Fig. 2. The (O C ) 2 diagram for GR Vir after removal of the long-term period decrease. A cyclic change is clearly seen.

2432 QIAN & YANG Vol. 128 Fig. 3. Residuals for GR Vir with respect to eq. (2). 19.3 yr and an amplitude of 0.0140 days for the period oscillation were determined. The residuals from equation (2) are displayed in Figure 3 and no changes can be found. This suggests that equation (2) can fit the (O C ) 1 curve very well. The scatters of the residuals in Figure 3 are up to 0.0030 days, which may be caused by the asymmetry and variation of the light curve due to the starspot activity in the components. However, Kalimeris et al. (2002) showed that the activity of starspots can only cause high-frequency, low-amplitude disturbances in the O C curve. The observed systematic variations in orbital period of GR Vir cannot be attributed to starspots. 3. PHOTOMETRIC SOLUTIONS OF GR VIRGINIS Complete photoelectric light curves in the B and V bandpasses for GR Vir have been published by Cereda et al. (1988) and Halbedel (1988), but no photometric solutions of the TABLE 2 Photometric Solutions for GR Virginis Parameter Photometric Elements Errors g 1 = g 2... 0.32 Assumed A 1 = A 2... 0.5 Assumed x 1bol = x 2bol... 0.491 Assumed x 1B = x 2 B... 0.729 Assumed x 1V = x 2V... 0.629 Assumed q... 0.122 Assumed T 1 (K)... 6300 Assumed in... 2.0247 out... 1.9454 T 2 (K)... 6163 9 i... 83.36 0.34 L 1 /(L 1 + L 2 )(B)... 0.8681 0.0002 L 1 /(L 1 + L 2 )(V)... 0.8655 0.0004 1 = 2... 1.9624 0.0006 r 1 (pole)... 0.5391 0.0002 r 1 (side)... 0.6051 0.0003 r 1 ( back)... 0.6296 0.0004 r 2 (pole)... 0.2229 0.0002 r 2 (side)... 0.2351 0.0003 r 2 ( back)... 0.3051 0.0012 The degree of overcontact ( f ) (%)... 78.6 0.76 Fig. 4. Observed (diamonds and circles) and theoretical(solid lines) light curves in the B and V bands for GR Vir. system have yet been obtained. To understand the geometrical structure and to derive the absolute parameters of the system, we analyzed the observations of Cereda et al. using the 1992 version of the Wilson-Devinney program (R. E. Wilson 1993, private communication). According to the spectral classification F7/F8 of GR Vir given by Rucinski & Lu (1999), we adopted the temperature of 6300 K for star 1 (the star eclipsed at primary light minimum). The gravity-darkening coefficients g 1 ¼ g 2 ¼ 0:32 (Lucy 1967) and the values of the bolometric albedo A 1 ¼ A 2 ¼ 0:5 (Rucinski 1969) were used, which correspond to the common convective envelope of this binary system. The limb-darkening coefficients x 1 ¼ x 2 ¼ 0:729 in the V bandpass and x 1 ¼ x 2 ¼ 0:628 in the B bandpass were obtained from Claret & Gimenez (1990). The mass ratio q was fixed to the value from the spectroscopic solution by Rucinski & Lu (1999). The adjustable parameters were inclination i, mean temperature of star 2 T 2, monochromatic luminosity of star 1 L 1B and L 1V, and the dimensionless potentials of star 1 ( 1 ¼ 2 for mode 3). The photometric solutions are shown in Table 2. The theoretical and the observed light curves are shown in Figure 4. As displayed in this figure, the theoretical light curves fit the observations by Cereda et al. (1988) very well. Combing our photometric parameters (listed in Table 3) with the spectroscopic elements published by Rucinski & Lu (1999), we determined the absolute parameters of GR Vir, and they are shown in Table 3. Our solution reveals that the system is an A-type overcontact binary system with a degree of overcontact of f ¼ 78:6%. TABLE 3 Absolute Parameters for GR Virginis Parameter Values M 1 (M )... 1.37 0.16 M 2 (M )... 0.17 0.06 R 1 (R )... 1.42 0.07 R 2 (R )... 0.61 0.04 L 1 (L )... 2.87 0.28 L 2 (L )... 0.48 0.06 A (R )... 2.40 0.12

No. 5, 2004 GR VIRGINIS 2433 4. DISCUSSION AND CONCLUSIONS 4.1. Triplicity of the System Combining two CCD times of minimum light obtained using the 1.0 m telescope at the Yunnan Observatory with other photoelectric eclipse times compiled from the literature, we analyzed the O C residuals of GR Vir. Through a consideration of the continuous variation, a periodic change with a period of 19.3 yr was found to be superposed on a long-term increase. The properties of the period variation resemble those of AW UMa (Pribulla et al. 1999). Although the O C curve shown in Figure 1 could also be described by broken lines, indicating that several period jumps have occurred in the system, we think that continuous period variations are more acceptable. This type of period variation, period oscillation superposed on a long-term change, is commonly encountered in W UMa type binary stars, e.g., V839 Oph (Akalin & Derman 1997) and V417 Aql (Qian 2003b). After the long-term continuous period was removed, the (O C ) 2 residuals plotted in Figure 2 reveal a cyclic variation. This can be explained by the presence of a third body in the system. Since those observations do not cover an entire cycle, information on the orbital eccentricity of the third body cannot be derived. However, as shown in Figure 2, the sine-like term in equation (2) can fit those residuals very well, indicating that the orbital eccentricity may be close to zero. Therefore, we assume that the third body is moving in a circular orbit. By using a12 0 sin i0 ¼ A ; c, wherec is the speed of light, a12 0 sin i0 was computed to be a12 0 sin i0 ¼ 2:43(0:14) AU. Then a calculation with the equation f (m) ¼ 4 2 GT 2 ; (a0 12 sin i0 ) 3 ð3þ leads to the mass function for the third body f (m) ¼ 0:0383(0:0066) M. Finally, with the absolute parameters determined in previous section, the masses and the orbital radii of the third body for different values of i 0 are computed by using the equation (M 3 sin i 0 ) 3 f (m) ¼ (M 1 þ M 2 þ M 3 ) 2 : ð4þ The relation between the mass and the orbital radius of the third star is shown in Figure 5. If the orbital plane of the tertiary component is coplanar to the eclipsing pair, its mass and orbital radius should be M 3 ¼ 0:55(0:06) and a 3 ¼ 8:0(1:0), respectively. As shown in Figure 5, the mass of the tertiary component is no less than M 3 0:55 M.Therefore, it should be possible to determine the spectral lines of the third component. However, no such lines were reported by the spectroscopic study of Rucinski & Lu (1999). Moreover, to check the presence of the tertiary component during the photometric solution, we also searched for the third light (L 3 ). But the value of L 3 is close to zero. These results suggest that, if the assumed third component really does exist, it may be an unseen component, e.g., a white dwarf. On the other hand, the spectral type of GR Vir is F7/F8 (Rucinski & Lu (1999), so the mechanism of a magnetic active cycle cannot be excluded (e.g., Applegate 1992; Lanza et al. 1998) as an explanation of the cyclic period change. 4.2. Evvolutionary State of the System The general O C trendinfigure1(dashed line) reveals a longterm period increase at a rate of dp=dt ¼ 4:32 ; 10 7 days Fig. 5. Relation between masses and orbital inclinations (i 0 )fortheassumed third-component star in GR Vir. yr 1. The photometric solution given in the previous section indicates that GR Vir is a very deep overcontact binary system with a high degree of overcontact ( f ¼ 78:6%). The surface of the binary star is very close the outer critical Roche lobe. Mass outflow from the outer Lagrangian point L 2 is inevitable. The long-term continuous period decrease is explained by mass transfer from the more massive to the less massive object, accompanied by an angular momentum loss due to mass outflow from L 2. In the case of conservative mass transfer, by taking the determined absolute parameters and using the well-known equation Ṗ P ¼ 3Ṁ 1 1 1 M 1 M 2 ; ð5þ a mass transfer rate was estimated to be dm 1 =dt ¼ 7:89 ; 10 8 M yr 1. The timescale of mass transfer in this situation is M 1 =Ṁ 1 1:73 ; 10 7 yr, which is larger than the thermal timescale of the primary component (2 ; 10 7 M 2 =RL 0:9 ; 10 7 ). This indicates that thermal conservative mass transfer from the primary to the secondary component is not enough to cause the observed period decrease. Mass outflow from L 2 should contribute to the orbital period decrease. The situation of GR Vir resembles that of AW UMa. The physical parameters of both systems are shown in Table 4. The TABLE 4 Physical Parameters for GR Virginis and AW Ursae Majoris Parameters GR Vir AW UMa P (days)... 0.3469788 0.43873305 M 1 (M )... 1.37 1.79 M 2 (M )... 0.17 0.14 q... 0.122 0.803 Fill-out (%)... 78.6 84.6 i (deg)... 83.36 78.3 dp/dt (10 7 days yr 1 )... 4.32 1.85 a 0 12 sin i 0 (AU)... 2.43 0.47 f (m 3 )(M )... 0.0383 0.0004 T (yr)... 19.3 17.1

2434 QIAN & YANG parameters of AW UMa were taken from a recent paper by Pribulla et al. (1999). For an overcontact binary with given masses of two components, its stability depends on its exact interior structure and on the degree of overcontact (Rasio 1995). Systems with a high degree of overcontact are more susceptible to instability. The study by Rasio & Shapiro (1995) indicates that for systems with q 0:25 a dynamical instability is encountered before the Roche limit. As shown in Table 4, both GR Vir and AW UMa are deep overcontact binary systems with very low mass ratios (q < 0:15, f > 75%). As their orbital periods are decreasing, the shrinking of inner and outer critical Roche lobes will cause f to increase. According to Rasio & Shapiro (1995), they will finally evolve into single rapid-rotation stars before the fluid surfaces of the two contact binaries reach the outer critical Roche lobe. This work was supported by Chinese Academy of Sciences (grant KJCXZSW-T06), Yunnan Natural Science Foundation (grants 2001A0026Q and 2003A0072M), the Science and Technology Department of Yunnan Province (grant 2003RC19), and the National Key Fundamental Research Project through grant G1999075405. We have used the data observed with the 1 m telescope at Yunnan Observatory. Agerer, F., Dahm, M., & Hubscher, J. 1999, Inf. Bull. Variable Stars, 4712 Akalin, A., & Derman, E. 1997, A&AS, 125, 407 Albayrak, B., Tanriverdi, T., Aydin, C. 2002, Inf. Bull. Variable Stars, 5300 Applegate, J., H. 1992, ApJ, 385, 621 Binnendijk, L. 1969, AJ, 74, 1031 Cereda, L. Misto, A., Poretti, E., & Piarchos, P. G. 1988, A&AS, 76, 255 Claret, A., & Gimenez, A. 1990, A&A, 230, 412 Derman, E., Demircan, O., & Dundar, H. 1991, Inf. Bull. Variable Stars, 3630 Halbedel, E. M. 1988, Inf. Bull. Variable Stars, 3132 Harris, A. W. 1979, Inf. Bull. Variable Stars, 1691 Hoffmann, M., & Hopp, U. 1982, Ap&SS, 83, 391 Kalimeris, A., Rovithis-Livaniou, H., & Rovithis, P. 2002, A&A, 387, 969 Kreiner, J. M., Kim, C.-H., & Nha, I.-S. 2001, An Atlas of O C Diagrams of Eclipsing Binary Stars (Cracow: Wydawnictwo Nauk. Akad. Pedag.), 1424 Lanza, A., F., Rodonò, M., & Rosner, R. 1998, MNRAS, 296, 893 REFERENCES Lucy, L. B. 1967, Z. Astrophys., 65, 89 Müyesseroglu, Z., Torum, E., Ozdemir, T., Gurol, B., Ozavci, I., Tunc, T., Kaya, F. 2003, Inf. Bull. Variable Stars, 5463 Olsen, E. H. 1983, A&AS, 54, 55 Pribulla, T., Chochol, D., Rovithis-Livaniou, H., & Rovithis, P. 1999, A&A, 345, 137 Qian, S.-B. 2001, MNRAS, 328, 635. 2003a, MNRAS, 342, 1260. 2003b, A&A, 400, 649 Rasio F. A. 1995, ApJ, 444, L41 Rasio F. A., & Shapiro, S. L. 1995, ApJ, 438, 887 Rucinski, S. M. 1969, Acta Astron., 19, 245 Rucinski, S. M., & Lu, W., 1999, AJ, 118, 2451 Selam, S. O., et al. 2003, Inf. Bull. Variable Stars, 5471 Strohmeier, W., Knigge, R., & Ott, H. 1965, Inf. Bull. Variable Stars, 115